- Pauli matrices (Pauli matrices)

by Prof. Hasan Keleş16 Feb 2018 07:45 - Almost disjoint family (Almost disjoint family)

by Dr. Jonathan Verner08 Jan 2018 14:22 - SSFM (SSFM)

by Emmanouil Markoulakis19 Dec 2017 15:46 - Ferrolens (Ferrolens)

by Emmanouil Markoulakis19 Dec 2017 15:35 - Neutrino trident production (Neutrino trident production)

by Dr. Oleg Ruchayskiy21 Jul 2017 18:29 - Wigner transform (Wigner transform)

by Dr. Claude Becker06 Apr 2011 14:04 - Fingers of God (Fingers of God)

by Dr. Ganna Ivashchenko18 May 2011 22:42 - RKKY interaction (RKKY interaction)

by Dr. Vadim Cheianov31 Aug 2009 09:28 - Fermi surface (Fermi surface)

by Dr. Vadim Cheianov05 Dec 2010 22:11 - Grey-body radiation (Grey-body radiation)

by Prof. Carlo Beenakker08 Jan 2011 20:36

- The fine grained energy spectrum of quantum chaotic systems is widely believed to be described by random matrix statistics. A basic scale in such a system is the energy range over which this behavior persists. We define the corresponding time scale by the time at which the linearly growing ramp region in the spectral form factor begins. We call this time $t_{\rm ramp}$. The purpose of this paper is to study this scale in many-body quantum systems that display strong chaos, sometimes called scrambling systems. We focus on randomly coupled qubit systems, both local and $k$-local (all-to-all interactions) and the Sachdev--Ye--Kitaev (SYK) model. Using numerical results, analytic estimates for random quantum circuits, and a heuristic analysis of Hamiltonian systems we find the following results. For geometrically local systems with a conservation law we find $t_{\rm ramp}$ is determined by the diffusion time across the system, order $N^2$ for a 1D chain of $N$ qubits. This is analogous to the behavior found for local one-body chaotic systems. For a $k$-local system like SYK the time is order $\log N$ but with a different prefactor and a different mechanism than the scrambling time. In the absence of any conservation laws, as in a generic random quantum circuit, we find $t_{\rm ramp} \sim \log N$, independent of connectivity.Sachdev-Ye-Kitaev modelRandom matrixQuantum circuitQubitStatisticsChaosHamiltonianForm factorRandom matrix theoryQuantum chaos...
- Generative Adversarial Networks (GANs) are a class of generative algorithms that have been shown to produce state-of-the art samples, especially in the domain of image creation. The fundamental principle of GANs is to approximate the unknown distribution of a given data set by optimizing an objective function through an adversarial game between a family of generators and a family of discriminators. In this paper, we offer a better theoretical understanding of GANs by analyzing some of their mathematical and statistical properties. We study the deep connection between the adversarial principle underlying GANs and the Jensen-Shannon divergence, together with some optimality characteristics of the problem. An analysis of the role of the discriminator family via approximation arguments is also provided. In addition, taking a statistical point of view, we study the large sample properties of the estimated distribution and prove in particular a central limit theorem. Some of our results are illustrated with simulated examples.Generative Adversarial NetOptimizationCentral Limit TheoremNeural networkKullback-Leibler divergenceMachine learningMaximum likelihoodStatistical estimatorEnvelope theoremNearest-neighbor site...
- We uncover a fairly general principle in online learning: If regret can be (approximately) expressed as a function of certain "sufficient statistics" for the data sequence, then there exists a special Burkholder function that 1) can be used algorithmically to achieve the regret bound and 2) only depends on these sufficient statistics, not the entire data sequence, so that the online strategy is only required to keep the sufficient statistics in memory. This characterization is achieved by bringing the full power of the Burkholder Method --- originally developed for certifying probabilistic martingale inequalities --- to bear on the online learning setting. To demonstrate the scope and effectiveness of the Burkholder method, we develop a novel online strategy for matrix prediction that attains a regret bound corresponding to the variance term in matrix concentration inequalities. We also present a linear-time/space prediction strategy for parameter free supervised learning with linear classes and general smooth norms.StatisticsMartingaleMinimaxMartingale difference sequencePrecisionComparatorSupervised learningVector spaceOptimizationPolynomial time...
- This paper presents a systematic survey on recent development of neural text generation models. Specifically, we start from recurrent neural network language models with the traditional maximum likelihood estimation training scheme and point out its shortcoming for text generation. We thus introduce the recently proposed methods for text generation based on reinforcement learning, re-parametrization tricks and generative adversarial nets (GAN) techniques. We compare different properties of these models and the corresponding techniques to handle their common problems such as gradient vanishing and generation diversity. Finally, we conduct a benchmarking experiment with different types of neural text generation models on two well-known datasets and discuss the empirical results along with the aforementioned model properties.Generative Adversarial NetRecurrent neural networkReinforcement learningSurveysLanguage...
- Analyzing large volumes of high-dimensional data is an issue of fundamental importance in data science, molecular simulations and beyond. Several approaches work on the assumption that the important content of a dataset belongs to a manifold whose Intrinsic Dimension (ID) is much lower than the crude large number of coordinates. Such manifold is generally twisted and curved, in addition points on it will be non-uniformly distributed: two factors that make the identification of the ID and its exploitation really hard. Here we propose a new ID estimator using only the distance of the first and the second nearest neighbor of each point in the sample. This extreme minimality enables us to reduce the effects of curvature, of density variation, and the resulting computational cost. The ID estimator is theoretically exact in uniformly distributed datasets, and provides consistent measures in general. When used in combination with block analysis, it allows discriminating the relevant dimensions as a function of the block size. This allows estimating the ID even when the data lie on a manifold perturbed by a high-dimensional noise, a situation often encountered in real world data sets. We demonstrate the usefulness of the approach on molecular simulations and image analysis.Intrinsic dimensionManifoldStatistical estimatorData scienceNearest-neighbor siteCurvatureSimulationsDimensions...
- One of the most compelling features of Gaussian process (GP) regression is its ability to provide well calibrated posterior distributions. Recent advances in inducing point methods have drastically sped up marginal likelihood and posterior mean computations, leaving posterior covariance estimation and sampling as the remaining computational bottlenecks. In this paper we address this shortcoming by using the Lanczos decomposition algorithm to rapidly approximate the predictive covariance matrix. Our approach, which we refer to as LOVE (LanczOs Variance Estimates), substantially reduces the time and space complexity over any previous method. In practice, it can compute predictive covariances up to 2,000 times faster and draw samples 18,000 time faster than existing methods, all without sacrificing accuracy.CovarianceGaussian processCovariance matrixInferenceOptimizationRegressionRankBayesianCholesky decompositionEntropy...
- Absorption, distribution, metabolism, and excretion (ADME) studies are critical for drug discovery. Conventionally, these tasks, together with other chemical property predictions, rely on domain-specific feature descriptors, or fingerprints. Following the recent success of neural networks, we developed Chemi-Net, a completely data-driven, domain knowledge-free, deep learning method for ADME property prediction. To compare the relative performance of Chemi-Net with Cubist, one of the popular machine learning programs used by Amgen, a large-scale ADME property prediction study was performed on-site at Amgen. The results showed that our deep neural network method improved current methods by a large margin. We foresee that the significantly increased accuracy of ADME prediction seen with Chemi-Net over Cubist will greatly accelerate drug discovery.GraphDeep Neural NetworksDeep learningMachine learningNeural networkNetworks...
- We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy measure that can be estimated from data under some mild assumptions. We also also provide novel analysis of stable time series forecasting algorithm using this new notion of discrepancy that we introduce. We use our learning bounds to devise new algorithms for non-stationary time series forecasting for which we report some preliminary experimental results.Time SeriesOptimizationRademacher complexityHyperparameterRegressionRegularizationBregman divergenceUniform distributionGeneralization errorGenerative model...
- We place constraints on the propagation velocity of bulk turbulence within the intracluster medium of three clusters and an elliptical galaxy. Using Reflection Grating Spectrometer measurements of turbulent line broadening, we show that for these clusters, the 90% upper limit on turbulent velocities when accounting for instrumental broadening is too low to propagate energy radially to the cooling radius of the clusters within the required cooling time. In this way, we extend previous Hitomi-based analysis on the Perseus cluster to more clusters, with the intention of applying these results to a future, more extensive catalog. These results constrain models of turbulent heating in AGN feedback by requiring a mechanism which can not only provide sufficient energy to offset radiative cooling, but resupply that energy rapidly enough to balance cooling at each cluster radius.TurbulenceReflection Grating SpectrometerCoolingRadiative coolingCool core galaxy clusterCluster of galaxiesIntra-cluster mediumCooling timescaleAstro-HPerseus galaxy cluster...
- We analyze the stellar growth of Brightest Cluster Galaxies (BCGs) produced by cosmological zoom-in hydrodynamical simulations of the formation of massive galaxy clusters. The evolution of the stellar mass content is studied considering different apertures, and tracking backwards either the main progenitor of the $z=0$ BCG or that of the cluster hosting the BCG at $z=0$. Both methods lead to similar results up to $z \simeq 1.5$. The simulated BCGs masses at $z=0$ are in agreement with recent observations. In the redshift interval from z=1 to z=0 we find growth factors 1.3, 1.6 and 3.6 for stellar masses within 30kpc, 50kpc and 10% of R_{500} respectively. The first two factors, and in general the mass evolution in this redshift range, are in agreement with most recent observations. The last larger factor is similar to the growth factor obtained by a semi-analytical model (SAM). Half of the star particles that end up in the inner 50 kpc was typically formed by redshift about 3.7, while the assembly of half of the BCGs stellar mass occurs on average at lower redshifts $\sim 1.5$. This assembly redshift correlates with the mass attained by the cluster at high $z \gtrsim 1.3$, due to the broader range of the progenitor clusters at high-z. The assembly redshift of BCGs decreases with increasing apertures. Our results are compatible with the inside-out scenario. Simulated BCGs could lack intense enough star formation (SF) at high redshift, while possibly exhibit an excess of residual SF at low redshift.Star formationGalaxyStellar massMessier 50StarMassive clusterMessier 30Messier 10Hydrodynamical simulationsCluster of galaxies...
- This paper presents a versatile robotic system for sewing 3D structured object. Leveraging on using a customized robotic sewing device and closed-loop visual servoing control, an all-in-one solution for sewing personalized stent graft is demonstrated. Stitch size planning and automatic knot tying are proposed as the two key functions of the system. By using effective stitch size planning, sub-millimetre sewing accuracy is achieved for stitch sizes ranging from 2mm to 5mm. In addition, a thread manipulator for thread management and tension control is also proposed to perform successive knot tying to secure each stitch. Detailed laboratory experiments have been performed to access the proposed instruments and allied algorithms. The proposed framework can be generalised to a wide range of applications including 3D industrial sewing, as well as transferred to other clinical areas such as surgical suturing.RoboticsCalibrationKinematicsMountingSoftwareAnatomyFocal lengthCrossed productTensionTrajectory...
- In 2015, the LHCb collaboration has measured $\frac{d{\mathcal{B}}}{dq^2}$, the lepton- and hadron-side forward-backward asymmetries, denoted by $A^\ell_{FB}$ and $A^{\Lambda}_{FB}$, respectively in the range $15 < q^2(=s) < 20$ GeV$^2$ with 3 fb$^{-1}$ of data. Motivated by these measurements, we perform an analysis of $q^2$ dependent $\Lambda_b \to \Lambda (\to p \pi ) \mu^+\mu^-$ angular observables at large- and low-recoil in the SM and in a family non-universal $Z^{\prime}$ model. In the present study we use the recently performed high-precision lattice QCD calculations of the form factors that have well controlled uncertainties especially in $15 < s < 20$ GeV$^2$ bin. Using the full four-folded angular distribution of $\Lambda_b \to \Lambda (\to p \pi ) \mu^+\mu^-$ decay, firstly we calculate the values of these measured quantitites in the SM and compare their numerical values with the measurements in appropriate bins of $s$. In case of the possible discrepancy between the SM prediction and measurements, we try to see if these can be accommodated though the extra neutral $Z^{\prime}$ boson. In addition, the fraction of longitudinal polarization of the dimuon $F_{L}$ is measured to be $0.61^{+0.11}_{-0.14}\pm 0.03$ in $15 < s < 20$ GeV$^2$ at the LHCb. We find that in this bin the value found in the $Z^{\prime}$ model is close to the observed values. After comparing the results of these observables, we have proposed a number of other observables whose values are calculated in different bins of $s$ in the SM and $Z^{\prime}$ model. We illustrate that the experimental observations of these observables in several bins of $s$ can help to test the predictions of the SM and unravel NP contributions arises due to $Z^{\prime}$ model in these decays.Form factorLHCbForward-backward asymmetryHelicityWilson coefficientsBranching ratioDecay ratePrecisionLattice QCDBELLE II...
- Applying the method of light-cone sum rules with photon distribution amplitudes, we compute the subleading-power correction to the radiative leptonic $B \to \gamma \ell \nu$ decay, at next-to-leading order in QCD for the twist-two contribution and at leading order in $\alpha_s$ for the higher-twist contributions, induced by the hadronic component of the collinear photon. The leading-twist hadronic photon effect turns out to preserve the symmetry relation between the two $B \to \gamma$ form factors due to the helicity conservation, however, the higher-twist hadronic photon corrections can yield symmetry-breaking effect already at tree level in QCD. Using the conformal expansion of photon distribution amplitudes with the non-perturbative parameters estimated from QCD sum rules, the twist-two hadronic photon contribution can give rise to approximately 30\% correction to the leading-power "direct photon" effect computed from the perturbative QCD factorization approach. In contrast, the subleading-power corrections from the higher-twist two-particle and three-particle photon distribution amplitudes are estimated to be of ${\cal O} (3 \sim 5\%)$ with the light-cone sum rule approach. We further predict the partial branching fractions of $B \to \gamma \ell \nu $ with a photon-energy cut $E_{\gamma} \geq E_{\rm cut}$, which are of interest for determining the inverse moment of the leading-twist $B$-meson distribution amplitude thanks to the forthcoming high-luminosity Belle II experiment at KEK.Form factorLight-cone sum rulesSoft-collinear effective theoryTwo-point correlation functionRenormalizationLight conesResummationQCD correctionsHeavy quarkBranching ratio...
- In this thesis we try to discuss certain phenomenological aspects of an R-parity violating non-minimal supersymmetric model, called $\mu\nu$SSM. We show that $\mu\nu$SSM can provide a solution to the $\mu$-problem of supersymmetry and can simultaneously accommodate the existing three flavour global data from neutrino experiments even at the tree level with the simple choice of flavour diagonal neutrino Yukawa couplings. We show that it is also possible to achieve different mass hierarchies for light neutrinos at the tree level itself. In $\mu\nu$SSM, the effect of R-parity violation together with a seesaw mechanism with TeV scale right-handed neutrinos are instrumental for light neutrino mass generation. We also analyze the stability of tree level neutrino masses and mixing with the inclusion of one-loop radiative corrections. In addition, we investigate the sensitivity of the one-loop corrections to different light neutrino mass orderings. Decays of the lightest supersymmetric particle were also computed and ratio of certain decay branching ratios was observed to correlate with certain neutrino mixing angle. We extend our analysis for different natures of the lightest supersymmetric particle as well as with various light neutrino mass hierarchies. We present estimation for the length of associated displaced vertices for various natures of the lightest supersymmetric particle which can act as a discriminating feature at a collider experiment. We also present an unconventional signal of Higgs boson in supersymmetry which can lead to a discovery, even at the initial stage of the large hadron collider running. Besides, we show that a signal of this kind can also act as a probe to the seesaw scale. Certain other phenomenological issues have also been addressed.SupersymmetryNeutrino mass hierarchyLightest Supersymmetric ParticleNeutrino massFlavourR-parity violationDisplaced verticesTeV scaleLHC RunNeutrino Yukawa coupling...
- A self-duality group $\cal G$ in quantum field theory can have anomalies. In that case, the space of ordinary coupling constants $\cal M$ can be extended to include the space $\cal F$ of coefficients of counterterms in background fields. The extended space $\cal N$ forms a bundle over $\cal M$ with fiber $\cal F$, and the topology of the bundle is determined by the anomaly. For example, the ${\cal G}=SL(2,\mathbb{Z})$ duality of the 4d Maxwell theory has an anomaly, and the space ${\cal F}=S^1$ for the gravitational theta-angle is nontrivially fibered over ${\cal M}=\mathbb{H}/SL(2,\mathbb{Z})$. We will explain a simple method to determine the anomaly when the 4d theory is obtained by compactifying a 6d theory on a Riemann surface in terms of the anomaly polynomial of the parent 6d theory. Our observations resolve an apparent contradiction associated with the global structure of the K\"ahler potential on the space of exactly marginal couplings of supersymmetric theories.DualityManifoldBundleQCD angleCoupling constantRiemann surfaceQuantum field theoryTheoryContradictionPolynomial...
- The Picard-Fuchs equation is a powerful mathematical tool which has numerous applications in physics, for it allows to evaluate integrals without resorting to direct integration techniques. We use this equation to calculate both the classical action and the higher-order WKB corrections to it, for the sextic double-well potential and the Lam\'e potential. Our development rests on the fact that the Picard-Fuchs method links an integral to solutions of a differential equation with the energy as a parameter. Employing the same argument we show that each higher-order correction in the WKB series for the quantum action is a combination of the classical action and its derivatives. From this, we obtain a computationally simple method of calculating higher-order quantum-mechanical corrections to the classical action, and demonstrate this by calculating the second-order correction for the sextic and the Lam\'e potential.Picard-Fuchs equationRiemann surfaceWentzel-Kramers-Brillouin approximationManifoldComplex manifoldComplex planeBranch pointPicardPerturbative expansionTorus...
- We study F-theory duals of heterotic line bundle models on elliptically fibered Calabi-Yau threefolds. These models necessarily contain NS5-branes which are geometrised in the dual F-theory compactifications. We initiate a systematic study of the correspondence between various configurations of NS5-branes and the dual geometries in F-theory and perform several checks of the duality. Furthermore, we discuss the singular transitions between different configurations of NS5-branes.NS5-braneF-theoryLine bundleDualityCompactificationGeometry...
- We consider $G_2$-manifolds with an effective torus action that is multi-Hamiltonian for one or more of the defining forms. The case of $T^3$-actions is found to be distinguished. For such actions multi-Hamiltonian with respect to both the three- and four-form, we derive a Gibbons-Hawking type ansatz giving the geometry on an open dense set in terms a symmetric $3\times 3$-matrix of functions. This leads to particularly simple examples of explicit metrics with holonomy equal to $G_2$. We prove that the multi-moment maps exhibit the full orbit space topologically as a smooth four-manifold containing a trivalent graph as the image of the set of special orbits and describe these graphs in some complete examples.ManifoldHamiltonianHolonomyTorusBundleTorsion tensorGraphMaximal torusCurvatureRank...
- We propose 5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories. From a Higgsing of the $SO(7)$ gauge theory with a hypermultiplet in the spinor representation, we construct two types of 5-brane web configurations for the pure $G_2$ gauge theory using an O5-plane or an $\widetilde{\text{O5}}$-plane. Adding flavors to the 5-brane web for the pure $G_2$ gauge theory is also discussed. Based on the obtained 5-brane webs, we compute the partition functions for the 5d $G_2$ gauge theories using the recently suggested topological vertex formulation with an O5-plane, and we find agreement with known results.Gauge theoryPartition functionD5 braneInstantonSpinor representationMagnetic monopoleFlop-transitionMonodromyD3 braneGauge coupling constant...
- We study the behaviour of abelian gauge symmetries in six-dimensional N=(1,0) theories upon decoupling gravity and investigate abelian flavour symmetries in the context of 6d N=(1,0) SCFTs. From a supergravity perspective, the anomaly cancellation mechanism implies that abelian gauge symmetries can only survive as global symmetries as gravity is decoupled. The flavour symmetries obtained in this way are shown to be free of ABJ anomalies, and their 't Hooft anomaly polynomial in the decoupling limit is obtained explicitly. In an F-theory realisation the decoupling of abelian gauge symmetries implies that a mathematical object known as the height pairing of a rational section is not contractible as a curve on the base of an elliptic Calabi-Yau threefold. We prove this prediction from supergravity by making use of the properties of the Mordell-Weil group of rational sections. In the second part of this paper we study the appearance of abelian flavour symmetries in 6d N=(1,0) SCFTs. We elucidate both the geometric origin of such flavour symmetries in F-theory and their field theoretic interpretation in terms of suitable linear combinations of geometrically massive U(1)s. Our general results are illustrated in various explicit examples.Flavour symmetryF-theoryGauge symmetryGlobal symmetryFibrationSupergravityGauge theoryFlavourCompactificationGauge coupling constant...
- Here I introduce basic methods of qualitative analysis of differential equations used in mathematical biology for people with minimal mathematical background.GraphEquilibrium pointAttractorManifoldSaddle pointCharacteristic equationComplex numberInitial value problemTwo-dimensional systemRational function...
- We present a conceptually clear introduction to quantum theory at a level suitable for high-school students attending the International Summer School for Young Physicists (ISSYP) at Perimeter Institute. It is entirely self-contained and no university-level background knowledge is required. The lectures we given over four days, four hours each day. On the first day the students were given all the relevant mathematical background from linear algebra and probability theory. On the second day, we used the acquired mathematical tools to define the full quantum theory in the case of a finite Hilbert space and discuss some consequences such as entanglement, Bell's theorem and the uncertainty principle. Finally, in days three and four we presented an overview of advanced topics related to infinite-dimensional Hilbert spaces, including canonical and path integral quantization, the quantum harmonic oscillator, quantum field theory, the Standard Model, and quantum gravity.QubitQuantum theoryComplex numberQuantum mechanicsHermitian operatorProbability amplitudeUnitary operatorHamiltonianStandard ModelQuantum field theory...
- Kepler's laws are derived from the inverse square law without the use of calculus and are simplified over previous such derivations.Kepler's lawsSemimajor axisDifferential formVectorForceOrbitNewtonVelocityObjectUnits...
- In this work we discuss different interpretations of mass in the relativistic dynamics. A new way to introduce mass is proposed. Our way is based on the relativistic equation of motion expressed in the form of the Newton$'$s second law. In this approach mass appears as a tensor, not as a scalar. The tensor mass allows us simply to describe anisotropic character of inert features of a relativistic object.KinematicsInvariant massSpecial relativityProper timeEinstein relationMassNewtonEquation of motionTensorForce...
- The purpose of this study, mainly historical and pedagogical, is to investigate the physical-mathematical similitudes of the spectroscopic and beta decay Fermi theories. Both theories were formulated using quantum perturbative theory that allowed obtaining equations whose algebraic structure and physical interpretation suggest that the two phenomena occur according to the same mechanism. Fermi, therefore, could have guessed well in advance of the times that the two theories could be unified into a single physical-mathematical model that led to different results depending on the considered energy. The electroweak unification found its full realization only in the 1960s within the Standard Model that, however, is mainly based on a mathematical approach. Retracing the reasoning made by Fermi facilitates the understanding of the physical foundations that underlie the unification of the electromagnetic and weak forces.Electroweak unificationFermi theory of weak interactionsWeak interactionStandard ModelBeta decayTheoryEnergy...
- To understand the formation and evolution of galaxies at redshifts z < 10, one must invariably introduce specific models (e.g., for the star formation) in order to fully interpret the data. Unfortunately, this tends to render the analysis compliant to the theory and its assumptions, so consensus is still somewhat elusive. Nonetheless, the surprisingly early appearance of massive galaxies challenges the standard model, and the halo mass function estimated from galaxy surveys at z > 4 appears to be inconsistent with the predictions of LCDM, giving rise to what has been termed "The Impossibly Early Galaxy Problem" by some workers in the field. A simple resolution to this question may not be forthcoming. The situation with the halos themselves, however, is more straightforward and, in this paper, we use linear perturbation theory to derive the halo mass function over the redshift range z < 10 for the R_h=ct universe. We use this predicted halo distribution to demonstrate that both its dependence on mass and its very weak dependence on redshift are compatible with the data. The difficulties with LCDM may eventually be overcome with refinements to the underlying theory of star formation and galaxy evolution within the halos. For now, however, we demonstrate that the unexpected early formation of structure may also simply be due to an incorrect choice of the cosmology, rather than to yet unknown astrophysical issues associated with the condensation of mass fluctuations and subsequent galaxy formation.Halo mass functionGalaxyStandard ModelVirial massLuminosityHigh massGalactic evolutionCosmologyMilky WayMass function...
- We discuss the possibility to find an upper bound on the lepton number violation scale using the cosmological bound on the cold dark matter relic density. We investigate a simple relation between the origin of neutrino masses and the properties of a dark matter candidate in a simple theory where the new symmetry breaking scale defines the seesaw scale. Imposing the cosmological bounds we find an upper bound of order multi-TeV on the lepton number violation scale. We investigate the predictions for direct and indirect detection dark matter experiments and the possible signatures at the Large Hadron Collider.Lepton number violationDark matterNeutrino massColliderDark matter candidateLarge Hadron ColliderCold dark matterSterile neutrinoSymmetry breakingGauge symmetry...
- We consider dark matter as Strongly Interacting Massive Particles (SIMPs) in a hidden sector, thermally decoupled from the Standard Model heat bath. Due to its strong interactions, the number changing processes of the SIMP lead to its thermalisation at temperature $T_{\rm{D}}$ different from the visible sector temperature $T$, and subsequent decoupling as the Universe expands. We study the evolution of the dark SIMP abundance in detail and find that a hidden SIMP provides for a consistent framework for self-interacting dark matter. Thermalisation and decoupling of a composite SIMP can be treated within the domain of validity of chiral perturbation theory unlike the simplest realisations of the SIMP, where the SIMP is in thermal equlibrium with the Standard Model.Hidden sectorStrongly Interacting Massive ParticleStandard ModelFreeze-outDark matterChiral perturbation theoryEntropyDegree of freedomDark sectorDark matter particle...
- Recent X-ray observations of galaxy clusters show that the distribution of intra-cluster medium (ICM) metallicity is remarkably uniform in space and in time. In this paper, we analyse a large sample of simulated objects, from poor groups to rich clusters, to study the dependence of the metallicity and related quantities on the scale of systems. The simulations are performed with an improved version of the Smoothed-Particle-Hydrodynamics \texttt{GADGET-3} code and consider various astrophysical processes including radiative cooling, metal enrichment and feedback from stars and active galactic nuclei (AGN). The scaling between the metallicity and the temperature and its evolution obtained in the simulations agrees well with the observational results obtained from two data samples characterised by a wide range of masses and a large redshift coverage. We find that at present time ($z=0$) the iron abundance in the cluster core ($r<0.1R_{500}$) does not correlate with the temperature and does not present a significant evolution. The scale invariance is confirmed when the metallicity is related directly with the total mass. The slope of the best-fitting relations is shallow ($\beta\sim-0.1$) in the innermost regions ($r<0.5R_{500}$) and consistent with zero outside. We investigate the impact of the AGN feedback and find that it plays a key role in producing a constant value of the outskirts metallicity from groups to clusters. This finding additionally supports the picture of early enrichment.MetallicityHydrodynamical simulationsGalaxy groups and clustersActive Galactic NucleiIntra-cluster mediumMetal enrichmentRadiative coolingFe abundanceCluster coreAGN feedback...
- One of the most striking features of quantum theory is the existence of entangled states, responsible for Einstein's so called "spooky action at a distance". These states emerge from the mathematical formalism of quantum theory, but to date we do not have a clear idea of the physical principles that give rise to entanglement. Why does nature have entangled states? Would any theory superseding classical theory have entangled states, or is quantum theory special? One important feature of quantum theory is that it has a classical limit, recovering classical theory through the process of decoherence. We show that any theory with a classical limit must contain entangled states, thus establishing entanglement as an inevitable feature of any theory superseding classical theory.Quantum theoryEntanglementEntangled stateTensor productClassical limitConvex setVector spaceAutomorphismLinear functionalPermutation...
- We consider a minimal model of a quantum rotator composed of a single particle confined in an harmonic potential and driven by two temperature-biased heat reservoirs. In the case the particle potential is rendered asymmetric and rotated an angle, a finite angular momentum develops, corresponding to a directed rotary motion. At variance with the classical case, the thermal fluctuations in the baths give rise to a non-vanishing average torque contribution; this is a genuine quantum effect akin to the Casimir effect. In the steady state the heat current flowing between the two baths is systematically converted into particle rotation. We derive exact expressions for the work rate and heat currents in the case where the system is driven by an external time periodic mechanical force. We show, in agreement with previous works on classical systems, that for this choice of external manipulation protocol, the rotator cannot work either as a heat pump or as a heat engine. We finally use our exact results to extend an ab-initio quantum simulation algorithm to the out-of-equilibrium regime.HamiltonianLangevin equationQuantum noiseClassical limitCasimir effectSteady stateMinimal modelsThermal fluctuationsDensity of statesUpper half-plane...
- We study spectral statistics in spatially extended chaotic quantum many-body systems, using simple lattice Floquet models without time-reversal symmetry. Computing the spectral form factor $K(t)$ analytically and numerically, we show that it follows random matrix theory (RMT) at times longer than a many-body Thouless time, $t_{\rm Th}$. We obtain a striking dependence of $t_{\rm Th}$ on the spatial dimension $d$ and size of the system. For $d>1$, $t_{\rm Th}$ is finite in the thermodynamic limit and set by the inter-site coupling strength. By contrast, in one dimension $t_{\rm Th}$ diverges with system size, and for large systems there is a wide window in which spectral correlations are not of RMT form.Random matrix theoryStatisticsMany-body systemsTime-reversal symmetryForm factorDomain wallCyclic permutationPeriodic orbitPartition functionMonte Carlo method...
- We investigate both the classical and quantum dynamics for a simple kicked system (the standard map) that classically has mixed phase space. For initial conditions in a portion of the chaotic region that is close enough to the regular region, the phenomenon of sticking leads to a power-law decay with time of the classical correlation function of a simple observable. Quantum mechanically, we find the same behavior, but with a smaller exponent. We consider various possible explanations of this phenomenon, and settle on a modification of the Meiss--Ott Markov tree model that takes into account quantum limitations on the flux through a turnstile between regions corresponding to states on the tree. Further work is needed to better understand the quantum behavior.Two-point correlation functionPhase spaceSurvival probabilityQuantum correlationTurnstileWave packetTorusPlanck's constantClassical limitHamiltonian...
- Phase space dynamics in classical mechanics is described by transport along trajectories. Anharmonic quantum mechanical systems do not allow for a trajectory-based description of their phase space dynamics. This invalidates some approaches to quantum phase space studies. We first demonstrate the absenceof trajectories in general terms. We then give an explicit proof for all quantum phase space distributions with negative values: we show that the generation of coherences in anharmonic quantum mechanical systems is responsible for the occurrence of singularities in their phase space velocity fields, and vice versa. This explains numerical problems repeatedly reported in the literature, and provides deeper insight into the nature of quantum phase space dynamics.Phase spaceContinuity equationEvolution equationQuantum coherenceHamiltonianQuantum phasesStagnation pointIntegral curveQuantum mechanicsQ-function...
- We consider a network of n spin 1/2 systems which are pairwise interacting via Ising interaction and are controlled by the same electro-magnetic control field. Such a system presents symmetries since the Hamiltonian is unchanged if we permute two spins. This prevents full (operator) controllability in that not every unitary evolution can be obtained. We prove however that controllability is verified if we restrict ourselves to unitary evolutions which preserve the above permutation invariance. For low dimensional cases, n=2 and n=3, we provide an analysis of the Lie group of available evolutions and give explicit control laws to transfer between any two permutation invariant states. This class of states includes highly entangled states such as GHZ states and W states, which are of interest in quantum information.PermutationSpin networkEntangled stateQuantum informationHamiltonianW stateGreenberger-Horne-Zeilinger stateLie subalgebrasLie group decompositionLie group...
- It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. Since a finite volume of space can't contain more than a finite amount of information, I argue that the mathematical real numbers are not physically real. Moreover, a better terminology for the so-called real numbers is "random numbers", as their series of bits are truly random. I propose an alternative classical mechanics that uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. I argue that it is more economical and natural to accept non-determinism with potentialities as a real mode of existence, both for classical and quantum physics.Quantum theoryBohmian mechanicsFoundation of PhysicsChaosMeasurement problemPrecisionDeityQuantum measurementBaker's mapBig Bang...
- Free fermion systems enjoy a privileged place in physics. With their simple structure they can explain a variety of effects, ranging from insulating and metallic behaviours to superconductivity and the integer quantum Hall effect. Interactions, e.g. in the form of Coulomb repulsion, can dramatically alter this picture by giving rise to emerging physics that may not resemble free fermions. Examples of such phenomena include high-temperature superconductivity, fractional quantum Hall effect, Kondo effect and quantum spin liquids. The non-perturbative behaviour of such systems remains a major obstacle to their theoretical understanding that could unlock further technological applications. Here, we present a pedagogical review of "interaction distance" [Nat. Commun. 8, 14926 (2017)] -- a systematic method that quantifies the effect interactions can have on the energy spectrum and on the quantum correlations of generic many-body systems. In particular, the interaction distance is a diagnostic tool that identifies the emergent physics of interacting systems. We illustrate this method on the simple example of a one-dimensional Fermi-Hubbard dimer.HamiltonianFree fermionsEntanglementDensity matrixEntanglement spectrumReduced density matrixMany-body systemsQuantum correlationPerturbation theoryPartition function...
- We present a novel finite-size scaling for both interaction and disorder strengths in the critical regime of the many-body localization (MBL) transition for a spin-1/2 XXZ spin chain with random field by studying the level statistics. We show how the dynamical transition from the thermal to MBL phase depends on interaction together with disorder by evaluating the adjacent gap ratio, and thus, extend previous studies in which the interaction coupling is fixed. We introduce an extra critical exponent in order to describe the nontrivial interaction dependence of the MBL transition. It is characterized by the ratio of the disorder strength to the power of the interaction coupling with respect to the extra critical exponent and not by the simple ratio between them.Many-body localizationFinite size scalingStatisticsCritical exponentXXZ spin chainRandom FieldWigner DysonEntanglement entropyPoisson distributionHamiltonian...
- We propose a geometric multiparty extension of Clauser-Horne (CH) inequality. The standard CH inequality can be shown to be an implication of the fact that statistical separation between two events, $A$ and $B$, defined as $P(A\oplus B)$, where $A\oplus B=(A-B)\cup(B-A)$, satisfies the axioms of a distance. Our extension for tripartite case is based on triangle inequalities for the statistical separations of three probabilistic events $P(A\oplus B \oplus C)$. We show that Mermin inequality can be retrieved from our extended CH inequality for three subsystems. With our tripartite CH inequality, we investigate quantum violations by GHZ-type and W-type states. Our inequalities are compared to another type, so-called $N$-site CH inequality. In addition we argue how to generalize our method for more subsystems and measurement settings. Our method can be used to write down several Bell-type inequalities in a systematic manner.QubitGreenberger-Horne-Zeilinger stateW stateTriangle inequalityBell's inequalityPolytopeEPR stateBell operatorQuantum mechanicsEntanglement...
- A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). For single particle systems with fully chaotic classical counterparts, the problem has been partly solved by Berry (1985) within the so-called diagonal approximation of semiclassical periodic-orbit sums. Derivation of the full RMT spectral form factor $K(t)$ from semiclassics has been completed only much later in a tour de force by Mueller et al (2004). In recent years, the questions of long-time dynamics at high energies, for which the full many-body energy spectrum becomes relevant, are coming at the forefront even for simple many-body quantum systems, such as locally interacting spin chains. Such systems display two universal types of behaviour which are termed as `many-body localized phase' and `ergodic phase'. In the ergodic phase, the spectral fluctuations are excellently described by RMT, even for very simple interactions and in the absence of any external source of disorder. Here we provide the first theoretical explanation for these observations. We compute $K(t)$ explicitly in the leading two orders in $t$ and show its agreement with RMT for non-integrable, time-reversal invariant many-body systems without classical counterparts, a generic example of which are Ising spin 1/2 models in a periodically kicking transverse field.Random matrix theoryQuantum chaosPermutationForm factorPeriodic orbitCyclic permutationIsing modelTime-reversal symmetryMany-body systemsPropagator...
- We analyze the variance of stochastic gradients along negative curvature directions in certain non-convex machine learning models and show that stochastic gradients exhibit a strong component along these directions. Furthermore, we show that - contrary to the case of isotropic noise - this variance is proportional to the magnitude of the corresponding eigenvalues and not decreasing in the dimensionality. Based upon this observation we propose a new assumption under which we show that the injection of explicit, isotropic noise usually applied to make gradient descent escape saddle points can successfully be replaced by a simple SGD step. Additionally - and under the same condition - we derive the first convergence rate for plain SGD to a second-order stationary point in a number of iterations that is independent of the problem dimension.CurvatureSaddle pointNeural networkOptimizationMachine learningDistance boundingDeep Neural NetworksPolynomial timeHidden layerCovariance...
- It is a known fact that training recurrent neural networks for tasks that have long term dependencies is challenging. One of the main reasons is the vanishing or exploding gradient problem, which prevents gradient information from propagating to early layers. In this paper we propose a simple recurrent architecture, the Fourier Recurrent Unit (FRU), that stabilizes the gradients that arise in its training while giving us stronger expressive power. Specifically, FRU summarizes the hidden states $h^{(t)}$ along the temporal dimension with Fourier basis functions. This allows gradients to easily reach any layer due to FRU's residual learning structure and the global support of trigonometric functions. We show that FRU has gradient lower and upper bounds independent of temporal dimension. We also show the strong expressivity of sparse Fourier basis, from which FRU obtains its strong expressive power. Our experimental study also demonstrates that with fewer parameters the proposed architecture outperforms other recurrent architectures on many tasks.Recurrent neural networkLong short term memoryHidden stateArchitectureMNIST datasetLower and upperDeep Neural NetworksStatisticsExponential functionVandermonde determinant...
- We report the first observation of the decay D^+ -> eta' e^+ nu_e in two analyses, which combined provide a branching fraction of B(D+ -> eta' e nu) = (2.16 +/- 0.53 +/- 0.07) x 10^{-4}. We also provide an improved measurement of B(D+ -> eta e nu) = (11.4 +/- 0.9 +/- 0.4) x 10^{-4}, provide the first form factor measurement, and set the improved upper limit B(D+ -> phi e nu) < 0.9 x 10^{-4} (90% C.L.).Monte Carlo methodStatisticsHadronizationSemileptonic decaySystematic errorElectron neutrinoDecay modeNeutrinoStatistical significanceBranching ratio...
- While Euler characteristic X(G)=sum_x w(x) super counts simplices, Wu characteristics w_k(G) = sum_(x_1,x_2,...,x_k) w(x_1)...w(x_k) super counts simultaneously pairwise interacting k-tuples of simplices in a finite abstract simplicial complex G. More general is the k-intersection number w_k(G_1,...G_k), where x_i in G_i. We define interaction cohomology H^p(G_1,...,G_k) compatible with w_k and invariant under Barycentric subdivison. It allows to distinguish spaces which simplicial cohomology can not: it can identify algebraically the Moebius strip and the cylinder for example. The cohomology satisfies the Kuenneth formula: the Poincare polynomials p_k(t) are ring homomorphisms from the strong ring to the ring of polynomials in t. The Dirac operator D=d+d^* defines the block diagonal Hodge Laplacian L=D^2 which leads to the generalized Hodge correspondence b_p(G)=dim(H^p_k(G)) = dim(ker(L_p)) and Euler-Poincare w_k(G)=sum_p (-1)^p dim(H^p_k(G)) for Wu characteristic. Also, like for traditional simplicial cohomology, isospectral Lax deformation D' = [B(D),D], with B(t)=d(t)-d^*(t)-ib(t), D(t)=d(t)+d(t)^* + b(t) can deform the exterior derivative d. The Brouwer-Lefschetz fixed point theorem generalizes to all Wu characteristics: given an endomorphism T of G, the super trace of its induced map on k'th cohomology defines a Lefschetz number L_k(T). The Brouwer index i_T,k(x_1,...,x_k) = product_j=1^k w(x_j) sign(T|x_j) attached to simplex tuple which is invariant under T leads to the formula L_k(T) = sum_T(x)=x i_T,k(x). For T=Id, the Lefschetz number L_k(Id) is equal to the k'th Wu characteristic w_k(G) of the graph G and the Lefschetz formula reduces to the Euler-Poincare formula for Wu characteristic.CohomologyGraphEuler characteristicOrientationExterior derivativeAutomorphismManifoldQuaternionsSimple graphRing homomorphism...
- We examine the current constraints and future sensitivity of Coherent Elastic Neutrino-Nucleus Scattering (CE$\nu$NS) experiments to mixing scenarios involving a $Z^\prime$ which interacts via portals with the Standard Model. We contrast the results against those from fixed target, atomic parity violation, and solar neutrino experiments. We demonstrate a significant dependence of the experimental reach on the $Z'$ coupling non-universality and the complementarity of CE$\nu$NS to existing searches.NeutrinoStandard ModelHyperchargeParity violationSolar neutrinoBorexinoReactor neutrino experimentsStandard Model fermionKinetic mixingFixed target experiments...
- In this article, we consider a dark matter scenario in the context of the minimal extension of the Standard Model (SM) with a $B-L$ (baryon number minus lepton number) gauge symmetry, where three right-handed neutrinos with a $B-L$ charge $-1$ and a $B-L$ Higgs field with a $B-L$ charge $+2$ are introduced to make the model anomaly-free and to break the $B-L$ gauge symmetry, respectively. The $B-L$ gauge symmetry breaking generates the Majorana masses for the right-handed neutrinos. We introduce a Z$_2$ symmetry to the model and assign an odd parity only for one right-handed neutrino, and hence the Z$_2$-odd right-handed neutrino is stable and the unique dark matter candidate in the model. The so-called minimal seesaw works with the other two right-handed neutrinos and reproduces the current neutrino oscillation data. We consider the case that the dark matter particle communicates with the SM particles through the $B-L$ gauge boson ($Z^{\prime}_{B-L}$ boson), and obtain a lower bound on the $B-L$ gauge coupling ($\alpha_{B-L}$) as a function of the $Z^{\prime}_{B-L}$ boson mass ($m_{Z^{\prime}}$) from the observed dark matter relic density. On the other hand, we interpret the recent LHC Run-2 results on the search for a $Z^{\prime}$ boson resonance to an upper bound on $\alpha_{B-L}$ as a function of $m_{Z^{\prime}}$. These two constraints are complementary to narrow down an allowed parameter region for this "$Z^{\prime}$ portal" dark matter scenario, leading to a lower mass bound of $m_{Z^{\prime}} \geq 3.9$ TeV.Dark matterStandard ModelSterile neutrinoMinimal modelsHiggs bosonDark matter particleGauge symmetryATLAS Experiment at CERNHiggs fieldLHC Run 2...
- We calculate the electromagnetic multipole moments of the $P_c^+(4380)$ pentaquark by modeling it as the diquark-diquark-antiquark and $\bar D^*\Sigma_c$ molecular state with quantum numbers $J^P = \frac{3}{2}^-$. In particular, the magnetic dipole, electric quadrupole and magnetic octupole moments of this particle are extracted in the framework of light-cone QCD sum rule. The values of the electromagnetic multipole moments obtained via two pictures differ substantially from each other, which can be used to pin down the underlying structure of $P_c^+(4380)$. The comparison of any future experimental data on the electromagnetic multipole moments of the $P_c^+(4380)$ pentaquark with the results of the present work can shed light on the nature and inner quark organization of this state.Multipole momentsPentaquarkDiquarkQuadrupoleTwo-point correlation functionLight conesPropagatorForm factorLight-cone sum rulesQCD sum rules...
- The scalar field plays an fundamental role in the investigation of confinement property characterising many particle physics models. This is achieved by coupling this particle directly with gauge fields at the lagrangian level. We have adopted the same approach {[}10{]} to determine a potential as a perturbative series in terms of interquark distance. In order to introduce the gravitational effects and inspired from bag models, we implement a scalar field which interacts both with the vacuum and the electron field. In this context and with presence of the vacuum condensates, it is possible to derive a more accurate expression of the electron energy.Scalar fieldConfinementGauge fieldDilatonBag Model of Quark ConfinementGravitational effectsString theorySurface tensionEffective LagrangianHiggs potential...
- These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field theory -- it is a property of the algebra of observables and not just of the states.Quantum field theoryEntropyVon Neumann algebraReeh-Schlieder theoremTensor productPath integralCommutantDensity matrixReduced density matricesBounded operator...