• #### Electroweak Splitting Functions and High Energy Showeringver. 2

We derive the electroweak (EW) collinear splitting functions for the Standard Model, including the massive fermions, gauge bosons and the Higgs boson. We first present the splitting functions in the limit of unbroken SU(2)xU(1) and discuss their general features in the collinear and soft-collinear regimes. We then systematically incorporate EW symmetry breaking (EWSB), which leads to the emergence of additional "ultra-collinear" splitting phenomena and naive violations of the Goldstone-boson Equivalence Theorem. We suggest a particularly convenient choice of non-covariant gauge (dubbed "Goldstone Equivalence Gauge") that disentangles the effects of Goldstone bosons and gauge fields in the presence of EWSB, and allows trivial book-keeping of leading power corrections in the VEV. We implement a comprehensive, practical EW showering scheme based on these splitting functions using a Sudakov evolution formalism. Novel features in the implementation include a complete accounting of ultra-collinear effects, matching between shower and decay, kinematic back-reaction corrections in multi-stage showers, and mixed-state evolution of neutral bosons (gamma/Z/h) using density-matrices. We employ the EW showering formalism to study a number of important physical processes at O(1-10 TeV) energies. They include (a) electroweak partons in the initial state as the basis for vector-boson-fusion; (b) the emergence of "weak jets" such as those initiated by transverse gauge bosons, with individual splitting probabilities as large as O(30%); (c) EW showers initiated by top quarks, including Higgs bosons in the final state; (d) the occurrence of O(1) interference effects within EW showers involving the neutral bosons; and (e) EW corrections to new physics processes, as illustrated by production of a heavy vector boson (W') and the subsequent showering of its decay products.
Goldstone bosonKinematicsElectroweak symmetry breakingParton showerInterferencePartonIsospinHiggs bosonQuantum electrodynamicsPropagator...
• #### Feynman integral relations from parametric annihilatorsver. 2

We study shift relations between Feynman integrals via the Mellin transform through parametric annihilation operators. These contain the momentum space IBP relations, which are well-known in the physics literature. Applying a result of Loeser and Sabbah, we conclude that the number of master integrals is computed by the Euler characteristic of the Lee-Pomeransky polynomial. We illustrate techniques to compute this Euler characteristic in various examples and compare it with numbers of master integrals obtained in previous works.
Path integralGraphEuler characteristicMellin transformMomentum spacePropagatorLoop momentumVector spaceFeynman diagramsTorus...
• #### Fabrication of micro fluidic cavities using Si-to-glass anodic bonding

We demonstrate the fabrication of ~1.08 um deep micro fluidic cavities with characteristic size as large as 7 mm x 11 mm, using a silicon-glass anodic bonding technique. A pre-cut piece of Hoya SD-2 glass is bonded to a patterned piece of silicon (each with 1 mm thickness) in which the cavity is defined by etching. Bonding was carried out at 425C with 200 V, and we observe that pressurizing the cell to failure (> 30 bar pressure) results in the glass breaking, rather than the glass-silicon bond separation. In this article, we discuss the detailed fabrication of the cavity, its edges, and details of the joint of the coin silver fill line to the silicon base of the cavity.
GlassOxideNuclear magnetic resonanceTorsion tensorDeep Reactive Ion EtchingReactive-ion etchingCoolingNanofluidicsAdhesionWetting...
• #### The LDA-1/2 method applied to atoms and molecules

The LDA-1/2 method has proven to be a viable approach for calculating band gaps of semiconductors. To address its accuracy for finite systems, we apply LDA-1/2 to atoms and the molecules of the $GW100$ test set. The obtained energies of the highest-occupied molecular orbitals are validated against CCSD(T) data and the $G_0W_0$ approach of many-body perturbation theory. The accuracy of LDA-1/2 and $G_0W_0$ is found to be the same, where the latter is computationally much more involved. To get insight into the benefits and limitations of the LDA-1/2 method, we analyze the impact of each assumption made in deriving the methodology.
Self-energyAtoms and moleculesPerturbation theoryIonizationWavefunctionSemiconductorBand gapElectrostaticsDensity functional theoryIonization energy...
• #### Excitations energies from diffusion Monte Carlo using selected Configuration Interaction nodes

Quantum Monte Carlo (QMC) is a stochastic method which has been particularly successful for ground-state electronic structure calculations but mostly unexplored for the computation of excited-state energies. Here, we show that, within a Jastrow-free QMC protocol relying on a deterministic and systematic construction of nodal surfaces using selected configuration interaction (sCI) expansions, one is able to obtain accurate excitation energies at the fixed-node diffusion Monte Carlo (FN-DMC) level. This evidences that the fixed-node errors in the ground and excited states obtained with sCI wave functions cancel out to a large extent. Our procedure is tested on two small organic molecules (water and formaldehyde) for which we report all-electron FN-DMC calculations. For both the singlet and triplet manifolds, accurate vertical excitation energies are obtained with relatively compact multideterminant expansions built with small (typically double-$\zeta$) basis sets.
Excited stateQuantum Monte CarloMonte Carlo methodManifoldOrganic moleculeSoftwareStatistical errorLinear optimizationQuantum chemistrySteady state...
• #### Black holes, hidden symmetries, and complete integrabilityver. 3

The study of higher-dimensional black holes is a subject which has recently attracted a vast interest. Perhaps one of the most surprising discoveries is a realization that the properties of higher-dimensional black holes with the spherical horizon topology and described by the Kerr-NUT-(A)dS metrics are very similar to the properties of the well known four-dimensional Kerr metric. This remarkable result stems from the existence of a single object called the principal tensor. In our review we discuss explicit and hidden symmetries of higher-dimensional black holes. We start with the overview of the Liouville theory of completely integrable systems and introduce Killing and Killing-Yano objects representing explicit and hidden symmetries. We demonstrate that the principal tensor can be used as a seed object' which generates all these symmetries. It determines the form of the black hole geometry, as well as guarantees its remarkable properties, such as special algebraic type of the spacetime, complete integrability of geodesic motion, and separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations. The review also contains a discussion of different applications of the developed formalism and its possible generalizations.
Killing tensorBlack holeGeodesicRankTwo-formHamiltonianKerr metricPhase spaceHamilton-Jacobi equationCovariant derivative...
• #### Quantization of Pseudoclassical Systems in the Schrodinger Realization

We examine the quantization of pseudoclassical dynamical systems, models that have classically anticommuting variables, in the Schrodinger picture. We quantize these systems, which can be viewed as classical models of particle spin, using the Dirac-Gupta-Bleuler method as well as the reduced phase space method when applicable. We show that, with minimal modifications, the standard constructions of Schrodinger quantum mechanics for constrained systems work for pseudoclassical systems as well. In particular, we construct the space of spinors as physical wave functions of anticommuting variables.
QuantizationPhase spaceHamiltonianPoisson bracketDirac bracketIrreducible representationClifford algebraQuantum mechanicsInvoluteSquare-integrable function...
• #### Supersymmetry, Vacuum Statistics, and the Fundamental Theorem of Algebraver. 2

I give an interpretation of the fundamental theorem of algebra based on supersymmetry and the Witten index. The argument gives a physical explanation of why a real polynomial of degree $n$ need not have $n$ real zeroes, while a complex polynomial of degree $n$ must have $n$ complex zeroes. This paper also addresses in a general and model-independent way the statistics of the perturbative ground states (the states which correspond to classical vacua) in supersymmetric theories with complex and with real superfields.
Witten indexFundamental theorem of algebraStatisticsSupersymmetryHamiltonianMass gapField theoryQuantum theorySuperfieldSuperpotential...
• #### Duality, Partial Supersymmetry, and Arithmetic Number Theoryver. 2

We find examples of duality among quantum theories that are related to arithmetic functions by identifying distinct Hamiltonians that have identical partition functions at suitably related coupling constants or temperatures. We are led to this after first developing the notion of partial supersymmetry-in which some, but not all, of the operators of a theory have superpartners-and using it to construct fermionic and parafermionic thermal partition functions, and to derive some number theoretic identities. In the process, we also find a bosonic analogue of the Witten index, and use this, too, to obtain some number theoretic results related to the Riemann zeta function.
Partition functionSupersymmetryDualityArithmeticHamiltonianParafermionString theoryCoupling constantQuantum theoryNumber theory...
• #### On the Use of Integrals to Evaluate Series of Rational Terms

This article is written with the hope to draw attention to a method that uses integral transforms to find exact values for a large class of convergent series (and, in particular, series of rational terms). We apply the method to some series that generalize a problem published in The College Mathematics Journal'. Some of the results thus obtained have not been founded in standard references.
Path integralFeynman parameterRational functionLaplace transformPolygamma functionRight Hand Side of the expressionReal numbersFactorialPolynomialTaylor series...
• #### A Class of Periodic Continued Radicals

We compute the limits of a class of periodic continued radicals and we establish a connection between them and the fixed points of the Chebycheff polynomials.
Definable setPeriodatePolynomialP-symmetryMotiveRight Hand Side of the expressionReal numbers...
• #### Investigation of Skyscraper's Feat (original version with an addendum)

Skyscraper is a Hollywood action film directed and written by Rawson M. Thurber scheduled to be released on July 13, 2018. We present an exhaustive analysis of the feat shown in the recently released teaser poster and trailer of the film. Although the feat appears to be unrealistic at first glance, after close investigation using back-of-the-envelope calculations, it is seen to be within human capabilities. This article is the original version of an abridged article published in Physics Education. It was written very soon after the poster and clip were released by Universal Pictures.
SchedulingPhysics EducationStarActionImpulsePictureForceTrajectoryPressureCenter of mass...
• #### Arithmetic analogues of Hamiltonian systems

The paper reviews various arithmetic analogues of Hamiltonian systems and presents some new facts suggesting ways to relate/unify these examples.
ArithmeticHamiltonianFormal schemeElliptic curveSymplectic formValuation ringResidue fieldFibrationEuler equationsIsomorphism...
• #### Arithmetic Levi-Civita connection

This paper is part of a series of papers where an arithmetic analogue of classical differential geometry is being developed. In this arithmetic differential geometry functions are replaced by integer numbers, derivations are replaced by Fermat quotient operators, and connections (respectively curvature) are replaced by certain adelic (respectively global) objects attached to symmetric matrices with integral coefficients. Previous papers were devoted to an arithmetic analogue of the Chern connection. The present paper is devoted to an arithmetic analogue of the Levi-Civita connection.
ArithmeticCurvatureRing homomorphismHomomorphismMorphismIsomorphismTorsion tensorLevi-Civita connectionAutomorphismEndomorphism...
• #### Conformal perturbation theoryver. 4

Statistical systems near a classical critical point have been intensively studied both from theoretical and experimental points of view. In particular, correlation functions are of relevance in comparing theoretical models with the experimental data of real systems. In order to compute physical quantities near a critical point one needs to know the model at the critical (conformal) point. In this line, recent progresses in the knowledge of conformal field theories, through the conformal bootstrap, give the hope to get some interesting results also outside of the critical point. In this note we will review and clarify how, starting from the knowledge of the critical correlators, one can calculate in a safe way their behavior outside the critical point. The approach illustrated requires the model to be just scale invariant at the critical point. We will clarify the method by applying it to different kind of perturbations of the $2D$ Ising model.
Critical pointWilson coefficientsIsing modelOperator product expansionConformal field theoryTwo-point correlation functionPerturbation theoryExpectation ValueMellin transformConformal Bootstrap...
• #### Unified Foundations for Mathematics

There are different meanings of foundation of mathematics: philosophical, logical, and mathematical. Here foundations are considered as a theory that provides means (concepts, structures, methods etc.) for the development of whole mathematics. Set theory has been for a long time the most popular foundation. However, it was not been able to win completely over its rivals: logic, the theory of algorithms, and theory of categories. Moreover, practical applications of mathematics and its inner problems caused creation of different generalization of sets: multisets, fuzzy sets, rough sets etc. Thus, we encounter a problem: Is it possible to find the most fundamental structure in mathematics? The situation is similar to the quest of physics for the most fundamental "brick" of nature and for a grand unified theory of nature. It is demonstrated that in contrast to physics, which is still in search for a unified theory, in mathematics such a theory exists. It is the theory of named sets.
Foundations of mathematicsRough setGrand unification theoryAlgorithms...
• #### Special temperatures in frustrated ferromagnets

The description and detection of unconventional magnetic states such as spin liquids is a recurring topic in condensed matter physics. While much of the efforts have traditionally been directed at geometrically frustrated antiferromagnets, recent studies reveal that systems featuring competing antiferromagnetic and ferromagnetic interactions are also promising candidate materials. We find that this competition leads to the notion of special temperatures, analogous to those of gases, at which the competing interactions balance, and the system is quasi-ideal. Although induced by weak perturbing interactions, these special temperatures are surprisingly high and constitute an accessible experimental diagnostic of eventual order or spin liquid properties. The well characterised Hamiltonian and extended low-temperature susceptibility measurement of the canonical frustrated ferromagnet Dy$_2$Ti$_2$O$_7$ enables us to formulate both a phenomenological and microscopic theory of special temperatures for magnets. Other members of this new class of magnets include kapellasite Cu$_3$Zn(OH)$_6$Cl$_2$ and the spinel GeCo$_2$O$_4$.
Spin iceFerromagnetJouleAntiferromagneticHamiltonianSpin liquidAntiferromagnetCoolingMean fieldPyrochlore...
• #### A variation of Euler's approach to values of the Riemann zeta functionver. 2

An elementary method of computing the values at negative integers of the Riemann zeta function is presented. The principal ingredient is a new q-analogue of the Riemann zeta function. We show that for any argument other than 1 the classical limit of this q-analogue exists and equals the value of the Riemann zeta.
• #### Three theorems of quantum mechanics and their classical counterparts

The Hellmann-Feynman, virial and comparison theorems are three fundamental theorems of quantum mechanics. For the first two, counterparts exist for classical mechanics with relativistic or nonrelativistic kinetic energy. It is shown here that these three theorems are valid for classical mechanics with a nonstandard kinetic energy. This brings some information about the connections between the quantum and classical worlds. Constraints about the functional form of the kinetic energy are also discussed.
HamiltonianQuantum mechanicsHellmann-Feynman theoremComparison theoremVirial theoremEhrenfest theoremWentzel-Kramers-Brillouin approximationEuler-Lagrange equationKinetic energyClassical mechanics...
• #### C. F. von Weizsaecker's Reconstruction of Physics: Yesterday, Today, Tomorrow

Carl Friedrich von Weizsaecker's thinking has always crossed the borders between physics and philosophy. Being a physicist by training he still feels at home in the physics community, as a philosopher by passion, however, his mind cannot stop thinking at the limits of physics. His physical ideas are based on the general conceptual and methodological preconditions of physical theories. Such a line of reasoning about the foundations of physics has brought Weizsaecker into an abstract program of a possible reconstruction of physics in terms of yes-no-alternatives, which he called "ur-theory." I shall start this paper with a review of the basic ideas of ur-theory: the definition of an ur and the connection between ur-spinors and spacetime. I then go over to some of ur-theory's present borders: the construction of quantized spacetime tetrads and the difficulties to incorporate gravity and gauge theories. Finally, I shall discuss the possible prospects of ur-theory -- partly with a view to modern quantum gravity approaches, but mainly in connection with its philosophical implications. Here, one of the crucial questions is, whether form, or, modern, information is an entity per se and what particular consequences this may have.
TetradQuantum gravityEntropyWavefunctionQuantum theoryGauge theoryQubitSymmetry groupSpin structureQuantization...
• #### The status of varying constants: a review of the physics, searches and implications

The observational evidence for the recent acceleration of the universe demonstrates that canonical theories of cosmology and particle physics are incomplete---if not incorrect---and that new physics is out there, waiting to be discovered. A key task for the next generation of laboratory and astrophysical facilities is to search for, identify and ultimately characterize this new physics. Here we highlight recent developments in tests of the stability of nature's fundamental couplings, which provide a direct handle on new physics: a detection of variations will be revolutionary, but even improved null results provide competitive constraints on a range of cosmological and particle physics paradigms. A joint analysis of all currently available data shows a preference for variations of $\alpha$ and $\mu$ at about the two-sigma level, but inconsistencies between different sub-sets (likely due to hidden systematics) suggest that these statistical preferences need to be taken with caution. On the other hand, these measurements strongly constrain Weak Equivalence Principle violations. Plans and forecasts for forthcoming studies with facilities such as ALMA, ESPRESSO and the ELT, which should clarify these issues, are also discussed, and synergies with other probes are briefly highlighted. The goal is to show how a new generation of precision consistency tests of the standard paradigm will soon become possible.
Scalar fieldDark energyESPRESSOHIRES spectrometerEquation of state of dark energyCosmologyDilatonFine structure constantSpectrographsCosmological parameters...
• #### Learning to Optimize Tensor Programs

We introduce a learning-based framework to optimize tensor programs for deep learning workloads. Efficient implementations of tensor operators, such as matrix multiplication and high dimensional convolution, are key enablers of effective deep learning systems. However, existing systems rely on manually optimized libraries such as cuDNN where only a narrow range of server class GPUs are well-supported. The reliance on hardware-specific operator libraries limits the applicability of high-level graph optimizations and incurs significant engineering costs when deploying to new hardware targets. We use learning to remove this engineering burden. We learn domain-specific statistical cost models to guide the search of tensor operator implementations over billions of possible program variants. We further accelerate the search by effective model transfer across workloads. Experimental results show that our framework delivers performance competitive with state-of-the-art hand-tuned libraries for low-power CPU, mobile GPU, and server-class GPU.
OptimizationDeep learningInductive transferSchedulingEmbeddingRankBayesianGraphMachine learningRegression...
• #### Compressive sensing lattice dynamics. I. General formalism

{\it Ab initio\/} calculations have been successful in evaluation of lattice dynamical properties of solids with the (quasi-)harmonic approximation, i.e. assuming non-interacting phonons with infinite lifetimes. However, it remains difficult to account for anharmonicity for all but the simplest structures. We detail a systematic information theory based approach to deriving {\it ab initio\/} force constants: compressive sensing lattice dynamics (CSLD). The non-negligible terms necessary to reproduce the interatomic forces are selected by minimizing the $\ell_1$ norm (sum of absolute values) of the scaled force constants. The part I of this series mainly focuses on the theoretical and computational details of our approach, along with select examples.
PhononMolecular dynamicsDensity functional theorySupercellPerturbation theoryPreconditionerRelaxation timeVibrationRotational invarianceNearest-neighbor site...
• #### Reevaluating Old Stellar Populations

Determining the properties of old stellar populations (those with age >1 Gyr) has long involved the comparison of their integrated light, either in the form of photometry or spectroscopic indexes, with empirical or synthetic templates. Here we reevaluate the properties of old stellar populations using a new set of stellar population synthesis models, designed to incorporate the effects of binary stellar evolution pathways as a function of stellar mass and age. We find that single-aged stellar population models incorporating binary stars, as well as new stellar evolution and atmosphere models, can reproduce the colours and spectral indices observed in both globular clusters and quiescent galaxies. The best fitting model populations are often younger than those derived from older spectral synthesis models, and may also lie at slightly higher metallicities.
Stellar populationsMetallicityStarGalaxyGlobular clusterInitial mass functionStellar evolutionSpectral energy distributionPhotometryAsymptotic giant branch...
• #### Zero-temperature glass transition in two dimensions

The nature of the glass transition is theoretically understood in the mean-field limit of infinite spatial dimensions, but the problem remains totally open in physical dimensions. Nontrivial finite-dimensional fluctuations are hard to control analytically, and experiments fail to provide conclusive evidence regarding the nature of the glass transition. Here, we use Monte Carlo simulations that fully bypass the glassy slowdown, and access equilibrium states in two-dimensional glass-forming liquids at low enough temperatures to directly probe the transition. We find that the liquid state terminates at a thermodynamic glass transition at zero temperature, which is associated with an entropy crisis and a diverging static correlation length.
EntropyGlassMonte Carlo methodGlass transitionPermutationLiquidsRelaxation timePolydispersityTwo-point correlation functionMean field...
• #### Spectral signatures of fractionalization in the frustrated Heisenberg model on the square lattice

We employ a variational Monte Carlo approach to efficiently obtain the dynamical structure factor for the spin-1/2 $J_1-J_2$ Heisenberg model on the square lattice. Upon increasing the frustrating ratio $J_2/J_1$, the ground state undergoes a continuous transition from a N\'eel antiferromagnet to a $\mathbb{Z}_{2}$ gapless spin liquid. We identify the characteristic spectral features in both phases and highlight the existence of a broad continuum of excitations in the proximity of the spin-liquid phase. The magnon branch, which dominates the spectrum of the unfrustrated Heisenberg model, gradually loses its spectral weight, thus releasing nearly-deconfined spinons, whose signatures are visible even in the magnetically ordered state. Our results show how free spinons emerge across a quantum critical point, providing evidence for the fractionalization of magnons into deconfined spinons.
MagnonSpinonHeisenberg modelSpin liquidHamiltonianLiquid phaseVariational Monte CarloExcited stateSpectral signatureQuantum critical point...
• #### Simulations of Jet Heating in Galaxy Clusters: Successes and Numerical Challenges

We study idealised hydrodynamical simulations of Perseus-like galaxy cluster cores, with the goal of studying cooling flow regulation by jets generated by active galactic nuclei (AGN). The simulations are performed with the Eulerian code athena using high-resolution Godunov methods with low numerical diffusion. We use novel analysis methods to measure the cooling rate, the total heating rate, the heating rate from weak shocks and the heating rate from the decay of turbulent motions excited by the jet. We find that successful regulation of the cooling flow can be achieved with kinetic jets. Heating is anisotropic and is mostly distributed along the jet axis where the cooling flow is suppressed. Away from the jet axis the cooling flow is reduced by weak shock heating, but not fully suppressed. Turbulence is a significant source of heating only near the cluster centre, but this mechanism becomes inefficient at $\sim$50 kpc scales where it only represents a few % of the total heating rate and where most of the heating is provided by weak shocks. This qualitative picture is in agreement with previous numerical work. However, we find that several details of the simulations depend on the choice made for the hydro solver. This is a consequence of the difficulty of achieving proper numerical convergence for this problem: current physics implementations and resolutions do not properly capture multiphase gas that develops as a consequence of thermal instability. These processes happen at the grid scale and leave numerical solutions sensitive to the properties of the chosen hydro solver.
Cooling flowEntropyCoolingInstabilityCluster coreNumerical diffusionIntra-cluster mediumAccretionStatistical estimatorCluster of galaxies...
• #### Cold Molecular Outflows in the Local Universe

We study molecular outflows in a sample of 45 local galaxies, both star forming and AGN, primarily by using CO data from the ALMA archive and from the literature. For a subsample we also compare the molecular outflow with the ionized and neutral atomic phases. We infer an empirical analytical function relating the outflow rate simultaneously to the SFR, $L_{\rm AGN}$, and galaxy stellar mass; this relation is much tighter than the relations with the individual quantities. The outflow kinetic power shows a larger scatter than in previous studies, spanning from 0.1 to 5~per cent of $L_{\rm AGN}$, while the momentum rate ranges from 1 to 30 times $L_{\rm AGN}/c$, indicating that these outflows can be both energy-driven, but with a broad range of coupling efficiencies with the ISM, and radiation pressure-driven. For about 10~per cent of the objects the outflow properties significantly exceed the maximum theoretical values; we interpret these as "fossil outflows" resulting from activity of a past strong AGN, which has now faded. We estimate that, in the stellar mass range probed here ($>$ 10$^{10}~\rm M_{\odot}$), less than 5~per cent of the outflowing gas escapes the galaxy. The molecular gas depletion time associated with the outflow can be as short as a few million years in powerful AGNs, however the total gas (H$_2$+HI) depletion times are much longer. Altogether, our findings suggest that even AGN-driven outflows might be relatively ineffective in clearing galaxies of their entire gas content, although they are likely capable of clearing and quenching the central region. Finally, we find no correlation between molecular outflow rate and radio power, suggesting that on average radio jets do not play a major role in driving massive molecular outflows in the luminosity range (log($L_{\rm AGN}$) = 41-46 erg s$^{-1}$) probed here.
Active Galactic NucleiGalaxyMolecular outflowLuminosityMilky WayStar formationStellar massHost galaxyStar-forming galaxyAtacama Large Millimeter Array...
• #### Theoretical mathematics'': Toward a cultural synthesis of mathematics and theoretical physics

Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice there can be benefits, but there can also be unpleasant and destructive consequences. Serious caution is required, and the issue should be considered before, rather than after, obvious damage occurs. With the hazards carefully in mind, we propose a framework that should allow a healthy and positive role for speculation.
• #### Responses to Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics'', by A. Jaffe and F. Quinn

This article is a collection of letters solicited by the editors of the Bulletin in response to a previous article by Jaffe and Quinn [math.HO/9307227]. The authors discuss the role of rigor in mathematics and the relation between mathematics and theoretical physics.
• #### What is matter? The fundamental ontology of atomism and structural realism

We set out a fundamental ontology of atomism in terms of matter points. While being most parsimonious, this ontology is able to match both classical and quantum mechanics, and it remains a viable option for any future theory of cosmology that goes beyond current quantum physics. The matter points are structurally individuated: all there is to them are the spatial relations in which they stand; neither a commitment to intrinsic properties nor to an absolute space is required. The spatial relations change. All that is needed to capture change is a dynamical structure, namely dynamical relations as expressed in terms of the dynamical parameters of a physical theory.
Foundation of PhysicsQuantum mechanicsBohmian mechanicsCosmologyQuantum theoryPermutationQuantum field theoryElectrodynamicsEntanglementRegularization...
• #### On the possibility of a realist ontological commitment in quantum mechanics

This paper reviews the structure of standard quantum mechanics, introducing the basics of the von Neumann-Dirac axiomatic formulation as well as the well-known Copenhagen interpretation. We review also the major conceptual difficulties arising from this theory, first and foremost, the well-known measurement problem. The main aim of this essay is to show the possibility to solve the conundrums affecting quantum mechanics via the methodology provided by the primitive ontology approach. Using Bohmian mechanics as an example, the paper argues for a realist attitude towards quantum theory. In the second place, it discusses the Quinean criterion for ontology and its limits when it comes to quantum physics, arguing that the primitive ontology programme should be considered as an improvement on Quine's method in determining the ontological commitments of a theory.
Quantum mechanicsFoundation of PhysicsQuantum theorySuperpositionBohmian mechanicsCopenhagen interpretationMeasurement problemDynamical variableDynamical evolutionUncertainty principle...
• #### Observables and unobservables in quantum mechanics: How the no-hidden-variables theorems support the Bohmian particle ontology

The paper argues that far from challenging - or even refuting - Bohm's quantum theory, the no-hidden-variables theorems in fact support the Bohmian ontology for quantum mechanics. The reason is that (i) all measurements come down to position measurements and (ii) Bohm's theory provides a clear and coherent explanation of the measurement outcome statistics based on an ontology of particle positions, a law for their evolution and a probability measure linked with that law. What the no-hidden-variables theorems teach us is that (i) one cannot infer the properties that the physical systems possess from observables and that (ii) measurements, being an interaction like other interactions, change the state of the measured system.
Quantum mechanicsBohmian mechanicsFoundation of PhysicsQuantum theoryStatisticsWave packetMeasurement problemStern-gerlachBell's theoremDegree of freedom...
• #### The radiation of a uniformly accelerated charge is beyond the horizon: a simple derivationver. 5

We show, by exploring some elementary consequences of the covariance of Maxwell's equations under general coordinate transformations, that, despite inertial observers can indeed detect electromagnetic radiation emitted from a uniformly accelerated charge, comoving observers will see only a static electric field. This simple analysis can help understanding one of the most celebrated paradoxes of last century.
• #### Levinson theorem for Dirac particles in two dimensions

The Levinson theorem for nonrelativistic quantum mechanics in two spatial dimensions is generalized to Dirac particles moving in a central field. The theorem relates the total number of bound states with angular momentum $j$ ($j=\pm 1/2, \pm 3/2, ...$), $n_j$, to the phase shifts $\eta_j(\pm E_k)$ of scattering states at zero momentum as follows: $\eta_j(\mu)+\eta_j(-\mu)= n_j\pi$.
Bound stateQuantum mechanicsRetarded propagatorBessel functionCurrent densityCompleteness relationNonnegativeField theoryHamiltonianCompleteness...
• #### Levinson theorem for Dirac particles in one dimension

The scattering of Dirac particles by symmetric potentials in one dimension is studied. A Levinson theorem is established. By this theorem, the number of bound states with even (odd) parity, $n_+$ ($n_-$), is related to the phase shifts $\eta_+(\pm E_k)$ [$\eta_-(\pm E_k)$] of scattering states with the same parity at zero momentum as follows: $$\eta_\pm(\mu)+\eta_\pm(-\mu)\pm{\pi\over 2}[\sin^2\eta_\pm(\mu) -\sin^2\eta_\pm(-\mu)]=n_\pm\pi.$$ The theorem is verified by several simple examples.
Bound stateGreen's functionCompleteness relationField theoryParticle massHamiltonianRegularizationGamma matricesQuantum mechanicsQuantum theory...
• #### On Improving Motor Imagery BCI Using A Novel Physical Feedback Technique

In this study, and through an understanding of neuronal system communication, A light was shed upon a novel model serves as an assistive technology for locked-in people suffering from Motor neuronal disease. MND patients, who have an intact minds, are able -till now- to make a mean of on-screen communication. Work was done upon the potential of brain wave activity patterns to be detected as electrical signals, classified and translated into commands following BCI constructing paradigm. However, The interface constructed was for the first time a device which can reconstruct this command physically. The intervention is in a software is used to classify imagined right and left limb movement into binary results, and then make use of the magnetic field produced by the amplified pulses to reconstruct the activity into ferrofluid droplets movement- these moved due rotation of a desk according to the data received. Objectives of the project is to address the challenges of the inaccurate performance and cost of user-training which are yet the main issues preventing BCI from being upgraded into more immersive and effective technology. The design requirements addressed were the communication speed of the droplet movement and the accuracy of hitting fixed targets . Tests were performed based on software programs accelerated changing motor imagery movement of left and right limbs. The tests achieved an average speed of 0.469 cm/s and average accuracy of 81.6% for the best volume from many were tried. A conclusion to be drawn was that the promise of this other point of view on BCI systems to be more Brain-Real World Systems.
SoftwareActivity patternsFerrofluidCommunicationDropletObjectivePotentialMagnetic field...
• #### More on the Asymmetric Infinite Square Well: Energy Eigenstates with Zero Curvature

We extend the standard treatment of the asymmetric infinite square well to include solutions that have zero curvature over part of the well. This type of solution, both within the specific context of the asymmetric infinite square well and within the broader context of bound states of arbitrary piecewise-constant potential energy functions, is not often discussed as part of quantum mechanics texts at any level. We begin by outlining the general mathematical condition in one-dimensional time-independent quantum mechanics for a bound-state wave function to have zero curvature over an extended region of space and still be a valid wave function. We then briefly review the standard asymmetric infinite square well solutions, focusing on zero-curvature solutions as represented by energy eigenstates in position and momentum space.
• #### Playing Quantum Physics Jeopardy with zero-energy eigenstates

We describe an example of an exact, quantitative Jeopardy-type quantum mechanics problem. This problem type is based on the conditions in one-dimensional quantum systems that allow an energy eigenstate for the infinite square well to have zero curvature and zero energy when suitable Dirac delta functions are added. This condition and its solution are not often discussed in quantum mechanics texts and have interesting pedagogical consequences.
• #### Addressing the Majorana vs. Dirac Question Using Neutrino Decays

We explain why it is so hard to determine whether neutrinos are Majorana or Dirac particles as long as the only neutrinos we study are ultra-relativistic. We then show how non-relativistic neutrinos could help, and focus on the angular distributions in the decays of an as-yet-to-be-discovered heavy neutrino $N$. We find that these angular distributions could very well tell us whether neutrinos are Majorana or Dirac particles.
NeutrinoSterile neutrinoHelicityMajorana fermionStandard ModelDecay rateAntineutrinoLepton numberDirac neutrinoFermilab...
• #### $T\bar{T}$ Partition Function from Topological Gravity

The $T{\bar T}$ deformation of a relativistic two-dimensional theory results in a solvable gravitational theory. Deformed scattering amplitudes can be obtained from coupling the undeformed theory to the flat space Jackiw--Teitelboim (JT) gravity. We show that the JT description is applicable and useful also in finite volume. Namely, we calculate the torus partition function of an arbitrary matter theory coupled to the JT gravity, formulated in the first order (vierbein) formalism. The first order description provides a natural set of dynamical clocks and rods for this theory, analogous to the target space coordinates in string theory. These dynamical coordinates play the role of relational observables allowing to define a torus path integral for the JT gravity. The resulting partition function is one-loop exact and reproduces the $T\bar{T}$ deformed finite volume spectrum.
Partition functionTorusPath integralWorldsheetE_nVacuum energyTopological gravityConformal field theoryQuantum field theoryField theory...
• #### Spatial fluctuations of the intergalactic temperature-density relation after hydrogen reionizationver. 2

The thermal state of the post-reionization IGM is sensitive to the timing of reionization and the nature of the ionizing sources. We have modelled here the thermal state of the IGM in cosmological radiative transfer simulations of a realistic, extended, spatially inhomogeneous hydrogen reionization process, carefully calibrated with Ly-alpha forest data. We compare these with cosmological simulations run using a spatially homogeneous ionizing background. The simulations with a realistic growth of ionized regions and a realistic spread in reionization redshifts show, as expected, significant spatial fluctuations in the temperature-density relation (TDR) of the post-reionization IGM. The most recently ionized regions are hottest and exhibit a flatter TDR. In simulations consistent with the average TDR inferred from Ly-alpha forest data, these spatial fluctuations have a moderate but noticeable effect on the statistical properties of the Ly-alpha opacity of the IGM at z ~ 4-6. This should be taken into account in accurate measurements of the thermal properties of the IGM and the free-streaming of dark matter from Ly-alpha forest data in this redshift range. The spatial variations of the TDR predicted by our simulations are, however, smaller by about a factor two than would be necessary to explain the observed large spatial opacity fluctuations on large (> 50 comoving Mpc/h) scales at z > 5.5.
ReionizationRadiative transfer simulationsIntergalactic mediumTemperature-density relationRadiative transferCoolingUltraviolet backgroundEffective optical depthReionization redshiftHistory of the reionization...
• #### Quantum Materials for Spin and Charge Conversion

Spintronics aims to utilize the spin degree of freedom for information storage and computing applications. One major issue is the generation and detection of spins via spin and charge conversion. Quantum materials have recently exhibited many unique spin-dependent properties, which can be used as promising material candidates for efficient spin and charge conversion. Here, we review recent findings concerning spin and charge conversion in quantum materials, including Rashba interfaces, topological insulators, two-dimensional materials, superconductors, and non-collinear antiferromagnets. Important progress in using quantum materials for spin and charge conversion could pave the way for developing future spintronics devices.
Quantum materialsSpintronicsDegree of freedomTopological insulatorSuperconductorAntiferromagnetSpinChargeMaterials...
• #### Quantum walk on a toral phase space

A quantum walk on a toral phase space involving translations in position and its conjugate momentum is studied in the simple context of a coined walker in discrete time. The resultant walk, with a family of coins parametrized by an angle is such that its spectrum is exactly solvable with eigenangles for odd parity lattices being equally spaced, a feature that is remarkably independent of the coin. The eigenvectors are naturally specified in terms the $q-$Pochhammer symbol, but can also be written in terms of elementary functions, and their entanglement can be analytically found. While the phase space walker shares many features in common with the well-studied case of a coined walker in discrete time and space, such as ballistic growth of the walker position, it also presents novel features such as exact periodicity, and formation of cat-states in phase-space. Participation ratio (PR) a measure of delocalization in walker space is studied in the context of both kinds of quantum walks; while the classical PR increases as $\sqrt{t}$ there is a time interval during which the quantum walks display a power-law growth $\sim t^{0.825}$. Studying the evolution of coherent states in phase space under the walk enables us to identify an Ehrenfest time after which the coin-walker entanglement saturates.
Phase spaceQuantum walkEntanglementCoherent stateCat statePochhammer symbolP-symmetryMomentumEigenvector...
• #### Quantum many-body scarsver. 2

Certain wave functions of non-interacting quantum chaotic systems can exhibit "scars" in the fabric of their real-space density profile. Quantum scarred wave functions concentrate in the vicinity of unstable periodic classical trajectories. We introduce the notion of many-body quantum scars which reflect the existence of a subset of special many-body eigenstates concentrated in certain parts of the Hilbert space. We demonstrate the existence of scars in the Fibonacci chain -- the one- dimensional model with a constrained local Hilbert space realized in the 51 Rydberg atom quantum simulator [H. Bernien et al., arXiv:1707.04344]. The quantum scarred eigenstates are embedded throughout the thermalizing many-body spectrum, but surprisingly lead to direct experimental signatures such as robust oscillations following a quench from a charge-density wave state found in experiment. We develop a model based on a single particle hopping on the Hilbert space graph, which quantitatively captures the scarred wave functions up to large systems of L = 32 atoms. Our results suggest that scarred many-body bands give rise to a new universality class of quantum dynamics, which opens up opportunities for creating and manipulating novel states with long-lived coherence in systems that are now amenable to experimental study.
Quantum simulatorsUniversality classGraphQuenchingRydberg atomReal spaceCharge density waveHilbert spaceTrajectoryAtom...
• #### Entanglement structure of current driven quantum many-body systemsver. 2

When an extended system is coupled at its opposite boundaries to two reservoirs at different temperatures or chemical potentials, it cannot achieve a global thermal equilibrium and is instead driven to a set of current carrying non-equilibrium states. Motivated by developments in the understanding of thermalization in closed quantum many-body systems, we find conditions under which such current-driven systems can achieve, or violate, local thermal equilibrium, by investigating their entropy, mutual information, and entanglement at long times. We focus on a specific model consisting of a two-parameter family of random unitary circuits acting locally on a chain of spin-1/2s (equivalently, qubits) that exhibits quantum chaotic behavior in most of its parameter space. The only conserved quantity is the $z$ component of the total magnetization of the spins. We choose the model so that for all parameter values the time-averaged correlation functions agree and are close to local equilibrium. However, computing the total von Neumann entropy of the system shows that there are in fact three distinct "phases" of the driven problem, with local equilibrium only emerging in the quantum chaotic regime, while one of the other phases exhibits volume-law mutual information and entanglement. We extend these results to the three-dimensional, non-interacting Anderson model in the diffusive regime, showing that the non-equilibrium steady-state for fermions realizes the volume-law mutual information phase of the random circuit. Our results suggest a generic picture for the emergence of local equilibrium in current-driven quantum chaotic systems, as well as provide insights into methods to stabilize highly-entangled many-body states out of equilibrium.
Mutual informationEntropyEntanglementDensity matrixTwo-point correlation functionMagnetizationAnderson modelSteady stateQubitWavefunction...
• #### Fluctuation dissipation theorem and electrical noise revisited

The fluctuation dissipation theorem (FDT) is the basis for a microscopic description of the interaction between electromagnetic radiation and matter.By assuming the electromagnetic radiation in thermal equilibrium and the interaction in the linear response regime, the theorem interrelates the spontaneous fluctuations of microscopic variables with the kinetic coefficients that are responsible for energy dissipation.In the quantum form provided by Callen and Welton in their pioneer paper of 1951 for the case of conductors, electrical noise detected at the terminals of a conductor was given in terms of the spectral density of voltage fluctuations, $S_V({\omega})$, and was related to the real part of its impedance, $Re[Z({\omega})]$, by a simple relation.The drawbacks of this relation concern with: (I) the appearance of a zero point contribution which implies a divergence of the spectrum at increasing frequencies; (ii) the lack of detailing the appropriate equivalent-circuit of the impedance, (iii) the neglect of the Casimir effect associated with the quantum interaction between zero-point energy and boundaries of the considered physical system; (iv) the lack of identification of the microscopic noise sources beyond the temperature model. These drawbacks do not allow to validate the relation with experiments. By revisiting the FDT within a brief historical survey, we shed new light on the existing drawbacks by providing further properties of the theorem, focusing on the electrical noise of a two-terminal sample under equilibrium conditions. Accordingly, we will discuss the duality and reciprocity properties of the theorem, its applications to the ballistic transport regime, to the case of vacuum and to the case of a photon gas.
Two-point correlation functionPlanck missionReciprocityLangevin equationDualityStatisticsZero-point energyPlasma frequencyStefan-Boltzmann lawElectromagnetic radiation...
• #### 100% of the zeros of the Riemann zeta-function are on the critical line

We consider a specific family of analytic functions $g_{\alpha,T}(s)$, satisfying certain functional equations and approximating to linear combinations of the Riemann zeta-function and its derivatives of the form $c_0\zeta(s)+c_1\frac{\zeta'(s)}{\log T}+c_2\frac{\zeta''(s)}{(\log T)^2}+\dots+c_{K}\frac{\zeta^{(K)}(s)}{(\log T)^{K}}$. We also consider specific mollifiers of the form $M(s)D(s)$ for these linear combinations, where $M(s)$ is the classical mollifier, that is, a short Dirichlet polynomial for $1/\zeta(s)$, and the Dirichlet polynomial $D(s)$ is arbitrarily long and arises from substitution for $w$, in Runge's complex approximation polynomial for $f(w)=\frac1{c_0+w}$, of a Dirichlet polynomial being the Selberg approximation for $\frac{c_1}{\log T}\frac{\zeta'}{\zeta}(s)+\frac{c_2}{(\log T)^2}\frac{\zeta''}{\zeta}(s)+\dots+\frac{c_{K}}{(\log T)^{K}}\frac{\zeta^{(K)}}{\zeta}(s)$ (analogous to Selberg's classical approximation for $\frac{\zeta'}{\zeta}(s)$). Exploiting the functional equations previously mentioned (which are about translation of the variable $s$), together with the mean-square asymptotics of the Levinson-Conrey method and the Selberg-Tsang approximation theory (with some additional results) we show that almost all of the zeros of the Riemann zeta-function are on the critical line.
MollifierRiemann zeta functionCritical lineZeta functionAnalytic continuationRiemann hypothesisDirichlet seriesBernoulli numberLaguerre polynomialsHypergeometric function...
• #### Geometry and Physics: An Overview

We present some episodes from the history of interactions between geometry and physics over the past century.
InstantonBundleManifoldQuantum field theoryMagnetic monopoleQuantum theoryMagnetic chargeAlgebraic geometryGauge theoryPath integral...
• #### On Noncontextual, Non-Kolmogorovian Hidden Variable Theories

One implication of Bell's theorem is that there cannot in general be hidden variable models for quantum mechanics that both are noncontextual and retain the structure of a classical probability space. Thus, some hidden variable programs aim to retain noncontextuality at the cost of using a generalization of the Kolmogorov probability axioms. We generalize a theorem of Feintzeig (2015) to show that such programs are committed to the existence of a finite null cover for some quantum mechanical experiments, i.e., a finite collection of probability zero events whose disjunction exhausts the space of experimental possibilities.
Quantum mechanicsHidden variable theoryBell's theoremEPR paradoxHidden stateProjection operatorStatisticsNo-go theoremQuantum theoryInterference...