Identical Particles Research Articles

Counting \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 8 black holes as algebraic varieties

We calculate the helicity trace index B14 for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 8 pure D-brane black holes using various techniques of computational algebraic geometry and find perfect agreement with the existing results in the literature. For these black holes, microstate counting is equivalent to finding the number of supersymmetric vacua of a multi-variable supersymmetric quantum mechanics which in turn is equivalent to solving a set of multi-variable polynomial equations modulo gauge symmetries. We explore four different techniques to solve a set of polynomial equations, namely Newton Polytopes, Homotopy continuation, Monodromy and Hilbert series. The first three methods rely on a mixture of symbolic and high precision numerics whereas the Hilbert series is symbolic and admit a gauge invariant analysis. Furthermore, exploiting various exchange symmetries, we show that quartic and higher order terms are absent in the potential, which if present would have spoiled the counting. Incorporating recent developments in algebraic geometry focusing on computational algorithms, we have extended the scope of one of the authors previous works [1, 2] and presented a new perspective for the black hole microstate counting problem. This further establishes the pure D-brane system as a consistent model, bringing us a step closer to \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 2 black hole microstate counting.

Higher-Order Structural Analysis of a Transparent and Flexible High Thermal Conductive Liquid Crystalline Elastomer Sheet and Its Composite.

Transparency, flexibility, and high thermal conductivity are trade-offs. Specifically, we have investigated a cross-linked acrylic liquid crystal elastomer (LCE) that exhibits both transparency and flexibility while maintaining a high level of thermal conductivity. The transparent monodomain LCE sheet was achieved through a process of stretching an initially opaque polydomain sheet to 80% elongation and subsequently subjecting it to photocuring. The thermal conductivity in the stretching direction (x) of the monodomain LCE sheet was found to be 1.8 times higher than that of the prestretched polydomain sheet, consistent with findings from previous studies. However, in the orthogonal direction (y) to the stretching (x) direction, the thermal conductivity exhibited an even higher value, being 1.7 times greater than in the x-direction, with a value of 3.0 W/(m·K). This unique observation prompted us to conduct further investigation through higher-order structural analysis of these LCE sheets using 2D wide-angle X-ray scattering (WAXS) analysis. In the transparent sheet, the LCE molecules were aligned in the sheet in the stretching x-direction (monodomain structure) for the out-of-plane direction. However, in the in-plane x-direction, the molecular plane spacing exhibited random orientation at a period of 0.45 nm. In contrast, within the y-direction of the inner layer, the molecular plane spacing exhibited a uniaxial horizontal orientation at the same period length as in the x-direction. The heat energy entering into the y-direction once spreads to the x-direction, but it was considered that the reason for the higher thermal conductivity to the y-direction would be forming covalent bonds that function as new heat transmission paths, in the direction intersecting to the x-direction during photocuring. Therefore, we concluded that the synergistic effect of the high level of the ordered inner structure and covalent bonding structure due to cross-linking in the y-direction contributes to its higher thermal conductivity compared to that in the x-direction, which exhibits a random in-plane structure. Additionally, we have fabricated an LCE composite sheet filled with 75 vol % of alumina particles using a polydomain-type LCE as the base material. The composite sheet exhibits remarkable thermal conductivity in the thickness direction, measuring at 9.8 W/(m·K), while maintaining a flexibility characterized by an elastic modulus of 70 MPa. This thermal conductivity surpasses that of a nonmesogenic acrylic composite sheet with identical alumina particle filling, which measured at 3.9 W/(m·K), more than twice as much. The presence of the mesogen skeleton has been demonstrated to enhance heat transfer, even within soft composites, by facilitating the formation of an ordered structure.

Spatially Resolved Raman Spectroscopic Investigation of Uranyl Fluoride: A Case Study in the Importance of Instrument Optimization.

Raman spectroscopy is an emerging technique for rapid and nondestructive analysis of nuclear materials for forensic and nonproliferation applications as it is a powerful tool for distinguishing multiple chemical forms of materials with similar stoichiometries. Recent developments in spectroscopic software have enabled rapid data collection with high-speed Raman spectroscopic mapping capabilities. However, some uranium-rich materials are susceptible to degradation in humid air and/or laser-induced phase transformations. To mitigate environmental or measurement-related sample degradation of potential samples of interest, we have taken a systematic approach to define optimized data collection parameters for high-throughput measurements of uranyl fluoride (UO2F2), which is an important intermediate material in the nuclear fuel cycle. First, we systematically describe the influence of optical magnification (5× to 100×), laser power, and exposure time on obtained signal for identical particles of UO2F2 and find that at low laser power and exposure times, comparable signal is obtained regardless of optical magnification. Second, we ensure sample integrity during data collection, and third, collect spectroscopic maps that employ optimized parameters to reduce the time required to obtain spatially resolved spectroscopic information. Reductions of 90% and 99% in measurement times are discussed as they relate to differences in resolving spectroscopic features of particles in identical mapping areas. During this work, we found that additional data processing options were needed and thus developed a customized Python script for importing, processing, analyzing, and visualizing Raman spectroscopic map data.

Hunting for hypercharge anapole dark matter in all spin scenarios

We conduct a combined analysis to investigate dark matter (DM) with hypercharge anapole moments, focusing on scenarios where Majorana DM particles with spin 1/2, 1, 3/2, and 2 interact exclusively with Standard Model particles through U(1)Y hypercharge anapole terms for the first time. For completeness, we construct general effective U(1) gauge-invariant three-point vertices. These enable the generation of hypercharge gauge-invariant interaction vertices for both a virtual photon γ and a virtual Z boson with two identical massive Majorana particles of any nonzero spin s, after the spontaneous breaking of electroweak gauge symmetry. For complementarity, we adopt effective operators tailored to each dark matter spin allowing crossing symmetry. We calculate the relic abundance, analyze current constraints and future sensitivities from dark matter direct detection and collider experiments, and apply the conceptual naive perturbativity bound. Our estimations based on a generalized vertex calculation demonstrate that the scenario with a higher-spin DM is more stringently constrained than a lower-spin DM, primarily due to the reduced annihilation cross section and/or the enhanced rate of LHC monojet events. As a remarkable outcome, the spin-2 anapole DM scenario is almost entirely excluded, while the high-luminosity LHC exhibits high sensitivities in probing spin-1 and -3/2 scenarios, except for a tiny parameter range of DM mass around 1 TeV. A significant portion of the remaining parameter space in the spin-1/2 DM scenario can be explored through upcoming Xenon experiments, with more than 20 ton-yr exposure equivalent to approximately 5 years of running the XENONnT experiment. Published by the American Physical Society 2024

Entropic relations for indistinguishable quantum particles

The von Neumann entropy of a k-body-reduced density matrix γ k quantifies the entanglement between k quantum particles and the remaining ones. In this paper, we rigorously prove general properties of this entanglement entropy as a function of k; it is concave for all 1⩽k⩽N and non-decreasing until the midpoint k⩽⌊N/2⌋ . The results hold for indistinguishable quantum particles and are independent of the statistics.

Discrete Scale Invariance and U(2) Family of Two-Body Contact Interactions in One Dimension

Because of the absence of indistinguishability constraint, interparticle interactions between nonidentical particles have in general much more variety than those between identical particles. In particular, it is known that there exists a U(2) family of two-body contact interactions between nonidentical particles in one spatial dimension. This paper studies breakdown of continuous scale invariance to discrete scale invariance under this U(2) family of two-body contact interactions in two-body problems of nonidentical particles on the half line. We show that, in contrast to the corresponding identical-particle problem, there exist two distinct channels that admit geometric sequences of two-body bound states.

Study of thermodynamic properties of N particles in one-dimensional harmonic oscillator potential

We have calculated the partition function and hence the energy and the specific heat of a two-particle system in n numbers of finite nondegenerate energy levels of equal spacing distributed according to classical and quantum statistics. We have then extended our study for N identical particles placed in 1D harmonic oscillator potential. It is observed that the specific heat of bosons and fermions are exactly the same in this potential at any temperature, and at high temperature the results are similar to that for the classical particles. The partition function of a system of two particles placed in 2D harmonic oscillator potential has also been determined as comparison.

Fractional diamagnetic Kepler problem and elastic collisions

In this work, we consider an application of fractional derivatives to realistic physical situations, namely the elastic collision of particles and the nonintegrable diamagnetic Kepler problem. The origin of fractional dynamics can be nonlocal interacting dynamics, memory effects, environments with fractal interacting properties, and relaxation processes, among others. In the case of collisions, considering identical and distinguishable particles, additional solutions appear compared to non-fractional dynamics. For specific velocities of one particle before the collision, several velocities of the other particle are allowed after the collision. Consequently, novel velocity distributions emerge. For the diamagnetic Kepler problem, the fractional dynamic strongly affects the regular and quasi-regular regimes of motion, while the completely chaotic motion remains essentially unaltered. Besides, we derive a fractional momentum-like integral of motion for the pure fractional Kepler problem.

Quantum exchange symmetry induces charge diffusion and trapping in ultracold gases

For a homonuclear ion-atom system, we show that the exchange symmetry leads to special outcomes for ion transport that manifest themselves in ultracold experiments. We compute the two body charge hopping probabilities and rates, which are used to model charge hopping in the dynamics of an ultracold 6/7 Li+ ion immersed within an ultracold gas of 6/7 Li atoms at micro-Kelvin temperatures. We show that the charge hopping and collisional diffusion compete, giving unique results leading to charge trapping in regions of high atomic density gradient. These investigations in ion-atom systems open a new approach to probe quantum phenomena in various systems with exchange symmetry.

Insights into the assessment of spreadability of stainless steel powders in additive manufacturing

This work investigates the link between the single particle and bulk flow properties of stainless steel (SS316L) powders and their spreading behaviour for additive manufacturing (AM) application. Two different batches of SS316L powders, noted to have significantly different spreading behaviour in AM machines, were investigated. The two batches had almost identical particle size, morphology and bulk flow properties as quantified by angle of repose, Hausner ratio, Carr index and basic flow energy; however one of the batches did not consistently flow during Hall and Carney flow tests and also had very poor spreadability when evaluated using an in-house spreading rig. The flow and spreading behaviours of the poorly spreading batch significantly improved and became almost identical to the good batch when tested following drying, either in a vacuum oven or a freeze dryer. Elemental analysis revealed that batches had some small but significant differences in chemical composition. This study revealed the complexity of defining a correlation between powder properties and spreading behaviour, and the importance of considering the environmental conditions.

Experimental Study on Coefficient of Restitution of Small-Sized Spherical Particles during Low-Speed Impact

This study presents experimental investigations on the normal restitution coefficients of a titanium bead (Ti), zirconia bead (ZrO2), and amorphous zirconium alloy sphere (Amor). The research explores the influence of particle diameter and collision velocity on the normal restitution coefficient between two independent, identical spherical particles of different materials. The experimental findings demonstrate that increasing the particle diameter results in more effective plastic deformation, leading to higher energy losses and, subsequently, smaller coefficients of restitution. Similarly, higher particle velocities cause more energy dissipation during collisions, resulting in smaller restitution coefficients. Comparing particles of different materials, those with larger yield strengths exhibit more elastic behavior, experience less initial energy loss due to deformation, and reach the maximum restitution coefficient (elastic state) with fewer collisions. This finding suggests that material properties significantly influence the overall energy dissipation and elastic response in the particles. To validate the experimental results, existing models are compared and discussed. Furthermore, potential physical mechanisms responsible for the observed behavior are explored, providing valuable insights into the collision dynamics in spherical particle interactions. Overall, this study contributes to a better understanding of the factors affecting the normal restitution coefficient in particle collisions, enabling the design and optimization of particle systems for diverse applications in condensed matter and related fields.

Classical nonrelativistic fractons

We initiate the study of the classical mechanics of nonrelativistic fractons in its simplest setting—that of identical one-dimensional particles with local Hamiltonians characterized by a conserved dipole moment in addition to the usual symmetries of space and time translation invariance. We introduce a family of models and study the N-body problem for them. We find that locality leads to a “Machian” dynamics in which a given particle exhibits finite inertia only if within a specified distance of another particle. For well-separated particles, this dynamics leads to immobility, much as for quantum models of fractons discussed before. For two or more particles within inertial reach of each other at the start of motion, we obtain an interesting interplay of inertia and interactions. Specifically, for a solvable “inertia only” model of fractons, we find that two particles always become immobile at long times. Remarkably, three particles generically evolve to a late time state with one immobile particle and two oscillating about a common center of mass with generalizations of such “Machian clusters” for N>3. Interestingly, these Machian clusters exhibit physical limit cycles in a Hamiltonian system even though mathematical limit cycles are forbidden by Liouville's theorem. Published by the American Physical Society 2024

Population and Energy Transfer Dynamics in an Open Excitonic Quantum Battery.

In a previous study, we proposed an open quantum network model of a quantum battery (QB) that possesses dark states owing to its structural exchange symmetries. While in a dark state, the QB is capable of storing an exciton without any environment-induced population losses. However, when the structural exchange symmetry is broken, the QB begins to discharge the exciton towards its exit site. In this article, we start by demonstrating that this QB is not only loss-free with respect to exciton population during the storage phase, but also with respect to the QB energy. We then explore the exciton population and energy transfer dynamics of the QB during the discharge phase over a wide range of site energies, bath temperatures, and bath reorganization energies. Our results shed light on how to optimize the QB's population and energy transfer dynamics for different purposes.

Multiparticle states in braided lightlike κ -Minkowski noncommutative QFT

In this study, we construct a 1+1-dimensional, relativistic, free, complex scalar quantum field theory on the noncommutative spacetime known as lightlike κ-Minkowski. The associated κ-Poincaré quantum group of isometries is triangular, and its quantum R matrix enables the definition of a braided algebra of N points that retains κ-Poincaré invariance. Leveraging our recent findings, we can now represent the generators of the deformed oscillator algebra as nonlinear redefinitions of undeformed oscillators, which are nonlocal in momentum space. The deformations manifest at the multiparticle level, as the one-particle states are identical to the undeformed ones. We successfully introduce a covariant and involutive deformed flip operator using the R matrix. The corresponding deformed (anti)symmetrization operators are covariant and idempotent, allowing for a well-posed definition of multiparticle states, a result long sought in quantum field theory on κ-Minkowski. We find that P and T are not symmetries of the theory, although PT (and hence CPT) is. We conclude by noticing that identical particles appear distinguishable in the new theory, and discuss the fate of the Pauli exclusion principle in this setting. Published by the American Physical Society 2024

Particle deposition and clogging as an Obstacle and Opportunity for sustainable energy

Fine particle motions have significant implications in porous media, manifesting in various natural phenomena and industrial applications. The movement of particles can lead to channel blockage, resulting in clogging. Depending on the context, clogging can be either advantageous or detrimental. At the scale of fine particles, physiochemical interactions play a crucial role in the clogging process. To examine the influence of these interactions, we have coupled the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory into the Computational Fluid Dynamic-Discrete Element (CFD-DEM) approach. Aside from the physical properties of the fracture systems and the characteristics of fine particles, the injection rate also plays a pivotal role in clogging occurrence. Consequently, we investigated 10 different injection rates and modeled 20 simulation setups with identical particle insertion rates to concurrently analyze the effects of the DLVO theory and injection rate. Our study focused on examining the impact of these parameters on particle behavior in various regions of the domain, including particle-particle force, fluid-particle force, transitional velocity, rotational velocity, fluid velocity, and fluid-particle momentum exchange. Our findings reveal that the DLVO force significantly influences fluid and particle characteristics within the throat blockage. Our results indicated that DLVO consideration increased the particle concentrations by more than 40% before the throat. Moreover, our results demonstrate a transition between different injection rates, where a slight change in injection rate (i.e., 0.06μm/s) can change the system's behavior. We identified a critical fluid injection rate, whereby injecting fluid into the system at a rate surpassing the critical velocity can prevent clogging, while lower rates result in clogging occurrence.

Exploring student reasoning in statistical mechanics: Identifying challenges in problem-solving groups

Statistical mechanics has received limited attention in physics education research and remains a relatively underrepresented topic even in research on upper-division physics courses. The purpose of this study was to explore potential challenges that physics students encounter when they solve statistical mechanics problems in groups. Adopting a grounded approach, we video recorded and analyzed nine small student groups engaging in collaborative problem solving on the topic. The analysis involved iterative thematic coding, which gave rise to ten emergent categories of challenges. These were later divided into two broad groupings: and . In the first grouping, we list seven identified categories related to the concepts of macrostates and microstates, distinguishable and indistinguishable particles, temperature, entropy, energy, equilibrium, heat bath, the Boltzmann distribution, and the partition function. In the second grouping, we list three categories related to the inappropriate application of common relations, difficulty managing tensions between calculated results and qualitative reasoning, and coming up with definitions of new and inconsistent concepts. Some of our findings are supported by existing research on the topic, and others are previously unreported. Based on our findings, we propose that future research should investigate the relations between the identified challenges on one hand, and students’ epistemological framing, reasoning, and use of multiple representations on the other. Finally, we suggest that teachers should spend time engaging students in a conceptual discussion of the central ideas of statistical mechanics, motivating the choice and pointing out limitations of commonly used toy models, and linking course content to real-world phenomena. Published by the American Physical Society 2024

Neutrino amplitude decomposition, S matrix rephasing invariance, and reparametrization symmetry

The S matrix rephasing invariance is one of the fundamental principles of quantum mechanics that originates in its probabilistic interpretation. For a given S matrix which describes neutrino oscillation, one can define the two different rephased amplitudes SαβReph−1≡eiλ1/2ExSαβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {S}_{\\alpha \\beta}^{\ extrm{Reph}-1}\\equiv {e}^{i\\left({\\lambda}_1/2E\\right)x}{S}_{\\alpha \\beta} $$\\end{document} and SαβReph−2≡eiλ2/2ExSαβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {S}_{\\alpha \\beta}^{\ extrm{Reph}-2}\\equiv {e}^{i\\left({\\lambda}_2/2E\\right)x}{S}_{\\alpha \\beta} $$\\end{document}, which are physically equivalent to each other, where λk/2E denotes the energy eigenvalue of the k-th mass eigenstate. We point out that the transformation of the reparametrization (Rep) symmetry obtained with “Symmetry Finder” maps SαβReph−1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {S}_{\\alpha \\beta}^{\ extrm{Reph}-1} $$\\end{document} to SαβReph−2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {S}_{\\alpha \\beta}^{\ extrm{Reph}-2} $$\\end{document}, and vice versa, providing a local and manifest realization of the S matrix rephasing invariance by the Rep symmetry of the 1–2 state exchange type. It is strongly indicative of quantum mechanical nature of the Rep symmetry. The rephasing and Rep symmetry relation, though its all-order treatment remains incomplete, is shown to imply absence of the pure 1–3 exchange symmetry in Denton et al. perturbation theory. It then triggers a study of convergence of perturbation series.

Indistinguishability of Identical Bosons from a Quantum Information Theory Perspective.

Using tools from quantum information theory, we present a general theory of indistinguishability of identical bosons in experiments consisting of passive linear optics followed by particle number detection. Our results do neither rely on additional assumptions on the input state of the interferometer, such as, for instance, a fixed mode occupation, nor on any assumption on the degrees of freedom that potentially make the particles distinguishable. We identify the expectation value of the projector onto the N-particle symmetric subspace as an operationally meaningful measure of indistinguishability, and derive tight lower bounds on it that can be efficiently measured in experiments. Moreover, we present a consistent definition of perfect distinguishability and characterize the corresponding set of states. In particular, we show that these states are diagonal in the computational basis up to a permutationally invariant unitary. Moreover, we find that convex combinations of states that describe partially distinguishable and perfectly indistinguishable particles can lead to perfect distinguishability, which itself is not preserved under convex combinations.

Ab Initio Path Integral Monte Carlo Simulations of the Uniform Electron Gas on Large Length Scales.

The accurate description of non-ideal quantum many-body systems is of prime importance for a host of applications within physics, quantum chemistry, materials science, and related disciplines. At finite temperatures, the gold standard is given by ab initio path integral Monte Carlo (PIMC) simulations, which do not require any empirical input but exhibit an exponential increase in the required computation time for Fermionic systems with an increase in system size N. Very recently, computing Fermionic properties without this bottleneck based on PIMC simulations of fictitious identical particles has been suggested. In our work, we use this technique to perform very large (N ≤ 1000) PIMC simulations of the warm dense electron gas and demonstrate that it is capable of providing a highly accurate description of the investigated properties, i.e., the static structure factor, the static density response function, and the local field correction, over the entire range of length scales.

On a family of finitely many point interaction Hamiltonians free of ultraviolet pathologies

Abstract We re-investigate the entire family of many center point interaction Hamiltonians. Under the assumption of exchange symmetry with respect to the point positions, we show that a large sub-family of point interaction Hamiltonian operators does not become either singular or trivial when the positions of two or more scattering centers tend to coincide. In this sense, they appear to be renormalized by default as opposed to the point interaction Hamiltonians usually considered in the literature. Functions in their domains satisfy regularized boundary conditions which turn out to be very similar to the ones proposed recently in many-body quantum mechanics to define three-particle system Hamiltonians with contact interactions bounded from below. In the two-center case, we study the behavior of the negative eigenvalues as a function of the center distance. The result is used to analyze a formal Born–Oppenheimer approximation of a three-particle system with two heavy bosons and one light particle. We demonstrate that this simplified model describes a stable system (no ‘fall to the center’ problem is present). Furthermore, in the unitary limit, the energy spectrum is characterized by an infinite sequence of negative energy eigenvalues accumulating at zero according to the geometrical Efimov law.