Statistical Mechanics
New submissions
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New submissions for Mon, 18 Oct 21
 [1] arXiv:2110.07715 [pdf, ps, other]

Title: Lévy walk dynamics in nonstatic mediaComments: 13 pages, 10 figuresSubjects: Statistical Mechanics (condmat.statmech); Classical Physics (physics.classph); Data Analysis, Statistics and Probability (physics.dataan)
Almost all the media the particles move in are nonstatic. Depending on the expected resolution of the studied dynamics and the amplitude of the displacement of the media, sometimes the nonstatic behaviours of the media can not be ignored. In this paper, we build the model describing L\'evy walks in nonstatic media, where the physical and comoving coordinates are connected by scale factor. We derive the equation governing the probability density function of the position of the particles in comoving coordinate. Using the Hermite orthogonal polynomial expansions, some statistical properties are obtained, such as mean squared displacements (MSDs) in both coordinates and kurtosis. For some representative nonstatic media and L\'{e}vy walks, the asymptotic behaviors of MSDs in both coordinates are analyzed in detail. The stationary distributions and mean first passage time for some cases are also discussed through numerical simulations.
 [2] arXiv:2110.07958 [pdf, other]

Title: Frustrated magnetism of spin1/2 Heisenberg diamond and octahedral chains as a statisticalmechanical monomerdimer problemComments: 28 pages, 16 figuresSubjects: Statistical Mechanics (condmat.statmech); Quantum Physics (quantph)
Latticegas models of hardcore monomers and dimers afford a proper description of lowtemperature features of spin1/2 Heisenberg diamond and octahedral chains. Besides monomeric particles assigned within the localizedmagnon theory to bound one and twomagnon eigenstates the effective latticegas model additionally includes dimeric particles assigned to a singlettetramer (singlethexamer) state as a cornerstone of dimertetramer (tetramerhexamer) ground state of a diamond (octahedral) chain. A feasibility of the effective description is confirmed through the exact diagonalization and finitetemperature Lanczos methods. Both quantum spin chains display rich groundstate phase diagrams including discontinuous as well as continuous fielddriven phase transitions, whereby the specific heat shows in vicinity of the former phase transitions an extraordinary lowtemperature peak coming from a highlydegenerate manifold of lowlying excitations.
 [3] arXiv:2110.07969 [pdf, other]

Title: Kibble Zurek mechanism in rapidly quenched phase transition dynamicsComments: 5 pages, 4 figsSubjects: Statistical Mechanics (condmat.statmech); Superconductivity (condmat.suprcon); High Energy Physics  Theory (hepth)
We propose a theory to explain the experimental observed deviation from the KibbleZurek mechanism (KZM) scaling in rapidly quenched critical phase transition dynamics. There is a critical quench rate $\tau_{Q}^{c1}$ above it the KZM scaling begins to appear. Smaller than $\tau_Q^{c1}$, the defect density $n$ is a constant independent of the quench rate but depends on the final temperature $T_f$ as $n \propto L^d \epsilon_{T_f} ^{d \nu}$, the freeze out time $\hat{t}$ admits the scaling law $\hat{t} \propto \epsilon_{T_f}^{\nu z}$ where $d$ is the spatial dimension, $\epsilon_{T_f}= (1T_f/T_c)$ is the dimensionless reduced temperature, $L$ is the sample size, $\nu$ and $z$ are spatial and dynamical critical exponents. Quench from $T_c$, the critical rate is determined by the final temperature $T_f$ as $\tau_Q^{c1} \propto \epsilon_{T_f}^{(1+z \nu)} $. All the scaling laws are verified in a rapidly quenched superconducting ring via the AdS/CFT correspondence.
 [4] arXiv:2110.08194 [pdf, other]

Title: On the Dynamics of FreeFermionic TauFunctions at Finite TemperatureSubjects: Statistical Mechanics (condmat.statmech); Quantum Gases (condmat.quantgas); Strongly Correlated Electrons (condmat.strel); Mathematical Physics (mathph)
In this work we explore an instance of the $\tau$function of vertex type operators, specified in terms of a constant phase shift in a freefermionic basis. From the physical point of view this $\tau$function has multiple interpretations: as a correlator of JordanWigner strings, a Loschmidt Echo in the AharonovBohm effect, or the generating function of the local densities in the TonksGirardeau gas. We present the $\tau$function as a formfactors series and tackle it from four vantage points: (i) we perform an exact summation and express it in terms of a Fredholm determinant in the thermodynamic limit, (ii) we use bosonization techniques to perform partial summations of soft modes around the Fermi surface to acquire the scaling at zero temperature, (iii) we derive large space and time asymptotic behavior for the thermal Fredholm determinant by relating it to effective formfactors with an asymptotically similar kernel, and (iv) we identify and sum the important basis elements directly through a tailormade numerical algorithm for finiteentropy states in a freefermionic Hilbert space. All methods confirm each other. We find that, in addition to the exponential decay in the finitetemperature case the dynamic correlation functions exhibit an extra power law in time, universal over any distribution and time scale.
Crosslists for Mon, 18 Oct 21
 [5] arXiv:2110.07627 (crosslist from hepth) [pdf, other]

Title: Entanglement Entropy of Disjoint Spacetime Intervals in Causal Set TheoryComments: 21 pages, 9 figuresSubjects: High Energy Physics  Theory (hepth); Statistical Mechanics (condmat.statmech); General Relativity and Quantum Cosmology (grqc)
A more complete understanding of entanglement entropy in a covariant manner could inform the search for quantum gravity. We build on work in this direction by extending previous results to disjoint regions in $1+1$D. We investigate the entanglement entropy of a scalar field in disjoint intervals within the causal set framework, using the spacetime commutator and correlator, $i\mathbf{\Delta}$ and $\mathbf{W}$ (or the PauliJordan and Wightman functions), respectively. A new truncation scheme for disjoint causal diamonds is presented, which follows from the single diamond truncation scheme. We investigate setups including two and three disjoint causal diamonds, as well as a single causal diamond that shares a boundary with a larger global causal diamond. In all the cases that we study, our results agree with the expected area laws. In addition, we study the mutual information in the two disjoint diamonds setup. The ease of our calculations indicate our methods to be a useful tool for numerically studying such systems. We end with a discussion of some of the strengths and future applications of the spacetime formulation we use in our entanglement entropy computations, both in causal set theory and in the continuum.
 [6] arXiv:2110.07632 (crosslist from quantph) [pdf, other]

Title: Effective theory for matter in nonperturbative cavity QEDSubjects: Quantum Physics (quantph); Statistical Mechanics (condmat.statmech)
Starting from a general material system of N particles coupled to a cavity, we use a coherentstate path integral formulation to produce a nonperturbative effective theory for the material degrees of freedom. We tackle the effects of image charges, the A2 term and a multimode arbitrarygeometry cavity. The resulting (nonlocal) action has the photonic degrees of freedom replaced by an effective positiondependent interaction between the particles. In the largeN limit, we show that the theory can be cast into an effective Hamiltonian where the cavity induced interactions are made explicit. The theory is applicable, beyond cavity QED, to any system where bulk material is linearly coupled to a diagonalizable bosonic bath. We showcase the descriptive power of the formalism with three examples: photon condensation, the 2D free electron gas in a cavity and the modification of magnetic interactions between molecular spins; recovering, condensing and extending some recent results in the literature.
 [7] arXiv:2110.07698 (crosslist from physics.socph) [pdf, other]

Title: Directed Percolation in Random Temporal Network Models with HeterogeneitiesComments: Implementation available at this https URLSubjects: Physics and Society (physics.socph); Disordered Systems and Neural Networks (condmat.disnn); Statistical Mechanics (condmat.statmech); Social and Information Networks (cs.SI)
The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similar to percolation theory on static networks, this mapping is valid under the approximation that the structure and interaction dynamics of the temporal network are determined by its local properties, and otherwise, it is maximally random. We challenge these conditions and demonstrate the robustness of this mapping in case of more complicated systems. We systematically analyze random and regular network topologies and heterogeneous linkactivation processes driven by bursty renewal or selfexciting processes using numerical simulation and finitesize scaling methods. We find that the critical percolation exponents characterizing the temporal network are not sensitive to many structural and dynamical network heterogeneities, while they recover known scaling exponents characterizing directed percolation on low dimensional lattices. While it is not possible to demonstrate the validity of this mapping for all temporal network models, our results establish the first batch of evidence supporting the robustness of the scaling relationships in the limitedtime reachability of temporal networks.
 [8] arXiv:2110.07838 (crosslist from condmat.soft) [pdf]

Title: A revisit of the density gradient theory and the mean field theory for the vaporliquid interface systemAuthors: Hongqin LiuComments: 23 pages; 19 figuresSubjects: Soft Condensed Matter (condmat.soft); Statistical Mechanics (condmat.statmech); Chemical Physics (physics.chemph)
In this work we define a meanfield crossover generated by the Maxwell construction as the dividing interface for the vaporliquid interface area. A highly accurate densityprofile equation is thus derived, which is physically favorable and leads to reliable predictions of interfacial properties. By using the density gradient theory and a meanfield equation of sate for the LennardJones fluid, we are able to extensively explore the interface system in terms of the Gibbs free energy, the Helmholtz free energy and heat capacity. The results show that the meanfield dividing interface is the natural extension of the Widom line into the coexistence region. Hence the entire phase space is coherently divided into liquidlike and gaslike regions in all three (temperaturepressurevolume) planes. Some unconventional behaviors are observed for the intrinsic heat capacity, being positive in low temperature region while negative in high temperature region. Finally, a complete picture of the meanfield equation of state is unfolded: all three solutions to a vaporliquid equilibrium problem have their respective significances.
 [9] arXiv:2110.07931 (crosslist from condmat.soft) [pdf, other]

Title: Collective drifts in vibrated granular packings: the interplay of friction and structureComments: 10 pages and 7 figures (main text and supplemental material)Subjects: Soft Condensed Matter (condmat.soft); Statistical Mechanics (condmat.statmech)
We simulate vertically shaken dense granular packings with horizontal periodic boundary conditions. A coordinated translating motion of the whole medium emerges when the horizontal symmetry is broken by disorder or defects in the packing and the shaking is weak enough to conserve the structure. We argue that such a drift originates in the interplay between structural symmetry breaking and frictional forces transmitted by the vibrating plate. A nonlinear ratchet model with stickslips reproduces many faces of the phenomenon. The collective motion discussed here underlies phenomena observed recently with vibrofluidized granular materials, such as persistent rotations and anomalous diffusion.
 [10] arXiv:2110.07941 (crosslist from heplat) [pdf, other]

Title: Breaking the gauge symmetry in lattice gaugeinvariant modelsComments: 8 pages, 1 pdf figure, proceeding for The 38th International Symposium on Lattice Field Theory, LATTICE2021, 26th30th July, 2021, Zoom/Gather@Massachusetts Institute of TechnologySubjects: High Energy Physics  Lattice (heplat); Statistical Mechanics (condmat.statmech)
We consider the role that gauge symmetry breaking terms play on the continuum limit of gauge theories in three dimensions. As a paradigmatic example we consider scalar electrodynamics in which $N_f$ complex scalar fields interact with a U(1) gauge field. We discuss under which conditions a gaugesymmetry breaking term destabilizes the critical behavior (continuum limit) of the gaugeinvariant theory. We find that the gauge symmetry is robust at transitions at which gauge fields are not critical. At charged transitions, where gauge fields are critical, gauge symmetry is lost as soon as the perturbation is added.
 [11] arXiv:2110.08082 (crosslist from condmat.strel) [pdf, ps, other]

Title: Learning Disentangled Representation for Ising ModelComments: 8 pages, 5 figuresSubjects: Strongly Correlated Electrons (condmat.strel); Statistical Mechanics (condmat.statmech)
Finding disentangled representation plays a predominant role in the success of modern deep learning applications, but the results lack a straightforward explanation. Here we apply the information bottleneck method to find as an example the disentangled lowdimensional representation of the Ising model. Our results reveal a deep connection between the disentangled features and the physical order parameters of the model. The widelyused Bernoulli decoder is found to be learning a meanfield Hamiltonian at fixed temperature, which motivates us to propose a modified architecture $\beta^2$VAE to enforce thermal fluctuations in the learned samples under generation. Our framework may be extended to other more complex models to reveal potential connection between their order parameters and disentangled lowdimensional representations.
 [12] arXiv:2110.08135 (crosslist from physics.fludyn) [pdf, ps, other]

Title: Reply to "Comment on `Directed motion of spheres by unbiased driving forces in viscous fluids beyond the Stokes' law regime' "Authors: Jesús CasadoPascualComments: 3 pages, 0 figuresSubjects: Fluid Dynamics (physics.fludyn); Statistical Mechanics (condmat.statmech)
We refute the criticism expressed in a Comment by P. J. Mart\'{\i}nez and R. Chac\'on [arXiv:2105.09308] on our paper Phys. Rev. E \textbf{97}, 032219 (2018). We first show that our paper is free of any mistakes and that the criticism expressed in the Comment is based on a misunderstanding or misrepresentation of what is actually claimed in our paper. We also show that the argument presented against the general formalism mentioned in the Comment is invalid because it is based on a confusion by the authors of the Comment between the general formalism per se and its lowest order approximation. In fact, the arguments contained in the Comment do not show that such a formalism is in general incorrect, as the authors of the Comment suggest, but rather that the supposedly universal predictions of the theory of ratchet universality are in general incorrect. In addition, we show that other arguments presented in Comment are invalid because they are based on incorrect equations.
Replacements for Mon, 18 Oct 21
 [13] arXiv:1805.01499 (replaced) [pdf, ps, other]

Title: Analytical results of the extensible freely jointed chain modelJournalref: Physica A: Statistical Mechanics and its Applications, Volume 532, Physica A 532 (2019) 121929Subjects: Statistical Mechanics (condmat.statmech); Soft Condensed Matter (condmat.soft); Biological Physics (physics.bioph)
 [14] arXiv:2001.01378 (replaced) [pdf, other]

Title: Periodic and aperiodic dynamics of flat bands in diamondoctagon latticeComments: 14 pages and 14 figuresJournalref: Phys. Rev. B 104, 134307 (2021)Subjects: Statistical Mechanics (condmat.statmech); Strongly Correlated Electrons (condmat.strel)
 [15] arXiv:2103.15007 (replaced) [pdf, other]

Title: Universal tradeoff relation between speed, uncertainty, and dissipation in nonequilibrium stationary statesAuthors: Izaak NeriComments: 50 pages, 5 figuresSubjects: Statistical Mechanics (condmat.statmech)
 [16] arXiv:2109.14374 (replaced) [pdf, ps, other]

Title: Stiffness of random walks with reflecting boundary conditionsComments: 6 pages, 9 figures, references added, small adjustments in the textSubjects: Statistical Mechanics (condmat.statmech)
 [17] arXiv:2106.15946 (replaced) [pdf, other]

Title: Symmetryresolved entanglement entropy in WessZuminoWitten modelsComments: 31 pages, v2: minor changesJournalref: JHEP 2021, 67 (2021)Subjects: High Energy Physics  Theory (hepth); Statistical Mechanics (condmat.statmech); Quantum Physics (quantph)
 [18] arXiv:2107.01510 (replaced) [pdf, other]

Title: Directed Percolation in Temporal NetworksComments: Implementation available at this https URLSubjects: Physics and Society (physics.socph); Disordered Systems and Neural Networks (condmat.disnn); Statistical Mechanics (condmat.statmech); Social and Information Networks (cs.SI)
 [19] arXiv:2110.06769 (replaced) [pdf, ps, other]

Title: Dynamical effects of inflation in ensemblebased data assimilation under the presence of model errorSubjects: Data Analysis, Statistics and Probability (physics.dataan); Statistical Mechanics (condmat.statmech); Chaotic Dynamics (nlin.CD)
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