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cond-mat.stat-mech

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preprint2016arXiv

Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach

We consider eigenvectors of the Hamiltonian $H_0$ perturbed by a generic perturbation $V$ modelled by a random matrix from the Gaussian Unitary Ensemble (GUE). Using the supersymmetry approach we derive analytical results for the statistics of the eigenvectors, which are non-perturbative in $V$ and valid for an arbitrary deterministic $H_0$. Further we generalise them to the case of a random $H_0$, focusing, in particular, on the Rosenzweig-Porter model. Our analytical predictions are confirmed by numerical simulations.

preprint2016arXiv

Tracer Particles in Two-Dimensional Elastic Networks Diffuse Logarithmically Slow

Several experiments on tagged molecules or particles in living systems suggest that they move anomalously slow - their mean squared displacement (MSD) increase slower than linearly with time. Leading models aimed at understanding these experiments predict that the MSD grows as a power law with a growth exponent that is smaller than unity. However, in some experiments the exponent is so small $(\sim 0.1-0.2)$ that they hint towards other mechanisms at play. In this paper, we theoretically demonstrate how in-plane collective modes excited by thermal fluctuations in a two dimensional membrane lead to logarithmic time dependence for the mean square displacement of a tracer particle.

preprint2017arXiv

Casimir entropy and internal energy of the objects in fluctuating scalar and electromagnetic fields

Casimir entropy is an important aspect of casimir effect.In this paper,we employ the path integral method to derive the total relation for casimir entropy and internal energy of arbitrary shaped objects in the presence of two,three and four dimensions scalar fields and electromagnetic field.We obtain the casimir entropy and internal energy of two nanoribbon immersed in scalar field and two nanospheres immersed in scalar field and electromagnetic field.The casmir entropy of two nanospheres immersed in the electromagnetic field in small interval of temperature variations,shown a different behavior.

preprint2017arXiv

Quantum quenches in two spatial dimensions using chain array matrix product states

We describe a method for simulating the real time evolution of extended quantum systems in two dimensions. The method combines the benefits of integrability and matrix product states in one dimension to avoid several issues that hinder other applications of tensor based methods in 2D. In particular it can be extended to infinitely long cylinders. As an example application we present results for quantum quenches in the 2D quantum (2+1 dimensional) Ising model. In quenches that cross a phase boundary we find that the return probability shows non-analyticities in time.

preprint2016arXiv

Statistical Entropy of Open Quantum Systems

Dissipative quantum systems are frequently described within the framework of the so-called "system-plus-reservoir" approach. In this work we assign their description to the Maximum Entropy Formalism and compare the resulting thermodynamic properties with those of the well - established approaches. Due to the non-negligible coupling to the heat reservoir, these systems are non-extensive by nature, and the former task may require the use of non-extensive parameter dependent informational entropies. In doing so, we address the problem of choosing appropriate forms of those entropies in order to describe a consistent thermodynamics for dissipative quantum systems. Nevertheless, even having chosen the most successful and popular forms of those entropies, we have proven our model to be a counterexample where this sort of approach leads us to wrong results.

preprint2016arXiv

V-T theory for the Self-Intermediate Scattering Function in a Monatomic Liquid

In V-T theory the atomic motion is harmonic vibrations in a liquid-specific potential energy valley, plus transits, which move the system rapidly among the multitude of such valleys. In its first application to the self intermediate scattering function (SISF), V-T theory produced an accurate account of molecular dynamics (MD) data at all wave numbers q and time t. Recently, analysis of the mean square displacement (MSD) resolved a crossover behavior that was not observed in the SISF study. Our purpose here is to apply the more accurate MSD calibration to the SISF, and assess the results. We derive and discuss the theoretical equations for vibrational and transit contributions to the SISF. The time evolution is divided into three successive intervals: the vibrational interval when the vibrational contribution alone accurately accounts for the MD data; the crossover when the vibrational contribution saturates and the transit contribution becomes resolved; and the diffusive interval when the transit contribution alone accurately accounts for the MD data. The resulting theoretical error is extremely small at all q and t. Comparison of V-T and mode-coupling theories for the MSD and SISF

preprint2016arXiv

Interacting Brownian dynamics in a nonequilibrium particle bath

We set up a mesoscopic theory for interacting Brownian particles embedded in a nonequilibrium environment, starting from the microscopic interacting many-body theory. Using nonequilibrium linear response theory, we characterize the effective dynamical interactions on the mesoscopic scale and the statistics of the nonequilibrium environmental noise, arising upon integrating out the fast degrees of freedom. As hallmarks of nonequilibrium, the breakdown of the fluctuation-dissipation and action-reaction relations for Brownian degrees of freedom are exemplified with two prototypical models for the environment, namely, active Brownian particles and stirred colloids.

preprint2016arXiv

Relaxational processes in the one-dimensional Ising model with long-range interactions

Relaxational processes in ordered phases of one-dimensional Ising models with long-range interactions are investigated by Monte Carlo simulations. Three types of spin model, the pure ferromagnetic, the diluted ferromagnetic, and the spin glass models, are examined. The effective dimension of the one-dimensional systems are controlled by a parameter $σ$, which tunes the rate of interaction decay. Systematical investigations of droplet dynamics, from the lower to the upper critical dimension, are conducted by changing the value of $σ$. Comparing numerical data with the droplet theory, it is found that the surface dimension of droplets is distributed around the effective dimension. The distribution in the surface dimension makes the droplet dynamics complex and extremely enhances dynamical crossover.

preprint2016arXiv

Disorder induced phase transition in an opinion dynamics model: results in 2 and 3 dimensions

We study a model of continuous opinion dynamics with both positive and negative mutual interaction. The model shows a continuous phase transition between a phase with consensus (order) and a phase having no consensus (disorder). The mean field version of the model was already studied. Using extensive numerical simulations, we study the same model in $2$ and $3$ dimensions. The critical points of the phase transitions for various cases and the associated critical exponents have been estimated. The universality class of the phase transitions in the model is found to be same as Ising model in the respective dimensions.

preprint2016arXiv

Percolation in Finite Matching Lattices

We derive an exact, simple relation between the average number of clusters and the wrapping probabilities for two-dimensional percolation. The relation holds for periodic lattices of any size. It generalizes a classical result of Sykes and Essam and it can be used to find exact or very accurate approximations of the critical density. The criterion that follows is related to the criterion Scullard and Jacobsen use to find precise approximate thresholds, and our work provides a new perspective on their approach.

preprint2016arXiv

Nonlinear inhomogeneous Fokker-Planck equations: entropy and free-energy time evolution

We extend a recently introduced free-energy formalism for homogeneous Fokker-Planck equations to a wide, and physically appealing, class of inhomogeneous nonlinear Fokker-Planck equations. In our approach, the free-energy functional is expressed in terms of an entropic functional and an auxiliary potential, both derived from the coefficients of the equation. With reference to the introduced entropic functional, we discuss the entropy production in a relaxation process towards equilibrium. The properties of the stationary solutions of the considered Fokker-Planck equations are also discussed.

preprint2016arXiv

Fracton Topological Order, Generalized Lattice Gauge Theory and Duality

We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, point-like topological excitations, and sub-extensive topological degeneracy. We demonstrate a duality between fracton topological order and interacting spin systems with symmetries along extensive, lower-dimensional subsystems, which may be used to systematically search for and characterize fracton topological phases. Commutative algebra and elementary algebraic geometry provide an effective mathematical toolset for our results. Our work paves the way for identifying possible material realizations of fracton topological phases.

preprint2016arXiv

Simulated Quantum Annealing Can Be Exponentially Faster than Classical Simulated Annealing

Simulated Quantum Annealing (SQA) is a Markov Chain Monte-Carlo algorithm that samples the equilibrium thermal state of a Quantum Annealing (QA) Hamiltonian. In addition to simulating quantum systems, SQA has also been proposed as another physics-inspired classical algorithm for combinatorial optimization, alongside classical simulated annealing. However, in many cases it remains an open challenge to determine the performance of both QA and SQA. One piece of evidence for the strength of QA over classical simulated annealing comes from an example by Farhi, Goldstone and Gutmann . There a bit-symmetric cost function with a thin, high energy barrier was designed to show an exponential seperation between classical simulated annealing, for which thermal fluctuations take exponential time to climb the barrier, and quantum annealing which passes through the barrier and reaches the global minimum in poly time, arguably by taking advantage of quantum tunneling. In this work we apply a comparison method to rigorously show that the Markov chain underlying SQA efficiently samples the target distribution and finds the global minimum of this spike cost function in polynomial time. Our work provi

preprint2016arXiv

Stochastic thermodynamics for active matter

The theoretical understanding of active matter, which is driven out of equilibrium by directed motion, is still fragmental and model oriented. Stochastic thermodynamics, on the other hand, is a comprehensive theoretical framework for driven systems that allows to define fluctuating work and heat. We apply these definitions to active matter, assuming that dissipation can be modelled by effective non-conservative forces. We show that, through the work, conjugate extensive and intensive observables can be defined even in non-equilibrium steady states lacking a free energy. As an illustration, we derive the expressions for the pressure and interfacial tension of active Brownian particles. The latter becomes negative despite the observed stable phase separation. We discuss this apparent contradiction, highlighting the role of fluctuations, and we offer a tentative explanation.

preprint2017arXiv

Transport properties for driven granular fluids in situations close to homogeneous steady states

The transport coefficients of a granular fluid driven by a stochastic bath with friction are obtained by solving the inelastic Enskog kinetic equation from the Chapman-Enskog method. The heat and momentum fluxes as well as the cooling rate are determined to first order in the deviations of the hydrodynamic field gradients from their values in the homogeneous steady state. Since the collisional cooling cannot be compensated locally for the heat produced by the external driving force, the reference distribution $f^{(0)}$ (zeroth-order approximation) depends on time through its dependence on temperature. This fact gives rise to conceptual and practical difficulties not present in the undriven case. On the other hand, to simplify the analysis and given that we are interested in computing transport in the first order of deviations from the reference state, the steady-state conditions are considered to get explicit forms for the transport coefficients and the cooling rate. A comparison with recent molecular dynamics simulations for driven granular fluids shows an excellent agreement for the kinematic viscosity although some discrepancies are observed for the longitudinal viscosity and th

preprint2016arXiv

Master Equation approach to Reversible and Conservative Discrete Systems

A master equation approach is applied to a reversible and conservative cellular automata model (Q2R). The Q2R model is a dynamical variation of the Ising model for ferromagnetism that possesses quite a rich and complex dynamics. The configurational space is composed by a huge number of cycles with exponentially long periods. Following Nicolis and Nicolis [Phys. Rev. A 38, 427-433 (1988)], a coarse-graining approach is applied to the time series of the total magnetization leading to a master equation that governs the macroscopic irreversible dynamics of the Q2R automata. The methodology is replicated for various lattice sizes. In the case of small systems, it is shown that the master equation leads to a tractable probability transfer matrix of moderate size which provides a master equation for a coarse-grained probability distribution. The method is validated and some explicit examples are discussed.

preprint2016arXiv

Order-disorder transition in repulsive self-propelled particle systems

We study the collective dynamics of repulsive self-propelled particles. The particles are governed by coupled equations of motion that include polar self-propulsion, damping of velocity and of polarity, repulsive particle-particle interaction, and deterministic dynamics. Particle dynamics simulations show that the collective coherent motion with large density fluctuations spontaneously emerges from a disordered, isotropic state. In the parameter region where the rotational damping of polarity is strong, the systems undergoes an abrupt shift to the absorbing ordered state after a waiting period in the metastable disordered state. In order to obtain a simple understanding of the mechanism underlying the collective behavior, we analyze binary particle scattering process. We show that this approach correctly predicts the order-disorder transition at dilute limit. The same approach is expanded for finite densities, although it disagrees with the result from many-particle simulations due to many-body correlations and density fluctuations.

preprint2016arXiv

Gaussian theory for spatially distributed self-propelled particles

Obtaining a reduced description with particle and momentum flux densities outgoing from the microscopic equations of motion of the particles requires approximations. The usual method, we refer to as truncation method, is to zero Fourier modes of the orientation distribution starting from a given number. Here we propose another method to derive continuum equations for interacting self-propelled particles. The derivation is based on a Gaussian approximation (GA) of the distribution of the direction of particles. First, by means of simulation of the microscopic model we justify that the distribution of individual directions fits well to a wrapped Gaussian distribution. Second, we numerically integrate the continuum equations derived in the GA in order to compare with results of simulations. We obtain that the global polarization in the GA exhibits a hysteresis in dependence on the noise intensity. It shows qualitatively the same behavior as we find in particles simulations. Moreover, both global polarizations agree perfectly for low noise intensities. The spatio-temporal structures of the GA are also in agreement with simulations. We conclude that the GA shows qualitative agreement fo

preprint2016arXiv

Random Fractal Ansatz for the configurations of Two-Dimensional Critical Systems

Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in their classical configurations, whose computation do not require full knowledge of the wavefunction. Inspired by holographic duality, we investigated the entanglement properties of the classical configurations (snapshots) of the Potts model by introducing an ansatz ensemble of random fractal images. By virtue of the central limit theorem, our ansatz accurately reproduces the entanglement spectra of actual Potts snapshots without any fine-tuning of parameters or artificial restrictions on ensemble choice. It provides a microscopic interpretation of the results of previous studies, which established a relation between the scaling behavior of snapshot entropy and the critical exponent. More importantly, it elucidates the role of ensemble disorder in restoring conformal invariance, an aspect previously ignored. Away from criticality, the breakdown of scale invariance leads to a renormalization of the parameter $Σ$ in the random fractal ansatz, whose variation can be used as an alternative determination of the cri

preprint2016arXiv

Emergent hydrodynamics in integrable quantum systems out of equilibrium

Understanding the general principles underlying strongly interacting quantum states out of equilibrium is one of the most important tasks of current theoretical physics. With experiments accessing the intricate dynamics of many-body quantum systems, it is paramount to develop powerful methods that encode the emergent physics. Up to now, the strong dichotomy observed between integrable and non-integrable evolutions made an overarching theory difficult to build, especially for transport phenomena where space-time profiles are drastically different. We present a novel framework for studying transport in integrable systems: hydrodynamics with infinitely-many conservation laws. This bridges the conceptual gap between integrable and non-integrable quantum dynamics, and gives powerful tools for accurate studies of space-time profiles. We apply it to the description of energy transport between heat baths, and provide a full description of the current-carrying non-equilibrium steady state and the transition regions in a family of models including the Lieb-Liniger model of interacting Bose gases, realized in experiments.

preprint2017arXiv

Critical assessment of the equilibrium melting-based, energy distribution theory of supercooled liquids and application to jammed systems

Despite decades of intense study, the mechanisms underlying the extraordinary dynamics of supercooled liquids as they approach the glass transition remain, at best, mis-characterized, and at worst, misunderstood. A long standing endeavor is to understand the remarkable increase of the viscosity with supercooling. Recently, a new theory of supercooled liquids has been proposed that starts from first principles, using elementary statistical mechanics arguments, to derive a form for the viscosity that contains only a single fitting parameter in its simplest form. In this we demonstrate that this exact same form may be derived from a different starting point, and then critically examine its performance. In the process we find that functional form proposed fits the viscosity data of a diverse group of 45 liquids exceptionally well over a wide temperature range, and uncover a number of interesting correlations of the single parameter with various thermodynamic quantities, ultimately allowing for the prediction of low temperature viscosity from high temperature data. Additionally, we find that similar physical reasoning can be used to derive a similar, single parameter form for the viscos

preprint2016arXiv

High-Temperature Series Expansion for Spin-1/2 Heisenberg Models

We present a high-temperature series expansion code for spin-1/2 Heisenberg models on arbitrary lattices. As an example we demonstrate how to use the application for an anisotropic triangular lattice with two independent couplings J1 and J2 and calculate the high-temperature series of the magnetic susceptibility and the static structure factor up to 12th and 10th order, respectively. We show how to extract effective coupling constants for the triangular Heisenberg model from experimental data on Cs2CuBr4.

preprint2017arXiv

Is microcanonical ensemble stable?

No, in a rigorous sense specified below.

preprint2016arXiv

Kinetics Modeling of Nanoparticle Growth on and Evaporation off Nanotubes

A kinetic Monte Carlo approach is developed for studying growth and evaporation of nanoparticles on/off nanotubes. This study has been motivated by recent experimental advances in using nanoparticle evaporation (sublimation) off nanoparticle-decorated nanotubes for nanoscale "thermometry." We demonstrate that the considered kinetic Monte Carlo approach can reproduce features of the process that are not included in phenomenological thermodynamic modeling, as well as provide snapshots of the growth and evaporation process morphology.

575 works