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arXiv2009

Non-equilibrium statistical mechanics of non-equilibrium damage phenomena

In this paper we investigate the applicability of non-equilibrium statistical mechanics to non-equilibrium damage phenomena. As an example, a fiber-bundle model with thermal noise and a fiber-bundle model with decay of fibers are considered. Initially we develop an analogy of the Gibbs formalism for nonequilibrium states. Later we switch from the approach of non-equilibrium states to the approach of non-equilibrium paths. Fluctuating behavior in the system is described in terms of effective temperature parameters. An equation of state and an analog of an energy-balance equation are obtained. Also the formalism of the free energy potential is developed. For fluctuations of paths in the system the statistical distribution is found to be Gaussian.

cond-mat.stat-mech↗

arXiv2009

Representation of intermediate time-scale motions in stochastic modeling: Analysis on stochastic description of classical Hamiltonian dynamics in relation with measurement imperfection

It is a well established result that, in classical dynamical systems with sufficient time-scale separation, the fast chaotic degrees of freedom are well modeled by (Gaussian) white noise. In this paper, we present the stochastic dynamical description for intermediate time-scale motions with insufficient time-scale separation from the slow dynamical system. First, we analyze how the fast deterministic dynamics can be viewed as stochastic dynamics under experimental observation by intrinsic errors of measurement. Then, we present how the stochastic dynamical description should be modified if intermediate time-scale motions exist: the time correlation of the noise ξis modified to <ξ(t)ξ(t')> = C(x,p)δ(t-t'), where C(x,p) is a smooth function of the slow coordinate (x,p), and generally the cumulants of ξexcept its average vary as a smooth function of the slow coordinates (x,p). The analysis given in this work actually shows that, regardless of the sufficiency of time-scale separation, any complex (chaotic and ergodic) dynamical system can be well described using Markov process, if we perfectly construct the deterministic part of (extended) stochastic dynamics.

cond-mat.stat-mech↗

arXiv2010

Citation entropy and research impact estimation

A new indicator, a real valued $s$-index, is suggested to characterize a quality and impact of the scientific research output. It is expected to be at least as useful as the notorious $h$-index, at the same time avoiding some its obvious drawbacks. However, surprisingly, the $h$-index is found to be quite a good indicator for majority of real-life citation data with their alleged Zipfian behaviour for which these drawbacks do not show up. The style of the paper was chosen deliberately somewhat frivolous to indicate that any attempt to characterize the scientific output of a researcher by just one number always has an element of a grotesque game in it and should not be taken too seriously. I hope this frivolous style will be perceived as a funny decoration only.

physics.soc-ph↗

arXiv2009

Grassmann techniques applied to classical spin systems

We review problems involving the use of Grassmann techniques in the field of classical spin systems in two dimensions. These techniques are useful to perform exact correspondences between classical spin Hamiltonians and field-theory fermionic actions. This contributes to a better understanding of critical behavior of these models in term of non-quadratic effective actions which can been seen as an extension of the free fermion Ising model. Within this method, identification of bare masses allows for an accurate estimation of critical points or lines and which is supported by Monte-Carlo results and diagrammatic techniques.

cond-mat.stat-mech↗

arXiv2009

Calculation of Drag and Superfluid Velocity from the Microscopic Parameters and Excitation Energies of a Two-Component Bose-Einstein Condensate on an Optical Lattice

We investigate a model of a two-component Bose-Einstein condensate residing on an optical lattice. Within a Bogolioubov-approach at the mean-field level, we derive exact analytical expressions for the excitation spectrum of the two-component condensate when taking into account hopping and interactions between arbitrary sites. Our results thus constitute a basis for works that seek to clarify the effects of higher-order interactions in the system. We investigate the excitation spectrum and the two branches of superfluid velocity in more detail for two limiting cases of particular relevance. Moreover, we relate the hopping and interaction parameters in the effective Bose-Hubbard model to microscopic parameters in the system, such as the laserlight wavelength and atomic masses of the components in the condensate. These results are then used to calculate analytically and numerically the drag coefficient between the components of the condensate. We find that the drag is most effective close to the symmetric case of equal masses between the components, regardless of the strength of the intercomponent interaction and the lattice well depth.

cond-mat.quant-gas↗

arXiv2012

Experimental demonstration of topological error correction

Topological error correction--a novel method to actively correct errors based on cluster states with topological properties--has the highest order of tolerable error rates known to date (10^{-2}). Moreover, the scheme requires only nearest-neighbour interaction, particularly suitable for most physical systems. Here we report the first experimental demonstration of topological error correction with an 8-qubit optical cluster state. In the experiment, it is shown that a correlation can be protected against a single error on any single qubit. In addition, when all qubits are simultaneously subjected to errors with equal probability, the effective error rate is significantly reduced, clearly verifying the advantage of topological error correction. The quantum gate with the error rate below the threshold is within the current experimental technology. We believe topological error correction should be a critical ingredient for the future large-scale quantum computation.

quant-ph↗

arXiv2011

Introduction to Monte Carlo Methods

Monte Carlo methods play an important role in scientific computation, especially when problems have a vast phase space. In this lecture an introduction to the Monte Carlo method is given. Concepts such as Markov chains, detailed balance, critical slowing down, and ergodicity, as well as the Metropolis algorithm are explained. The Monte Carlo method is illustrated by numerically studying the critical behavior of the two-dimensional Ising ferromagnet using finite-size scaling methods. In addition, advanced Monte Carlo methods are described (e.g., the Wolff cluster algorithm and parallel tempering Monte Carlo) and illustrated with nontrivial models from the physics of glassy systems. Finally, we outline an approach to study rare events using a Monte Carlo sampling with a guiding function.

cond-mat.stat-mech↗

arXiv2009

Tensor Temperature and Shockwave Stability in a Strong Two-Dimensional Shockwave

The anisotropy of temperature is studied here in a strong two-dimensional shockwave, simulated with conventional molecular dynamics. Several forms of the kinetic temperature are considered, corresponding to different choices for the local instantaneous stream velocity. A local particle-based definition omitting any "self" contribution to the stream velocity gives the best results. The configurational temperature is not useful for this shockwave problem. Configurational temperature is subject to a shear instability and can give local negative temperatures in the vicinity of the shock front. The decay of sinusoidal shockfront perturbations shows that strong two-dimensional planar shockwaves are stable to such perturbations.

cond-mat.stat-mech↗

arXiv2009

Amortissement Landau

Dans cette note nous présentons les principaux résultats du récent travail hal-00376547/arXiv:0904.2760, où le phénomène d'amortissement Landau est pour la première fois établi dans un contexte non linéaire. ----- In this note we present the main results from the recent work hal-00376547 / arXiv:0904.2760, which for the first time establish Landau damping in a nonlinear context.

math.AP↗

arXiv2011

Information erasure lurking behind measures of complexity

Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the amount of resources needed to forecasting a system's behaviour. Another one (the effective measure complexity, aka excess entropy) is a measure of mutual information stored in the system proper. We show that for any given system the two measures differ by the amount of information erased during forecasting. We interpret the difference as inefficiency of a given model. We find a bound to the ratio of the two measures defined as information-processing efficiency, in analogy to the second law of thermodynamics. This new link between two prominent measures of complexity provides a quantitative criterion for good models of complex systems, namely those with little information erasure.

physics.data-an↗

arXiv2009

Continuum and lattice heat currents for oscillator chains

We show that two commonly used definitions for the heat current give different results--through the Kubo formula--for the heat conductivity of oscillator chains. The difference exists for finite chains, and is expected to be important more generally for small structures. For a chain of N particles that are tethered at the ends, the ratio of the heat conductivities calculated with the two currents differs from unity by O(1/N). For a chain held at constant pressure, the difference from unity decays more slowly, and is consistent with O(1/N^eta) with 1 > eta > 0.5.

cond-mat.stat-mech↗

arXiv2010

Multipolar interactions and complex phases in ferromagnetic ultrathin films

We present a model to describe complex phases observed at mesoscopic scales in ultrathin magnetic films. The model is based on the interaction between dipolar as well as quadrupolar magnetic moments. In the special case of strong perpendicular crystal anisotropy, we show that quadrupolar degrees of freedom associated with orientation of domain walls are essential in order to correctly describe the observed phenomenology of domain formation. A nematic phase characterized by orientational order of domain walls (stripe-like) but without translational order is predicted. This isotropic-nematic transition belongs to the Kosterlitz-Thouless type in the thermodynamic limit. However, we found that in actual experimental scales, the fluctuations of the nematic order parameter are regularized by the sample size, and orientational long range order, as predicted by mean field, should be observable. The transition may be completely characterized experimentally from measurements of the magnetic structure factor as well as from the non-linear in-plane magnetic susceptibility.

cond-mat.stat-mech↗

arXiv2009

Time to fixation in the presence of recombination

We study the evolutionary dynamics of a haploid population of infinite size recombining with a probability $r$ in a two locus model. Starting from a low fitness locus, the population is evolved under mutation, selection and recombination until a finite fraction of the population reaches the fittest locus. An analytical method is developed to calculate the fixation time $T$ to the fittest locus for various choices of epistasis. We find that (1) for negative epistasis, $T$ decreases slowly for small $r$ but decays fast at larger $r$ (2) for positive epistasis, $T$ increases linearly for small $r$ and mildly for large $r$ (3) for compensatory mutation, $T$ diverges as a power law with logarithmic corrections as the recombination fraction approaches a critical value. Our calculations are seen to be in good agreement with the exact numerical results.

q-bio.PE↗

arXiv2009

Thermodynamics of non-equilibrium steady states

We consider the problem of constructing a thermodynamic theory of non-equilibrium steady states as a formal extension of the equilibrium theory. Specifically, studying a particular system, we attempt to construct a phenomenological theory describing the interplay between heat and mechanical work that takes place during operations through which the system undergoes transitions between non-equilibrium steady states. We find that, in contrast to the case of the equilibrium theory, apparently, there exists no systematic way within a phenomenological formulation to describe the work done by the system during such operations. With this observation, we conclude that the attempt to construct a thermodynamic theory of non-equilibrium steady states in analogy to the equilibrium theory has limited prospects for success and that the pursuit of such a theory should be directed elsewhere.

cond-mat.stat-mech↗

arXiv2009

An exactly solvable model of a highly efficient thermoelectric engine

We propose a simple classical dynamical model of a thermoelectric (or thermochemical) heat engine based on a pair of ideal gas containers connected by two unequal scattering channels. The model is solved analytically and it is shown that a suitable combination of parameters can be chosen such that the engine operates at Carnot's efficiency.

cond-mat.stat-mech↗

arXiv2009

Causal diffusions, causal Zeno effect and collision number

We consider diffusion processes with the help of Markov random walk models. Especially the process of diffusion of a relativistic particle in a relativistic equilibrium system is considered. We interpret one of the results as causal Zeno effect for its similarity to quantum Zeno effect. Another problem we considered is about collision number. Basing on our numerical results, we propose that in the considered situation the probability density distribution among different collision numbers is a lognormal distribution.

cond-mat.stat-mech↗

arXiv2009

Random Number Generators: A Survival Guide for Large Scale Simulations

Monte Carlo simulations are an important tool in statistical physics, complex systems science, and many other fields. An increasing number of these simulations is run on parallel systems ranging from multicore desktop computers to supercomputers with thousands of CPUs. This raises the issue of generating large amounts of random numbers in a parallel application. In this lecture we will learn just enough of the theory of pseudo random number generation to make wise decisions on how to choose and how to use random number generators when it comes to large scale, parallel simulations.

cond-mat.stat-mech↗

arXiv2009

The first passage problem for diffusion through a cylindrical pore with sticky walls

We calculate the first passage time distribution for diffusion through a cylindrical pore with sticky walls. A particle diffusively explores the interior of the pore through a series of binding and unbinding events with the cylinder wall. Through a diagrammatic expansion we obtain first passage time statistics for the particle's exit from the pore. Connections between the model and nucleocytoplasmic transport in cells are discussed.

cond-mat.soft↗