Search results for "statistical mechanic"
showing 10 items of 707 documents
Geometry of quantum phase transitions
2020
In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric information in the characterisation of quantum phase transitions, we describe recent developments of geometrical approaches based on mixed-state generalisation of the Berry-phase, i.e. the Uhlmann geometric phase, for the investigation of non-equilibrium steady-state quantum phase transitions (NESS-QPTs ). Equilibrium phase transitions fall invariably into two markedly non-overlapping categories: classical phase transitions and quantum phase transitions, whereas i…
Shortcut to Adiabaticity in the Lipkin-Meshkov-Glick Model
2015
We study transitionless quantum driving in an infinite-range many-body system described by the Lipkin-Meshkov-Glick model. Despite the correlation length being always infinite the closing of the gap at the critical point makes the driving Hamiltonian of increasing complexity also in this case. To this aim we develop a hybrid strategy combining shortcut to adiabaticity and optimal control that allows us to achieve remarkably good performance in suppressing the defect production across the phase transition.
Dynamical bifurcation as a semiclassical counterpart of a quantum phase transition
2011
We illustrate how dynamical transitions in nonlinear semiclassical models can be recognized as phase transitions in the corresponding -- inherently linear -- quantum model, where, in a Statistical Mechanics framework, the thermodynamic limit is realized by letting the particle population go to infinity at fixed size. We focus on lattice bosons described by the Bose-Hubbard (BH) model and Discrete Self-Trapping (DST) equations at the quantum and semiclassical level, respectively. After showing that the gaussianity of the quantum ground states is broken at the phase transition, we evaluate finite populations effects introducing a suitable scaling hypothesis; we work out the exact value of the…
Probing Quantum Frustrated Systems via Factorization of the Ground State
2009
The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure of frustration: strongly frustrated systems are those that cannot accommodate for classical-like solutions. The exact form of the factorized ground states and the critical frustration are determined for various classes of nonexactly solvable spin models with different spatial ranges of the interactions. For weak frustration, the existence of disentangling transitions determines the range of applicability of mean-field descriptions in biological and physica…
Queuing transitions in the asymmetric simple exclusion process
2003
Stochastic driven flow along a channel can be modeled by the asymmetric simple exclusion process. We confirm numerically the presence of a dynamic queuing phase transition at a nonzero obstruction strength, and establish its scaling properties. Below the transition, the traffic jam is macroscopic in the sense that the length of the queue scales linearly with system size. Above the transition, only a power-law shaped queue remains. Its density profile scales as $\delta \rho\sim x^{-\nu}$ with $\nu={1/3}$, and $x$ is the distance from the obstacle. We construct a heuristic argument, indicating that the exponent $\nu={1/3}$ is universal and independent of the dynamic exponent of the underlying…
Finite-size scaling in Ising-like systems with quenched random fields: Evidence of hyperscaling violation
2010
In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced by a modified hyperscaling relation. As a result, standard formulations of finite size scaling near critical points break down. In this work, the consequences of modified hyperscaling are analyzed in detail. The most striking outcome is that the free energy cost \Delta F of interface formation at the critical point is no longer a universal constant, but instead increases as a power law with system size, \Delta F proportional to $L^\theta$, with $\theta$ the violation of hyperscaling critical exponent, and L the linear ex…
Growth, percolation, and correlations in disordered fiber networks
1997
This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition model with effective fiber-fiber interactions represented by a parameter $p$ which controls the degree of clustering. For $p=1$, the deposited network is uniformly random, while for $p=0$ only a single connected cluster can grow. For $p=0$, we first derive the growth law for the average size of the cluster as well as a formula for its mass density profile. For $p>0$, we carry out extensive simulations on fibers, and also needles and disks to study the dependence of the percolation threshold on $p$. We also derive a mean-field theory for the threshold ne…
A Hebbian approach to complex-network generation
2011
Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic connection between the kind of interactions among components and the emergent topology describing the system itself; also, it allows to effectively address the statistical mechanics on the resulting networks. Indeed, a wide class of analytically treatable, weighted random graphs with a tunable level of correlation can be recovered and controlled. We especially focus on the case of imitative couplings among components endowed with similar patterns (i.e. attribute…
Monte-Carlo Methods
2003
The article conbtains sections titled: 1 Introduction and Overview 2 Random-Number Generation 2.1 General Introduction 2.2 Properties That a Random-Number Generator (RNG) Should Have 2.3 Comments about a Few Frequently Used Generators 3 Simple Sampling of Probability Distributions Using Random Numbers 3.1 Numerical Estimation of Known Probability Distributions 3.2 “Importance Sampling” versus “Simple Sampling” 3.3 Monte-Carlo as a Method of Integration 3.4 Infinite Integration Space 3.5 Random Selection of Lattice Sites 3.6 The Self-Avoiding Walk Problem 3.7 Simple Sampling versus Biased Sampling: the Example of SAWs Continued 4 Survey of Applications to Simulation of Transport Processes 4.…
The relaxation dynamics of a simple glass former confined in a pore
2000
We use molecular dynamics computer simulations to investigate the relaxation dynamics of a binary Lennard-Jones liquid confined in a narrow pore. We find that the average dynamics is strongly influenced by the confinement in that time correlation functions are much more stretched than in the bulk. By investigating the dynamics of the particles as a function of their distance from the wall, we can show that this stretching is due to a strong dependence of the relaxation time on this distance, i.e. that the dynamics is spatially very heterogeneous. In particular we find that the typical relaxation time of the particles close to the wall is orders of magnitude larger than the one of particles …