Search results for "statistical mechanic"

A dynamical mean field theory for the study of surface diffusion constants

1997

We present a combined analytical and numerical approach based on the Mori projection operator formalism and Monte Carlo simulations to study surface diffusion within the lattice-gas model. In the present theory, the average jump rate and the susceptibility factor appearing are evaluated through Monte Carlo simulations, while the memory functions are approximated by the known results for a Langmuir gas model. This leads to a dynamical mean field theory (DMF) for collective diffusion, while approximate correlation effects beyond DMF are included for tracer diffusion. We apply our formalism to three very different strongly interacting systems and compare the results of the new approach with th…

Low-temperature anharmonic lattice deformations near rotator impurities: A quantum Monte Carlo approach.

1994

At zero temperature the equilibrium structures of a system consisting of a quantum rotator (${\mathrm{N}}_{2}$) embedded in a relaxing lattice (Ar) surrounding are studied with a variational approach. With symmetric wave functions (para-${\mathrm{N}}_{2}$), we obtain a cubic lattice deformation near the rotator, while with antisymmetric wave functions (ortho-${\mathrm{N}}_{2}$), we obtain a tetragonal lattice deformation forming a stable oriented ground state. At low temperatures, we investigate the properties of this system with a quantum Monte Carlo simulation. On top of the tetragonal deformation the width of the nearest-neighbor oscillations follows classical ``scaling'' laws according …

SOLITON STATISTICAL MECHANICS AND THE THERMALISATION OF BIOLOGICAL SOLITONS

1989

D pseudo-bosons in quantum models

2013

Abstract We show how some recent models of PT-quantum mechanics perfectly fit into the settings of D pseudo-bosons, as introduced by one of us. Among the others, we also consider a model of non-commutative quantum mechanics, and we show that this model too can be described in terms of D pseudo-bosons.

Free-energy barriers for crystal nucleation from fluid phases.

2017

Monte Carlo simulations of crystal nuclei coexisting with the fluid phase in thermal equilibrium in finite volumes are presented and analyzed, for fluid densities from dense melts to the vapor. Generalizing the lever-rule for two-phase coexistence in the canonical ensemble to finite volume, "measurements" of the nucleus volume together with the pressure and chemical potential of the surrounding fluid allows to extract the surface free energy of the nucleus. Neither the knowledge of the (in general non-spherical) nucleus shape nor of the angle-dependent interface tension is required for this task. The feasibility of the approach is demonstrated for a variant of the Asakura-Oosawa model for c…

Nonlinearity and Disorder in the Statistical Mechanics of Integrable Systems

1992

Attention is drawn to a theory of the statistical mechanics (SM) of the integrable models in 1+1 dimension — a theory of ‘soliton statistical mechanics’ classical and quantum [1–17]. This SM provides a generic example of integrable nonlinearity interacting with disorder. In the generic classical examples, such as the classical SM of the sine-Gordon model, phonons provide disorder in which sit coherent structures — the kink-like solitons. But these solitons are dressed by the disorder, in equilibrium, while the breather-like solitons break up to form the disordered structures which are the phonons in thermal equilibrium. On the other hand quantum solitons, dressed by both the vacuum and fini…

Absence of hyperscaling violations for phase transitions with positive specific heat exponent

1994

Finite size scaling theory and hyperscaling are analyzed in the ensemble limit which differs from the finite size scaling limit. Different scaling limits are discussed. Hyperscaling relations are related to the identification of thermodynamics as the infinite volume limit of statistical mechanics. This identification combined with finite ensemble scaling leads to the conclusion that hyperscaling relations cannot be violated for phase transitions with strictly positive specific heat exponent. The ensemble limit allows to derive analytical expressions for the universal part of the finite size scaling functions at the critical point. The analytical expressions are given in terms of generalH-fu…

Tricritical universality in a two-dimensional spin fluid

1995

Monte Carlo simulations are used to investigate the tricritical point properties of a 2d spin fluid. Measurements of the scaling operator distributions are employed in conjunction with a finite-size scaling analysis to locate the tricritical point and determine the directions of the relevant scaling fields and their associated tricritical exponents. The scaling operator distributions and exponents are shown to match quantitatively those of the 2d Blume-Capel model, confirming that both models belong to the same universality class. Mean-field calculations of the tricritical point properties are also compared with the simulation measurements.

Direct Observation in 3d of Structural Crossover in Binary Hard Sphere Mixtures

2016

For binary fluid mixtures of spherical particles in which the two species are sufficiently different in size, the dominant wavelength of oscillations of the pair correlation functions is predicted to change from roughly the diameter of the large species to that of the small species along a sharp crossover line in the phase diagram [C. Grodon, M. Dijkstra, R. Evans & R. Roth, J.Chem.Phys. 121, 7869 (2004)]. Using particle-resolved colloid experiments in 3d we demonstrate that crossover exists and that its location in the phase diagram is in quantitative agreement with the results of both theory and our Monte-Carlo simulations. In contrast with previous work [J. Baumgartl, R. Dullens, M. …

Comparison of Dissipative Particle Dynamics and Langevin thermostats for out-of-equilibrium simulations of polymeric systems

2007

In this work we compare and characterize the behavior of Langevin and Dissipative Particle Dynamics (DPD) thermostats in a broad range of non-equilibrium simulations of polymeric systems. Polymer brushes in relative sliding motion, polymeric liquids in Poiseuille and Couette flows, and brush-melt interfaces are used as model systems to analyze the efficiency and limitations of different Langevin and DPD thermostat implementations. Widely used coarse-grained bead-spring models under good and poor solvent conditions are employed to assess the effects of the thermostats. We considered equilibrium, transient, and steady state examples for testing the ability of the thermostats to maintain const…