6533b836fe1ef96bd12a0ac1
RESEARCH PRODUCT
A Stochastic Approach to Quantum Statistics Distributions: Theoretical Derivation and Monte Carlo Modelling
R M Sperandeo-mineoIvan GuastellaL Bellomontesubject
Statistics and ProbabilityCanonical ensemblePhysicsclassical Monte Carlo simulations quantum Monte Carlo simulations stochastic particle dynamics (theory)Monte Carlo methodStatistical and Nonlinear PhysicsMarkov chain Monte CarloIdeal gasMicrostate (statistical mechanics)symbols.namesakeThermodynamic limitDynamic Monte Carlo methodsymbolsStatistical physicsStatistics Probability and UncertaintyQuantum statistical mechanicsdescription
Abstract. We present a method aimed at a stochastic derivation of the equilibrium distribution of a classical/quantum ideal gas in the framework of the canonical ensemble. The time evolution of these ideal systems is modelled as a series of transitions from one system microstate to another one and thermal equilibrium is reached via a random walk in the single-particle state space. We look at this dynamic process as a Markov chain satisfying the condition of detailed balance and propose a variant of the Monte Carlo Metropolis algorithm able to take into account indistinguishability of identical quantum particles. Simulations performed on different two-dimensional (2D) systems are revealed to be capable of reproducing the correct trends of the distribution functions and other thermodynamic properties. The simulations allow us to show that, away from the thermodynamic limit, a pseudo-Bose–Einstein condensation occurs for a 2D ideal gas of bosons.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-02-06 |