TY - JOUR

T1 - A Stochastic Approach to Quantum Statistics Distributions: Theoretical Derivation and Monte Carlo Modelling

AU - Guastella, Ivan

AU - Mineo, Rosa Maria

AU - Bellomonte, Leonardo

PY - 2009

Y1 - 2009

N2 - Abstract. We present a method aimed at a stochastic derivation of theequilibrium distribution of a classical/quantum ideal gas in the framework ofthe canonical ensemble. The time evolution of these ideal systems is modelledas a series of transitions from one system microstate to another one and thermalequilibrium 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 ofdetailed balance and propose a variant of the Monte Carlo Metropolis algorithmable to take into account indistinguishability of identical quantum particles.Simulations performed on different two-dimensional (2D) systems are revealedto be capable of reproducing the correct trends of the distribution functions andother thermodynamic properties. The simulations allow us to show that, awayfrom the thermodynamic limit, a pseudo-Bose–Einstein condensation occurs fora 2D ideal gas of bosons.

AB - Abstract. We present a method aimed at a stochastic derivation of theequilibrium distribution of a classical/quantum ideal gas in the framework ofthe canonical ensemble. The time evolution of these ideal systems is modelledas a series of transitions from one system microstate to another one and thermalequilibrium 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 ofdetailed balance and propose a variant of the Monte Carlo Metropolis algorithmable to take into account indistinguishability of identical quantum particles.Simulations performed on different two-dimensional (2D) systems are revealedto be capable of reproducing the correct trends of the distribution functions andother thermodynamic properties. The simulations allow us to show that, awayfrom the thermodynamic limit, a pseudo-Bose–Einstein condensation occurs fora 2D ideal gas of bosons.

KW - classical Monte Carlo simulations

KW - quantum Monte Carlo
simulations

KW - stochastic particle dynamics (theory)

KW - classical Monte Carlo simulations

KW - quantum Monte Carlo
simulations

KW - stochastic particle dynamics (theory)

UR - http://hdl.handle.net/10447/34101

M3 - Article

VL - P02021

SP - 1

EP - 11

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

ER -