Statistical mechanics is one of the most comprehensive theories in physics. From a boiling pot of water to the complex dynamics of quantum many-body systems it provides a successful connection between the microscopic dynamics of atoms and molecules and the macroscopic properties of matter. However, statistical mechanics only describes the thermal equilibrium situation of a system, and there is no general framework to describe how equilibrium is reached or under which circumstances it can be reached at all. This problem is particularly challenging in quantum mechanics, where unitarity appears to render the very concept of thermalization counterintuitive. With the rapid experimental progress in the control and probing of ultracold quantum gases this question has become within reach of detailed experimental investigations. In these notes we present a series of experiments with ultracold one-dimensional Bose gases, which provide novel insights into this fundamental question.Statistical mechanics is one of the most comprehensive theories in physics. From a boiling pot of water to the complex dynamics of quantum many-body systems it provides a successful connection between the microscopic dynamics of atoms and molecules and the macroscopic properties of matter. However, statistical mechanics only describes the thermal equilibrium situation of a system, and there is no general framework to describe how equilibrium is reached or under which circumstances it can be reached at all. This problem is particularly challenging in quantum mechanics, where unitarity appears to render the very concept of thermalization counterintuitive. With the rapid experimental progress in the control and probing of ultracold quantum gases this question has become within reach of detailed experimental investigations. In these notes we present a series of experiments with ultracold one-dimensional Bose gases, which provide novel insights into this fundamental question.

arXiv:1504.04288Apr 16, 20153 citations

Probing quantum statistical mechanics with Bose gases: Non-trivial order parameter topology from a Bose-Einstein quench

J. R. Anglin, Wojciech Hubert Zurek

This is a less technical presentation of the ideas in quant-ph/9804035 [Phys Rev Lett 83 (1999), 1707-1710]. A second order phase transition induced by a rapid quench can lock out topological defects with densities far exceeding their equilibrium expectation values. This phenomenon is a generic prediction of nonequilibrium statistical mechanics, and can appear in a wide range of physical systems. We discuss it qualitatively in the context of trapped dilute Bose-Einstein condensates, outline a simple quantitative theory based on the time-dependent Ginzburg-Landau equation, and briefly compare the results of quantum kinetic theory.This is a less technical presentation of the ideas in quant-ph/9804035 [Phys Rev Lett 83 (1999), 1707-1710]. A second order phase transition induced by a rapid quench can lock out topological defects with densities far exceeding their equilibrium expectation values. This phenomenon is a generic prediction of nonequilibrium statistical mechanics, and can appear in a wide range of physical systems. We discuss it qualitatively in the context of trapped dilute Bose-Einstein condensates, outline a simple quantitative theory based on the time-dependent Ginzburg-Landau equation, and briefly compare the results of quantum kinetic theory.

arXiv:cond-mat/0001146Jan 11, 20001 citation

Quantum statistics of a charged bose gas in the ground state

E. A. Nosal, Walter T. Grandy

Annals of PhysicsOct 1, 19695 citations

Revisiting the concept of chemical potential in classical and quantum gases: A perspective from Equilibrium Statistical Mechanics

Francisco J. Sevilla, Luis Olivares‐Quiroz

In this work we revisit the concept of chemical potential $μ$ in both classical and quantum gases from a perspective of Equilibrium Statistical Mechanics (ESM). Two new results regarding the equation of state $μ=μ(n,T)$ , where $n$ is the particle density and $T$ the absolute temperature, are given for the classical interacting gas and for the weakly-interacting quantum Bose gas. In order to make this review self-contained and adequate for a general reader we provide all the basic elements in an advanced-undergraduate or graduate statistical mechanics course required to follow all the calculations. We start by presenting a calculation of $μ(n,T)$ for the classical ideal gas in the canonical ensemble. After this, we consider the interactions between particles and compute the effects of them on $μ(n,T)$ for the van der Waals gas. For quantum gases we present an alternative approach to calculate the Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. We show that this scheme can be straightforwardly generalized to determine what we have called Intermediate Quantum Statistics (IQS) which deal with ideal quantum systems where a single-particle energy can be occupied by at most $j$ particles with $0 \leqslant j \leqslant N$ with $N$ the total number of particles. In the final part we address general considerations that underlie the theory of weakly interacting quantum gases. In the case of the weakly interacting Bose gas, we focus our attention to the equation of state $μ=μ(n,T)$ in the Hartree-Fock mean-field approximation (HF) and the implications of such results in the elucidation of the order of the phase transitions involved in the BEC phase for non-ideal Bose gases.In this work we revisit the concept of chemical potential $μ$ in both classical and quantum gases from a perspective of Equilibrium Statistical Mechanics (ESM). Two new results regarding the equation of state $μ=μ(n,T)$, where $n$ is the particle density and $T$ the absolute temperature, are given for the classical interacting gas and for the weakly-interacting quantum Bose gas. In order to make this review self-contained and adequate for a general reader we provide all the basic elements in an advanced-undergraduate or graduate statistical mechanics course required to follow all the calculations. We start by presenting a calculation of $μ(n,T)$ for the classical ideal gas in the canonical ensemble. After this, we consider the interactions between particles and compute the effects of them on $μ(n,T)$ for the van der Waals gas. For quantum gases we present an alternative approach to calculate the Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. We show that this scheme can be straightforwardly generalized to determine what we have called Intermediate Quantum Statistics (IQS) which deal with ideal quantum systems where a single-particle energy can be occupied by at most $j$ particles with $0 \leqslant j \leqslant N$ with $N$ the total number of particles. In the final part we address general considerations that underlie the theory of weakly interacting quantum gases. In the case of the weakly interacting Bose gas, we focus our attention to the equation of state $μ=μ(n,T)$ in the Hartree-Fock mean-field approximation (HF) and the implications of such results in the elucidation of the order of the phase transitions involved in the BEC phase for non-ideal Bose gases.

arXiv:1104.2611Apr 13, 20113 citations

In this work we revisit the concept of chemical potential

μ

in both classical and quantum gases from a perspective of Equilibrium Statistical Mechanics (ESM). Two new results regarding the equation of state

μ=μ(n,T)

, where

n

is the particle density and

T

the absolute temperature, are given for the classical interacting gas and for the weakly-interacting quantum Bose gas. In order to make this review self-contained and adequate for a general reader we provide all the basic elements in an advanced-undergraduate or graduate statistical mechanics course required to follow all the calculations. We start by presenting a calculation of

μ(n,T)

for the classical ideal gas in the canonical ensemble. After this, we consider the interactions between particles and compute the effects of them on

μ(n,T)

for the van der Waals gas. For quantum gases we present an alternative approach to calculate the Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. We show that this scheme can be straightforwardly generalized to determine what we have called Intermediate Quantum Statistics (IQS) which deal with ideal quantum systems where a single-particle energy can be occupied by at most

j

particles with

0 \leqslant j \leqslant N

with

N

the total number of particles. In the final part we address general considerations that underlie the theory of weakly interacting quantum gases. In the case of the weakly interacting Bose gas, we focus our attention to the equation of state

μ=μ(n,T)

in the Hartree-Fock mean-field approximation (HF) and the implications of such results in the elucidation of the order of the phase transitions involved in the BEC phase for non-ideal Bose gases.