Related papers: Classical fields method for a relativistic interac…
Classical fields approximation to cold weakly interacting bosons allows for a unified treatment of condensed and uncondensed parts of the system. Until now, however, the quantitative predictions were limited by a dependence of the results…
We present a stochastic matter field equation for an interacting many-body Bose system in equilibrium at ultracold finite temperature. Moreover, the proposed equation can be used for non-equilibrium dynamics on phenomenological grounds.…
We develop an approximate formalism suitable for performing simulations of the thermal dynamics of interacting Bose gases. The method is based on the observation that when the lowest energy modes of the Bose field operator are highly…
A classical fields approximation to the finite temperature microcanonical thermodynamics of weakly interacting Bose gas is applied to the idealized case of atoms confined in a box with periodic boundary conditions. We analyze in some detail…
We develop a semi-classical field method for the study of the weakly interacting Bose gas at finite temperature, which, contrarily to the usual classical field model, does not suffer from an ultraviolet cut-off dependence. We apply the…
We investigate a real scalar field whose dynamics is governed by a nonlinear wave equation. We show that classical description can be applied to a quantum system of many interacting bosons provided that some quantum ingredients are…
We study a dilute and ultracold Bose gas of interacting atoms by using an effective field theory which takes account finite-range effects of the inter-atomic potential. Within the formalism of functional integration from the grand canonical…
The classical region of a Bose gas consists of all single-particle modes that have a high average occupation and are well-described by a classical field. Highly-occupied modes only occur in massive Bose gases at ultra-cold temperatures, in…
We review some recent results on interacting Bose gases in thermal equilibrium. In particular, we study the convergence of the grand-canonical equilibrium states of such gases to their mean-field limits, which are given by the Gibbs…
We review phase space techniques based on the Wigner representation that provide an approximate description of dilute ultra-cold Bose gases. In this approach the quantum field evolution can be represented using equations of motion of a…
We propose a method to study the time evolution of Bose condensed gases perturbed from an initial thermal equilibrium, based on the Wigner representation of the $N$-body density operator. We show how to generate a collection of random…
We present a semiclassical treatment of one-dimensional many-body quantum systems in equilibrium, where quantum corrections to the classical field approximation are systematically included by a renormalization of the classical field…
We determine the regime where the widespread classical field description for quantum Bose gases is quantitatively accurate in 1d, 2d, and 3d by a careful study of the ideal gas limit. Numerical benchmarking in 1d shows that the ideal gas…
We consider the Nelson model which describes a quantum system of nonrelativistic identical particles coupled to a possibly massless scalar Bose field through a Yukawa type interaction. We study the limiting behaviour of that model in a…
These lectures are centered around a specific problem, the effect of weak repulsive interactions on the transition temperature $T_c$ of a Bose gas. This problem provides indeed a beautiful illustration of many of the techniques which have…
We derive a stochastic process that describes the kinetics of a one-dimensional Bose gas in a regime where three body collisions are important. In this situation the system becomes non integrable offering the possibility to investigate…
The ergodic hypothesis asserts that a classical mechanical system will in time visit every available configuration in phase space. Thus, for an ergodic system, an ensemble average of a thermodynamic quantity can equally well be calculated…
To finalize information about the accuracy of the classical field approach for the 1d Bose gas, the lowest temperature quasicondensate was studied by comparing the extended Bogoliubov model of Mora and Castin, to its classical field…
We first consider an exactly solvable classical field model to understand the coherence properties and the density fluctuations of a one-dimensional (1D) weakly interacting degenerate Bose gas with repulsive interactions at temperatures…
Equation of state of uncharged bosonic matter is studied within a field-theoretical approach in the mean-field approximation. Interaction of bosons is described by a scalar field $\sigma$ with a Skyrme-like potential which contains both…