An exact stochastic field method for the interacting Bose gas at thermal equilibrium

  title={An exact stochastic field method for the interacting Bose gas at thermal equilibrium},
  author={Iacopo Carusotto and Yvan Castin},
  journal={Journal of Physics B},
We present a new exact method to numerically compute the thermodynamical properties of an interacting Bose gas in the canonical ensemble. As in our previous paper (Carusotto I, Castin Y and Dalibard J 2001 Phys. Rev. A 63 023606), we write the density operator ρ as an average of Hartree dyadics |N:1N:2| and we find stochastic evolution equations for the wavefunctions 1,2 such that the exact imaginary-time evolution of ρ is recovered after averaging over noise. In this way, the thermal… 

Figures from this paper

Memory effects and conservation laws in the quantum kinetic evolution of a dilute Bose gas

We derive a non-Markovian generalization to the quantum kinetic theory described by Walser et al. [Phys. Rev. A 59, 3878 (1999)] in the absence of a condensed fraction for temperatures above the

Explicit finite-difference and particle method for the dynamics of mixed Bose-condensate and cold-atom clouds

We present a new numerical method for studying the dynamics of quantum fluids composed of a Bose-Einstein condensate and a cloud of bosonic or fermionic atoms in a mean-field approximation. The

Condensate statistics in one-dimensional interacting Bose gases: exact results.

The condensate statistics in the Bogoliubov theory are derived and this reproduces the exact results at low temperature and explains the suppression of odd numbers of noncondensed particles at T approximately 0.1.

Quantum Phase Transition in a Low-Dimensional Weakly Interacting Bose Gas

This thesis is devoted to the study of the effect of disorder on low-dimensional weakly interacting Bose gases. In particular, the disorder triggers a quantum phase transition in one dimension at

First-principles quantum dynamics in interacting bose gases: I. The positive P representation

The performance of the positive P phase-space representation for exact manybody quantum dynamics is investigated. Gases of interacting bosons are considered, where the full quantum equations to

First-principles quantum dynamics in interacting Bose gases II: stochastic gauges

First principles simulations of the quantum dynamics of interacting Bose gases using the stochastic gauge representation are analysed. In a companion paper, we showed how the positive-P

Non-thermal fixed points and superfluid turbulence in ultracold quantum gases

In this thesis the non-equilibrium dynamics of ultracold quantum gases is studied numerically and analytically in one, two, and three spatial dimensions. We focus on the regime of large occupation

Extension of Bogoliubov theory to quasicondensates

We present an extension of the well-known Bogoliubov theory to treat low-dimensional degenerate Bose gases in the limit of weak interactions and low density fluctuations. We use a density-phase

Temperature-dependent Bogoliubov approximation in the classical field approach to weakly interacting Bose gases

A classical field approximation to the finite temperature microcanonical thermodynamics of weakly interacting Bose gases is applied to the idealized case of atoms confined in a box with periodic

Condensation of N interacting bosons: a hybrid approach to condensate fluctuations.

A new method of calculating the distribution function and fluctuations for a Bose-Einstein condensate (BEC) of N interacting atoms is presented, applicable both for ideal and interacting Bogoliubov BEC and yields remarkable accuracy at all temperatures.



N-boson time-dependent problem: A reformulation with stochastic wave functions

act numerical calculation of the properties of the gas is available, using the quantum Monte Carlo techniques, based on Feynman path integral formulation of quantum mechanics @11,12#. The aim of this

LETTER TO THE EDITOR: Transition temperature of the weakly interacting Bose gas: perturbative solution of the crossover equations in the canonical ensemble

We compute the shift of the critical temperature Tc with respect to the ideal case for a weakly interacting uniform Bose gas. We work in the framework of the canonical ensemble, extending the


A gas of one-dimensional Bose particles interacting via a repulsive delta-function potential has been solved exactly. All the eigenfunctions can be found explicitly and the energies are given by the

Bose-Einstein condensation of a finite number of particles trapped in one or three dimensions.

1D atom traps, such as radially tightly confining magnetictraps or optical dipole traps, are promising for studying BEC and a transition temperature lower than in the thermodynamic limit is proposed.

Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum

We continue the analysis of the one-dimensional gas of Bose particles interacting via a repulsive delta function potential by considering the excitation spectrum. Among other things we show that: (i)


We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase-space representations. We

Quantum Monte Carlo Calculations for a Large Number of Bosons in a Harmonic Trap.

  • Krauth
  • Physics
    Physical review letters
  • 1996
It is shown that the critical temperature of the system decreases with the interaction, and the overall density and the one of condensed particles, and excellent agreement with solutions of the Gross-Pitaevskii equation are obtained.

Bose-einstein condensation in quasi-2D trapped gases

It is found that well below the transition temperature T(c) the equilibrium state is a true condensate, whereas at intermediate temperatures T<T( c) one has a quasicondensate (condensate with fluctuating phase).

Bose–Einstein condensation of atomic gases

Condensates have become an ultralow-temperature laboratory for atom optics, collisional physics and many-body physics, encompassing phonons, superfluidity, quantized vortices, Josephson junctions and quantum phase transitions.

Interatomic collisions in a tightly confined Bose gas

We discuss binary atomic collisions in a Bose gas tightly confined in one (axial) direction and identify two regimes of scattering. In the quasi-two-dimensional (quasi-2D) regime, where the