Bose-Einstein condensation has been experimentally found to take place in finite trapped systems when one of the confining frequencies is increased until the gas becomes effectively two-dimensional (2D). We confirm the plausibility of this result by performing path-integral Monte Carlo (PIMC) simulations of trapped Bose gases of increasing anisotropy and comparing them to the predictions of finite-temperature many-body theory. PIMC simulations provide an essentially exact description of these systems; they yield the density profile directly and provide two different estimates for the condensate fraction. For the ideal gas, we find that the PIMC column density of the squeezed gas corresponds quite accurately to that of the exact analytic solution and, moreover, is well mimicked by the density of a 2D gas at the same temperature; the two estimates for the condensate fraction bracket the exact result. For the interacting case, we find 2D Hartree-Fock solutions whose density profiles coincide quite well with the PIMC column densities and whose predictions for the condensate fraction are again bracketed by the PIMC estimates.Bose-Einstein condensation has been experimentally found to take place in finite trapped systems when one of the confining frequencies is increased until the gas becomes effectively two-dimensional (2D). We confirm the plausibility of this result by performing path-integral Monte Carlo (PIMC) simulations of trapped Bose gases of increasing anisotropy and comparing them to the predictions of finite-temperature many-body theory. PIMC simulations provide an essentially exact description of these systems; they yield the density profile directly and provide two different estimates for the condensate fraction. For the ideal gas, we find that the PIMC column density of the squeezed gas corresponds quite accurately to that of the exact analytic solution and, moreover, is well mimicked by the density of a 2D gas at the same temperature; the two estimates for the condensate fraction bracket the exact result. For the interacting case, we find 2D Hartree-Fock solutions whose density profiles coincide quite well with the PIMC column densities and whose predictions for the condensate fraction are again bracketed by the PIMC estimates.

arXiv:cond-mat/0606710AIP conference proceedingsJan 1, 20061 citation

CLASSICAL FIELD SIMULATION OF FINITE-TEMPERATURE BOSE GASES

Toshihiro Sato

Apr 1, 20140 citations

Bose-Einstein condensation temperature of a homogeneous weakly interacting Bose gas: Path integral Monte Carlo study

Kwangsik T. Nho, David Paul Landau

Using a finite-temperature path integral Monte Carlo simulation (PIMC) method and finite-size scaling, we have investigated the interaction-induced shift of the phase-transition temperature for Bose-Einstein condensation of homogeneous weakly interacting Bose gases in three dimensions, which is given by a proposed analytical expression ${T}_{c}={T}_{c}^{0}{1+{c}_{1}a{n}^{1∕3}+[{c}_{2}^{\ensuremath{'}}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}(a{n}^{1∕3})+{c}_{2}^{\ensuremath{''}}]{a}^{2}{n}^{2∕3}+\mathrm{O}({a}^{3}n)}$, where ${T}_{c}^{0}$ is the critical temperature for an ideal gas, $a$ is the $s$ -wave scattering length, and $n$ is the number density. We have used smaller number densities and more time slices than in the previous PIMC simulations [Gruter et al., Phys. Rev. Lett. 79, 3549 (1997)] in order to understand the difference in the value of the coefficient ${c}_{1}$ between their results and the (apparently) other reliable results in the literature. Our results show that ${({T}_{c}\ensuremath{-}{T}_{c}^{0})∕{T}_{c}^{0}}∕(a{n}^{1∕3})$ depends strongly on the interaction strength $a{n}^{1∕3}$ while the previous PIMC results are considerably flatter and smaller than our results. We obtain ${c}_{1}=1.32\ifmmode\pm\else\textpm\fi{}0.14$, in agreement with results from recent Monte Carlo methods of three-dimensional O(2) scalar ${\ensuremath{\phi}}^{4}$ field theory and variational perturbation theory.Using a finite-temperature path integral Monte Carlo simulation (PIMC) method and finite-size scaling, we have investigated the interaction-induced shift of the phase-transition temperature for Bose-Einstein condensation of homogeneous weakly interacting Bose gases in three dimensions, which is given by a proposed analytical expression ${T}_{c}={T}_{c}^{0}{1+{c}_{1}a{n}^{1∕3}+[{c}_{2}^{\ensuremath{'}}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}(a{n}^{1∕3})+{c}_{2}^{\ensuremath{''}}]{a}^{2}{n}^{2∕3}+\mathrm{O}({a}^{3}n)}$, where ${T}_{c}^{0}$ is the critical temperature for an ideal gas, $a$ is the $s$-wave scattering length, and $n$ is the number density. We have used smaller number densities and more time slices than in the previous PIMC simulations [Gruter et al., Phys. Rev. Lett. 79, 3549 (1997)] in order to understand the difference in the value of the coefficient ${c}_{1}$ between their results and the (apparently) other reliable results in the literature. Our results show that ${({T}_{c}\ensuremath{-}{T}_{c}^{0})∕{T}_{c}^{0}}∕(a{n}^{1∕3})$ depends strongly on the interaction strength $a{n}^{1∕3}$ while the previous PIMC results are considerably flatter and smaller than our results. We obtain ${c}_{1}=1.32\ifmmode\pm\else\textpm\fi{}0.14$, in agreement with results from recent Monte Carlo methods of three-dimensional O(2) scalar ${\ensuremath{\phi}}^{4}$ field theory and variational perturbation theory.

arXiv:cond-mat/0404238Physical Review ANov 18, 200456 citations

Finite-temperature excitations in a dilute Bose-condensed gas

Huaibin Shi

Physics ReportsOct 1, 1998290 citations

Application of machine learning in Bose-Einstein condensation critical-temperature analyses of path-integral Monte Carlo simulations

Adith Ramamurti

We detail the use of simple machine learning algorithms to determine the critical Bose-Einstein condensation (BEC) critical temperature $T_\text{c}$ from ensembles of paths created by path-integral Monte Carlo (PIMC) simulations. We quickly overview critical temperature analysis methods from literature, and then compare the results of simple machine learning algorithm analyses with these prior-published methods for one-component Coulomb Bose gases and liquid $^4$ He, showing good agreement.We detail the use of simple machine learning algorithms to determine the critical Bose-Einstein condensation (BEC) critical temperature $T_\text{c}$ from ensembles of paths created by path-integral Monte Carlo (PIMC) simulations. We quickly overview critical temperature analysis methods from literature, and then compare the results of simple machine learning algorithm analyses with these prior-published methods for one-component Coulomb Bose gases and liquid $^4$He, showing good agreement.

arXiv:1912.06654Dec 14, 20190 citations

{T}_{c}^{0}

is the critical temperature for an ideal gas,

a

is the

s

-wave scattering length, and

n

is the number density. We have used smaller number densities and more time slices than in the previous PIMC simulations [Gruter et al., Phys. Rev. Lett. 79, 3549 (1997)] in order to understand the difference in the value of the coefficient

{c}_{1}

between their results and the (apparently) other reliable results in the literature. Our results show that ${({T}_{c}\ensuremath{-}{T}_{c}^{0})∕{T}_{c}^{0}}∕(a{n}^{1∕3})$ depends strongly on the interaction strength

a{n}^{1∕3}

while the previous PIMC results are considerably flatter and smaller than our results. We obtain ${c}_{1}=1.32\ifmmode\pm\else\textpm\fi{}0.14$, in agreement with results from recent Monte Carlo methods of three-dimensional O(2) scalar ${\ensuremath{\phi}}^{4}$ field theory and variational perturbation theory.

We detail the use of simple machine learning algorithms to determine the critical Bose-Einstein condensation (BEC) critical temperature

T_\text{c}

from ensembles of paths created by path-integral Monte Carlo (PIMC) simulations. We quickly overview critical temperature analysis methods from literature, and then compare the results of simple machine learning algorithm analyses with these prior-published methods for one-component Coulomb Bose gases and liquid

^4

He, showing good agreement.