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Metropolis-Hastings thermal state sampling for numerical simulations of Bose-Einstein condensates.

Grišins P, Mazets IE - Comput Phys Commun (2014)

Bottom Line: We demonstrate the application of the Metropolis-Hastings algorithm to sampling of classical thermal states of one-dimensional Bose-Einstein quasicondensates in the classical fields approximation, both in untrapped and harmonically trapped case.For truncated Wigner simulations the quantum noise can be added with conventional methods (half a quantum of energy in every mode).The advantage of the presented method over the usual analytical and stochastic ones lies in its ability to sample not only from canonical and grand canonical distributions, but also from the generalized Gibbs ensemble, which can help to shed new light on thermodynamics of integrable systems.

View Article: PubMed Central - PubMed

Affiliation: Vienna Center for Quantum Science and Technology, Atominstitut TU Wien, 1020 Vienna, Austria.

ABSTRACT

We demonstrate the application of the Metropolis-Hastings algorithm to sampling of classical thermal states of one-dimensional Bose-Einstein quasicondensates in the classical fields approximation, both in untrapped and harmonically trapped case. The presented algorithm can be easily generalized to higher dimensions and arbitrary trap geometry. For truncated Wigner simulations the quantum noise can be added with conventional methods (half a quantum of energy in every mode). The advantage of the presented method over the usual analytical and stochastic ones lies in its ability to sample not only from canonical and grand canonical distributions, but also from the generalized Gibbs ensemble, which can help to shed new light on thermodynamics of integrable systems.

No MeSH data available.


Related in: MedlinePlus

Typical examples of the grand canonical thermal state with the temperatures  and 60 nK (labels on the panels) of the interacting 1D BEC, achieved after  Metropolis–Hastings iterations in the untrapped system with periodic boundary conditions (four top panels) and harmonically trapped case (four bottom panels). Quasicondensate local densities  (left), measured in atoms per micrometer, and phases  (right), measured in radians, as a function of the longitudinal direction  in micrometers. The initial conditions in the case of the untrapped system were taken to be the ground state of the non-interacting gas, and in the case of the harmonic confinement as a Thomas–Fermi parabolic density profile with constant zero phase. Note that achieved thermal state is not dependent on the initial conditions (see discussion in the text). Extensive fluctuations of the phase at the edges of harmonically trapped quasicondensate are due to the fact that the density there is close to zero, and the phase can take arbitrary values. Physical parameters of the simulations are summarized in Table 2.
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f000005: Typical examples of the grand canonical thermal state with the temperatures and 60 nK (labels on the panels) of the interacting 1D BEC, achieved after Metropolis–Hastings iterations in the untrapped system with periodic boundary conditions (four top panels) and harmonically trapped case (four bottom panels). Quasicondensate local densities (left), measured in atoms per micrometer, and phases (right), measured in radians, as a function of the longitudinal direction in micrometers. The initial conditions in the case of the untrapped system were taken to be the ground state of the non-interacting gas, and in the case of the harmonic confinement as a Thomas–Fermi parabolic density profile with constant zero phase. Note that achieved thermal state is not dependent on the initial conditions (see discussion in the text). Extensive fluctuations of the phase at the edges of harmonically trapped quasicondensate are due to the fact that the density there is close to zero, and the phase can take arbitrary values. Physical parameters of the simulations are summarized in Table 2.

Mentions: Typical examples of the grand canonical thermal state of the 1D Bose–Einstein quasicondensate after Metropolis–Hastings iterations are presented in Fig. 1.


Metropolis-Hastings thermal state sampling for numerical simulations of Bose-Einstein condensates.

Grišins P, Mazets IE - Comput Phys Commun (2014)

Typical examples of the grand canonical thermal state with the temperatures  and 60 nK (labels on the panels) of the interacting 1D BEC, achieved after  Metropolis–Hastings iterations in the untrapped system with periodic boundary conditions (four top panels) and harmonically trapped case (four bottom panels). Quasicondensate local densities  (left), measured in atoms per micrometer, and phases  (right), measured in radians, as a function of the longitudinal direction  in micrometers. The initial conditions in the case of the untrapped system were taken to be the ground state of the non-interacting gas, and in the case of the harmonic confinement as a Thomas–Fermi parabolic density profile with constant zero phase. Note that achieved thermal state is not dependent on the initial conditions (see discussion in the text). Extensive fluctuations of the phase at the edges of harmonically trapped quasicondensate are due to the fact that the density there is close to zero, and the phase can take arbitrary values. Physical parameters of the simulations are summarized in Table 2.
© Copyright Policy - CC BY
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4376078&req=5

f000005: Typical examples of the grand canonical thermal state with the temperatures and 60 nK (labels on the panels) of the interacting 1D BEC, achieved after Metropolis–Hastings iterations in the untrapped system with periodic boundary conditions (four top panels) and harmonically trapped case (four bottom panels). Quasicondensate local densities (left), measured in atoms per micrometer, and phases (right), measured in radians, as a function of the longitudinal direction in micrometers. The initial conditions in the case of the untrapped system were taken to be the ground state of the non-interacting gas, and in the case of the harmonic confinement as a Thomas–Fermi parabolic density profile with constant zero phase. Note that achieved thermal state is not dependent on the initial conditions (see discussion in the text). Extensive fluctuations of the phase at the edges of harmonically trapped quasicondensate are due to the fact that the density there is close to zero, and the phase can take arbitrary values. Physical parameters of the simulations are summarized in Table 2.
Mentions: Typical examples of the grand canonical thermal state of the 1D Bose–Einstein quasicondensate after Metropolis–Hastings iterations are presented in Fig. 1.

Bottom Line: We demonstrate the application of the Metropolis-Hastings algorithm to sampling of classical thermal states of one-dimensional Bose-Einstein quasicondensates in the classical fields approximation, both in untrapped and harmonically trapped case.For truncated Wigner simulations the quantum noise can be added with conventional methods (half a quantum of energy in every mode).The advantage of the presented method over the usual analytical and stochastic ones lies in its ability to sample not only from canonical and grand canonical distributions, but also from the generalized Gibbs ensemble, which can help to shed new light on thermodynamics of integrable systems.

View Article: PubMed Central - PubMed

Affiliation: Vienna Center for Quantum Science and Technology, Atominstitut TU Wien, 1020 Vienna, Austria.

ABSTRACT

We demonstrate the application of the Metropolis-Hastings algorithm to sampling of classical thermal states of one-dimensional Bose-Einstein quasicondensates in the classical fields approximation, both in untrapped and harmonically trapped case. The presented algorithm can be easily generalized to higher dimensions and arbitrary trap geometry. For truncated Wigner simulations the quantum noise can be added with conventional methods (half a quantum of energy in every mode). The advantage of the presented method over the usual analytical and stochastic ones lies in its ability to sample not only from canonical and grand canonical distributions, but also from the generalized Gibbs ensemble, which can help to shed new light on thermodynamics of integrable systems.

No MeSH data available.


Related in: MedlinePlus