Metropolis-Hastings thermal state sampling for numerical simulations of Bose-Einstein condensates.
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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.
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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 |
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Mentions: Another independent test whether the achieved state is thermal is the real-time development of the state, as by definition the thermal state should remain thermal during such evolution. To check this criterion we prepared the thermal state of the untrapped gas with Metropolis algorithm and then propagated it in real time with Gross–Pitaevskii equation (there exist efficient algorithms for solving real-time GPE, see e.g. [20,21]). The results, presented in the inset to Fig. 4, show that indeed the temperature of the state does not change on average, assuring that the initial state was thermal with respect to the Gross–Pitaevskii Hamiltonian. |
View Article: PubMed Central - PubMed
Affiliation: Vienna Center for Quantum Science and Technology, Atominstitut TU Wien, 1020 Vienna, Austria.
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.