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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

Natural logarithm of the  correlation function in the homogeneous case for the temperatures  and 120 nK (from top to bottom) at the last iteration  of the algorithm, averaged over the ensemble of 70 realizations. These  functions are used to calculate averaged temperatures presented in Fig. 3(a). The linear region of the logarithm spans from 0 till , and it is used in temperature measurement. The bending and fluctuations in the subsequent region are due to the finite size effects (as the total size of the system is ) and are to be discarded.
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f000010: Natural logarithm of the correlation function in the homogeneous case for the temperatures and 120 nK (from top to bottom) at the last iteration of the algorithm, averaged over the ensemble of 70 realizations. These functions are used to calculate averaged temperatures presented in Fig. 3(a). The linear region of the logarithm spans from 0 till , and it is used in temperature measurement. The bending and fluctuations in the subsequent region are due to the finite size effects (as the total size of the system is ) and are to be discarded.

Mentions: The Metropolis–Hastings ‘evolution’ of the temperature is presented in Fig. 3, with one particular example of the function in Fig. 2. It is evident that the thermal equilibrium is achieved after iterations.


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

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

Natural logarithm of the  correlation function in the homogeneous case for the temperatures  and 120 nK (from top to bottom) at the last iteration  of the algorithm, averaged over the ensemble of 70 realizations. These  functions are used to calculate averaged temperatures presented in Fig. 3(a). The linear region of the logarithm spans from 0 till , and it is used in temperature measurement. The bending and fluctuations in the subsequent region are due to the finite size effects (as the total size of the system is ) and are to be discarded.
© Copyright Policy - CC BY
Related In: Results  -  Collection

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

f000010: Natural logarithm of the correlation function in the homogeneous case for the temperatures and 120 nK (from top to bottom) at the last iteration of the algorithm, averaged over the ensemble of 70 realizations. These functions are used to calculate averaged temperatures presented in Fig. 3(a). The linear region of the logarithm spans from 0 till , and it is used in temperature measurement. The bending and fluctuations in the subsequent region are due to the finite size effects (as the total size of the system is ) and are to be discarded.
Mentions: The Metropolis–Hastings ‘evolution’ of the temperature is presented in Fig. 3, with one particular example of the function in Fig. 2. It is evident that the thermal equilibrium is achieved after iterations.

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