Statistical properties of cold bosons in a ring trap

Kruk, Maciej; Łebek, Maciej; Rza̧żewski, Kazimierz

doi:10.1103/physreva.101.023622

Cited by 5 publications

(5 citation statements)

References 32 publications

(51 reference statements)

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“…No exact canonical results are available for this case, but at low temperature reliable results can be obtained within the Bogoliubov approximation, valid for low temperatures and low interaction strengths. The results based on the Bogoliubov approximation show the expected suppression of fluctuations at low temperature in good agreement with our FSS method computation and earlier results based on the classical field approximation [33]. However, the FSS results show that this suppression is not general, but that the fluctuations surpass the non-interacting case at higher temperature.…”

Section: D Box With Periodic Boundary Conditions (Ring Trap)supporting

confidence: 90%

“…For the non-interacting gas, our present FSS method, as well as the classical field approximation with a well chosen cut-off [32,33], perfectly reproduce the exact result which is known analytically in this case [33]. Moreover, we also find good agreement with the result based on the Bogoliubov approximation within its range of validity at low temperatures.…”

Section: D Box With Periodic Boundary Conditions (Ring Trap)supporting

confidence: 77%

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Microcanonical and canonical fluctuations in atomic Bose-Einstein condensates – Fock state sampling approach

et al. 2023

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The fluctuations of the atom number between a Bose-Einstein condensate and the surrounding thermal gas have been the subject of a long standing theoretical debate. This discussion is centered around the appropriate thermodynamic ensemble to be used for theoretical predictions and the effect of interactions on the observed fluctuations. Here we introduce the so-called Fock state sampling method to solve this classic problem of current experimental interest for weakly interacting gases. A suppression of the predicted peak fluctuations is observed when using a microcanonical with respect to a canonical ensemble. Moreover, interactions lead to a shift of the temperature of peak fluctuations for harmonically trapped gases. The absolute size of the fluctuations furthermore depends on the total number of atoms and the aspect ratio of the trapping potential. Due to the interplay of these effect, there is no universal suppression or enhancement of fluctuations.

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Section: D Box With Periodic Boundary Conditions (Ring Trap)supporting

confidence: 90%

Section: D Box With Periodic Boundary Conditions (Ring Trap)supporting

confidence: 77%

Microcanonical and canonical fluctuations in atomic Bose-Einstein condensates – Fock state sampling approach

et al. 2023

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“…A classical-field approximation combined with the Monte Carlo method was employed to numerically study the statistical properties of the cold interacting bosons in a quasi-one-dimensional ring and harmonic traps at finite temperatures in [44][45][46][47]. It replaces creation and annihilation operators by complex c-number amplitudes and neglects modes of momenta higher than a suitable cutoff momentum.…”

Section: A Challenge Of Predicting and Measuring The Bec Fluctuationsmentioning

confidence: 99%

“…7 as a function of the interaction parameter L/ξ. It is convenient to rewrite the approximation (44) for the standard deviation in the form…”

Section: An Interplay Between Different Regimes In a Mesoscopic Systemmentioning

confidence: 99%

Bose-Einstein condensate fluctuations versus an interparticle interaction

Tarasov,

Kocharovsky,

Kocharovsky

2020

Preprint

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We calculate the Bose-Einstein condensate (BEC) occupation statistics vs. the interparticle interaction in a dilute gas with a nonuniform condensate in a box trap within the Bogoliubov approach. The results are compared against the previously found BEC-occupation statistics in (i) an ideal gas and (ii) a weakly interacting gas with a uniform condensate. In particular, we reveal and explicitly describe an appearance of a nontrivial transition from the ideal gas to the Thomas-Fermi regime. The results include finding the main regimes of the BEC statistics -the anomalous non-Gaussian thermally-dominated fluctuations and the Gaussian quantum-dominated fluctuations -as well as a crossover between them and their manifestations in a mesoscopic system. Remarkably, we show that the effect of the boundary conditions, imposed at the box trap, on the BEC fluctuations doesn't vanish in the thermodynamic limit of a macroscopic system even in the presence of the interparticle interactions. Finally, we discuss a challenging problem of an experimental verification of the theory of the BEC fluctuations addressing a much deeper level of the many-body statistical physics than usually studied quantities related to the mean condensate occupation.

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“…Given its pedagogical and now practical importance, as well as the long history of the problem of non-interacting quantum particles, the last 50 years has provided a host of results, varying from general recursive relations that govern the canonical partition functions and the corre-sponding occupation numbers [5,[57][58][59][60][61][62][63][64][65][66][67], to approximate [4,[68][69][70][71][72] and exact results for some special cases [73][74][75][76][77][78][79][80][81]. More recently, for the case of non-degenerate energy spectra, the exact decomposition of higher-order occupation number correlations in terms of the occupation numbers of individual bosonic and fermionic energy levels have been reported [63,64].…”

Section: Introductionmentioning

confidence: 99%

Theory of Non-Interacting Fermions and Bosons in the Canonical Ensemble

Barghathi,

Yu,

Del Maestro

2020

Preprint

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We present a self-contained theory for the exact calculation of particle number counting statistics of non-interacting indistinguishable particles in the canonical ensemble. This general framework introduces the concept of auxiliary partition functions, and represents a unification of previous distinct approaches with many known results appearing as direct consequences of the developed mathematical structure. In addition, we introduce a general decomposition of the correlations between occupation numbers in terms of the occupation numbers of individual energy levels, that is valid for both non-degenerate and degenerate spectra. To demonstrate the applicability of the theory in the presence of degeneracy, we compute energy level correlations up to fourth order in a bosonic ring in the presence of a magnetic field.

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Statistical properties of cold bosons in a ring trap

Cited by 5 publications

References 32 publications

Microcanonical and canonical fluctuations in atomic Bose-Einstein condensates – Fock state sampling approach

Microcanonical and canonical fluctuations in atomic Bose-Einstein condensates – Fock state sampling approach

Bose-Einstein condensate fluctuations versus an interparticle interaction

Theory of Non-Interacting Fermions and Bosons in the Canonical Ensemble

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