The ideal Bose-Einstein gas, revisited

Ziff, Robert M.; Uhlenbeck, G. E.; Kac, Mark

doi:10.1016/0370-1573(77)90052-7

Cited by 297 publications

(416 citation statements)

References 52 publications

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“…For the 3D gas this result requires the grand canonical description [90], whereas in 1D and 2D it is valid for any choice of the ensemble. On the other hand, the widely used mean-field Bogoliubov approach for an interacting Bose gas leads to g 2 ≈ n 2 .…”

Section: Finite-temperature Local Correlationsmentioning

confidence: 98%

Low-dimensional trapped gases

2004

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Recent developments in the physics of ultracold gases provide wide possibilities for reducing the dimensionality of space for magnetically or optically trapped atoms. The goal of these lectures is to show that regimes of quantum degeneracy in two-dimensional (2D) and one-dimensional (1D) trapped gases are drastically different from those in three dimensions and to stimulate an interest in low-dimensional systems. Attention is focused on the new physics appearing in currently studied low-dimensional trapped gases and related to finite-size and finite-temperature effects.

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Section: Finite-temperature Local Correlationsmentioning

confidence: 98%

Low-dimensional trapped gases

2004

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“…In the grand canonical statistical ensemble, the population of each energy state of the Bose gas performs uncorrelated number fluctuations of order of its mean occupation number [13]. When applied to the macroscopically occupied ground state of a Bose-Einstein condensate, this implies large statistical number fluctuations of order of the total particle number occurring deep in the condensed phase, a behavior termed the "grand canonical fluctuation catastrophe" [14][15][16][17][18].…”

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confidence: 99%

Spontaneous Symmetry Breaking and Phase Coherence of a Photon Bose-Einstein Condensate Coupled to a Reservoir

Schmitt¹,

Damm²,

Dung³

et al. 2016

Phys. Rev. Lett.

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We examine the phase evolution of a Bose-Einstein condensate of photons generated in a dye microcavity by temporal interference with a phase reference. The photoexcitable dye molecules constitute a reservoir of variable size for the condensate particles, allowing for grand canonical statistics with photon bunching, as in a lamptype source. We directly observe phase jumps of the condensate associated with the large statistical number fluctuations and find a separation of correlation timescales.For large systems, our data reveals phase coherence and a spontaneously broken symmetry, despite the statistical fluctuations.At the heart of Bose-Einstein condensation, the phase transition of a cold and dense gas of integer spin (bosonic) particles to a macroscopically populated ground state, is its phase coherence [1,2]. While for a thermal, incoherent ensemble each particle evolves individually, in a Bose-Einstein condensate the macroscopic ground state occupation leads to the whole condensate acting as a single, giant quantum wave. Each individual measurement will then yield a fixed, though random phase, as expected from spontaneous symmetry breaking [3,4,33]. The macroscopic phase of Bose-Einstein condensates has been verified in interference experiments with ultracold atomic gases [6]. For condensates of polaritons, mixed states of matter and light, polarization symmetry breaking was reported [7,8], while polariton arrays have shown phase locking [9]. Further, spatial coherence has been reported for equilibrium photon condensates [10], and also in a nonequilibrium regime [11]. Both atomic and polariton condensates are usually assumed to emit a single wave train of constant amplitude [1,12].They operate with an essentially fixed number of particles, corresponding to a description in the microcanonical or canonical ensemble limit. Such sources have both first and second-order * Present address: Institute for Quantum Electronics, ETH Zürich, Auguste-Piccard-Hof 1, 8093 Zürich, Switzerland arXiv:1512.07148v1 [cond-mat.quant-gas]

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“…Many authors have investigated the thermodynamic properties of Bose gas [1,2,4,6,7,8,9,10,11,12,13], particularly after it was possible to create Bose Einstein Condensation (BEC) in magnetically trapped alkali-metal gases [20,21,22]. The constrained role of external potential does change the characteristics of quantum gases [14,15,16,17,18,19], providing an exciting opportunity to study the quantum mechanical effects.…”

Section: Introductionmentioning

confidence: 99%

Investigation of Bose Condensation in Ideal Bose Gas Trapped under Generic Power Law Potential in d Dimension

Faruk¹,

Hossain²,

Rahman³

2016

Commun. Theor. Phys.

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The changes in characteristics of Bose condensation of ideal Bose gas due to an external generic power law potential (1999).) yielded the hierarchy of condensation transitions with changing fractional dimensionality. In this manuscript, some theorems regarding specific heat at constant volume CV are presented. Careful examination of these theorems reveal the existence of hidden hierarchy of the condensation transition in trapped systems as well.

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The ideal Bose-Einstein gas, revisited

Cited by 297 publications

References 52 publications

Low-dimensional trapped gases

Low-dimensional trapped gases

Spontaneous Symmetry Breaking and Phase Coherence of a Photon Bose-Einstein Condensate Coupled to a Reservoir

Investigation of Bose Condensation in Ideal Bose Gas Trapped under Generic Power Law Potential in d Dimension

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