Random point fields associated with certain Fredholm determinants I: fermion, Poisson and boson point processes

Shirai, Tomoyuki; Takahashi, Yōichirō

doi:10.1016/s0022-1236(03)00171-x

Cited by 305 publications

(461 citation statements)

References 21 publications

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“…In Ref. 15, typical limit theorems are given for a certain class of RPFs which include the particular cases of the fermion as well as boson RPFs. In Ref.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Large deviation principle for noninteracting boson random point processes

Tamura

Zagrebnov

2010

Journal of Mathematical Physics

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“…In Ref. 15, typical limit theorems are given for a certain class of RPFs which include the particular cases of the fermion as well as boson RPFs. In Ref.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Large deviation principle for noninteracting boson random point processes

Tamura

Zagrebnov

2010

Journal of Mathematical Physics

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“…This is an example of the Fermi point processes (also called determinantal point processes) discussed in [51] and [47]. It is determined by the matrix M √ C KM √ C .…”

Section: The Transfer Current Theoremmentioning

confidence: 99%

Markov Paths, Loops and Fields

Jan

2011

Lecture Notes in Mathematics

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“…The usual boson and the fermion RPFs [11][12][13] have been formulated in a unified way in terms of the Fredholm determinant together with other related RPFs, which are indexed by fractional numbers, in Ref. 17. They have been rederived as theories which describe position distributions of the constituent particles of quantum gases in the thermodynamic limit for canonical ensembles in Ref.…”

Section: ͑13͒mentioning

confidence: 99%

“…18. It was shown that the RPF, corresponding to fractional numbers, 17 describes the gases which consist of particles obeying the parastatistics. 20 The RPF describing a homogeneous Bose-Einstein condensation has been studied for the first time in Ref.…”

Section: ͑13͒mentioning

confidence: 99%

Mean-field interacting boson random point fields in weak harmonic traps

Tamura

Zagrebnov

2009

Journal of Mathematical Physics

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A model of the mean-field interacting boson gas trapped by a weak harmonic potential is considered by the boson random point field methods. We prove that in the weak harmonic trap limit there are two phases distinguished by the boson condensation and by a different behavior of the local particle density. For chemical potentials less than a certain critical value, the resulting random point field ͑RPF͒ coincides with the usual boson RPF, which corresponds to a noninteracting ͑ideal͒ boson gas. For the chemical potentials greater than the critical value, the boson RPF describes a divergent ͑local͒ density, which is due to localization of the macroscopic number of condensed particles. Notice that it is this kind of transition that observed in experiments producing the Bose-Einstein condensation in traps.

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Random point fields associated with certain Fredholm determinants I: fermion, Poisson and boson point processes

Cited by 305 publications

References 21 publications

Large deviation principle for noninteracting boson random point processes

Large deviation principle for noninteracting boson random point processes

Markov Paths, Loops and Fields

Mean-field interacting boson random point fields in weak harmonic traps

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