On condensation in the free-boson gas and the spectrum of the Laplacian

Berg, M. van den

doi:10.1007/bf01019501

Cited by 77 publications

(72 citation statements)

References 10 publications

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“…Similar exponential boundary relations were first proposed by Van den Berg and co-workers [21,23] for an anisotropic square well potential. But these explicit conditions for the anisotropic harmonic oscillator, in which the length factor in the exponent is squared were given by Beau and Zagrebnov [32,33] and we designate them as BZ conditions.…”

Section: Exponential Boundary Conditionssupporting

confidence: 73%

“…This peculiarity illustrates some interesting unexpected features of the statistical mechanics of BEC. The approach used by BZ to fix this second transition was originally invented by Van den Berg and co-workers [21,23] for an anisotropic square well potential. The energy levels of the cigar trap are…”

Section: The Cigar Trapmentioning

confidence: 99%

“…This is the flat plate geometry in which two large square plates of length L on a side are separated by a much smaller distance D. This problem was treated by Van den Berg and coworkers [21,23] in the 1980's. A third analogous case involves having two free dimensions and one harmonic dimension [32].…”

Section: Exponential Boundary Conditionsmentioning

confidence: 99%

“…Sonin [36] was the first to note that there could be multiple BEC transitions in a parallelepiped geometry corresponding to a variety of way of taking the TL, although he did not discuss any associated GBEC. The original case of a GBEC associated with the double BEC transition was considered by Van den Berg and coworkers in a flat-plate geometry [21,23]. There have been many experiments with gases in cigar traps; we comment on their relevance to the possible observation of GBEC.…”

Section: Introductionmentioning

confidence: 97%

“…Other terminology has referred to "smeared" [8] and "fragmented" condensations [14,15]. The most thorough analyses of GBEC have been done by Van den Berg and coworkers [16][17][18][19][20][21][22][23][24] and more recently by Zagrebnov et al [25][26][27][28][29][30][31][32][33]. Ho and Yip [34] claim that the spin-1 Bose gas is an example of fragmentation.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Bose–Einstein Condensation

Mullin

Sakhel

2011

J Low Temp Phys

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Generalized Bose-Einstein condensation (GBEC) involves condensates appearing simultaneously in multiple states. We review examples of the three types in an ideal Bose gas with different geometries. In Type I there is a discrete number of quantum states each having macroscopic occupation; Type II has condensation into a continuous band of states, with each state having macroscopic occupation; in Type III each state is microscopically occupied while the entire condensate band is macroscopically occupied. We begin by discussing Type I or "normal" BEC into a single state for an isotropic harmonic oscillator potential. Other geometries and external potentials are then considered: the "channel" potential (harmonic in one dimension and hard-wall in the other), which displays Type II, the "cigar trap" (anisotropic harmonic potential), and the "Casimir prism" (an elongated box), the latter two having Type III condensations. General box geometries are considered in an appendix. We particularly focus on the cigar trap, which Van Druten and Ketterle first showed had a two-step condensation: a GBEC into a band of states at a temperature Tc and another "one-dimensional" transition at a lower temperature T1 into the ground state. In a thermodynamic limit in which the ratio of the dimensions of the anisotropic harmonic trap is kept fixed, T1 merges with the upper transition, which then becomes a normal BEC. However, in the thermodynamic limit of Beau and Zagrebnov, in which the ratio of the boundary lengths increases exponentially, T1 becomes fixed at the temperature of a true Type I phase transition. The effects of interactions on GBEC are discussed and we show that there is evidence that Type III condensation may have been observed in the cigar trap.

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Section: Exponential Boundary Conditionssupporting

confidence: 73%

Section: The Cigar Trapmentioning

confidence: 99%