Bose-Einstein condensation in the relativistic pion gas: Thermodynamic limit and finite size effects

The spectacular properties of liquid helium at low temperature are generally accepted as the signature of the bosonic nature of this system. Particularly the superfluid phase is identified with a Bose–Einstein condensed fluid. However, the relationship between the superfluidity and the Bose–Einstein condensation is still largely unknown. Studying a perturbed liquid 4 He system would provide information on the relationship between the two phenomena. Liquid 4 He confined in porous media provides an excellent example of a boson system submitted to disorder and finite-size effects. Much care should be paid to the sample preparation, particularly the confining condition should be defined quantitatively. To achieve homogeneous confinement conditions, firstly a suitable porous sample should be selected, the experiments should then be conducted at a lower pressure than the saturated vapor pressure of bulk helium. Several interesting effects have been shown in confined 4 He samples prepared as described above. Particularly we report the observation of the separation of the superfluid-normal fluid transition temperature, T c , from the temperature at which the Bose–Einstein condensation is believed to start, T BEC , the existence of metastable densities for the confined liquid accessible to the bulk system as a short-lived metastable state only and strong clues for a finite lifetime of the elementary excitations at temperatures as low as 0.4 K .

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Vortices in Bose-Einstein condensates: Finite-size effects and the thermodynamic limit

Physical Review A ◽

10.1103/physreva.87.053615 ◽

2013 ◽

Vol 87 (5) ◽

Cited By ~ 10

Author(s):

J. C. Cremon ◽

G. M. Kavoulakis ◽

B. R. Mottelson ◽

S. M. Reimann

Keyword(s):

Thermodynamic Limit ◽

Size Effects ◽

Finite Size ◽

Finite Size Effects ◽

Bose Einstein

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Phase transitions in finite systems

Canadian Journal of Physics ◽

10.1139/p83-031 ◽

1983 ◽

Vol 61 (2) ◽

pp. 228-238 ◽

Cited By ~ 28

Author(s):

R. K. Pathria

Keyword(s):

Phase Transitions ◽

Thermodynamic Functions ◽

Finite Size ◽

Summation Formula ◽

Einstein Condensation ◽

Restricted Geometry ◽

Finite Size Effects ◽

Mathematical Techniques ◽

Bose Einstein ◽

The Given

Mathematical singularities, which are known to be at the heart of phase transitions and are responsible for making the thermodynamic functions of the given system nonanalytic, are a consequence of the thermodynamic limit, viz. N and V → ∞ with N/V staying constant. When a system containing a finite number of particles and confined to a restricted geometry undergoes a phase transition, these singularities get rounded off, with the result that all thermodynamic functions become analytic and vary smoothly with the relevant parameters of the problem. Theoretical analysis of such situations requires the use of special mathematical techniques which may vary drastically from case to case.In the present communication we report the results of a rigorous analysis of the problem of "Bose–Einstein condensation in restricted geometries", which has been carried out by making an extensive use of the Poisson summation formula. Particular emphasis is laid on the growth of the condensate fraction [Formula: see text] as the temperature of the system is lowered, and on the influence of the boundary conditions imposed on the wave functions of the particles. The relevance of these results, in relation to the scaling theory of finite size effects, is also discussed.

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Casimir forces in Bose–Einstein condensates: finite-size effects in three-dimensional rectangular cavities

Journal of Statistical Mechanics Theory and Experiment ◽

10.1088/1742-5468/2006/06/p06007 ◽

2006 ◽

Vol 2006 (06) ◽

pp. P06007-P06007 ◽

Cited By ~ 14

Author(s):

Ariel Edery

Keyword(s):

Size Effects ◽

Three Dimensional ◽

Finite Size ◽

Casimir Forces ◽

Finite Size Effects ◽

Bose Einstein

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Homogeneous one-dimensional Bose–Einstein condensate in the Bogoliubov’s regime

Modern Physics Letters B ◽

10.1142/s0217984916503073 ◽

2016 ◽

Vol 30 (22) ◽

pp. 1650307 ◽

Cited By ~ 2

Author(s):

Elías Castellanos

Keyword(s):

Ground State ◽

Size Effects ◽

Finite Size ◽

Einstein Condensate ◽

Finite Size Effects ◽

One Dimensional ◽

Bose Einstein Condensate ◽

Ground State Properties ◽

Low Dimensional ◽

Bose Einstein

We analyze the corrections caused by finite size effects upon the ground state properties of a homogeneous one-dimensional (1D) Bose–Einstein condensate. We assume from the very beginning that the Bogoliubov’s formalism is valid and consequently, we show that in order to obtain a well-defined ground state properties, finite size effects of the system must be taken into account. Indeed, the formalism described in the present paper allows to recover the usual properties related to the ground state of a homogeneous 1D Bose–Einstein condensate but corrected by finite size effects of the system. Finally, this scenario allows us to analyze the sensitivity of the system when the Bogoliubov’s regime is valid and when finite size effects are present. These facts open the possibility to apply these ideas to more realistic scenarios, e.g. low-dimensional trapped Bose–Einstein condensates.

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