scholarly journals Finite number and finite size effects in relativistic Bose-Einstein condensation

1999 ◽  
Vol 60 (10) ◽  
Author(s):  
K. Shiokawa ◽  
B. L. Hu
Keyword(s):  
Finite Number ◽  
Size Effects ◽  
Finite Size ◽  
Einstein Condensation ◽  
Finite Size Effects ◽  
Bose Einstein Condensation ◽  
Bose Einstein

EXCITATIONS IN CONFINED LIQUID 4He

2005 ◽  
Vol 19 (04) ◽  
pp. 135-156
Author(s):  
FRANCESCO ALBERGAMO
Keyword(s):  
Saturated Vapor Pressure ◽  
Saturated Vapor ◽  
Finite Size ◽  
Einstein Condensation ◽  
Normal Fluid ◽  
Finite Size Effects ◽  
Bose Einstein Condensation ◽  
Bulk System ◽  
Bose Einstein ◽  
The Relationship

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 .

Effect of a finite number of particles in the Bose-Einstein condensation of a trapped gas

1997 ◽  
Vol 55 (5) ◽  
pp. 3954-3956 ◽  
Author(s):  
R. Napolitano ◽  
J. De Luca ◽  
V. S. Bagnato ◽  
G. C. Marques
Keyword(s):  
Finite Number ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Trapped Gas ◽  
Bose Einstein ◽  
Number Of Particles

Phase transitions in finite systems

1983 ◽  
Vol 61 (2) ◽  
pp. 228-238 ◽  
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.

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

2016 ◽  
Vol 30 (22) ◽  
pp. 1650307 ◽  
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.

BOSE–EINSTEIN CONDENSATION OF PARTICLES TRAPPED IN A BOUNDED HARMONIC POTENTIAL

2001 ◽  
Vol 15 (15) ◽  
pp. 2169-2191 ◽  
Author(s):  
SHALINI LUMB ◽  
S. K. MUTHU
Keyword(s):  
Finite Number ◽  
Specific Heat ◽  
Temperature Curve ◽  
Harmonic Potential ◽  
Einstein Condensation ◽  
Condensate Fraction ◽  
Eigenvalue Spectrum ◽  
Heat Temperature ◽  
Bose Einstein Condensation ◽  
Bose Einstein

The behavior of a finite number of bosons trapped in a bounded harmonic potential is investigated. The eigenvalue spectrum is worked out numerically for three different sizes of the trap. The condensate fraction is determined and is found to increase suddenly below a certain temperature which is a characteristic signature of BEC. The specific heat-temperature curve also shows a peak, with the maximum shifting to lower values and occurring at higher temperatures, as the size of the assembly is reduced.

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