scholarly journals CRITICAL TEMPERATURE OF AN INTERACTING BOSE GAS IN A GENERIC POWER-LAW POTENTIAL

2002 ◽  
Vol 16 (16) ◽  
pp. 2185-2190 ◽  
Author(s):  
LUCA SALASNICH
Keyword(s):  
Critical Temperature ◽  
Power Law ◽  
Size Effects ◽  
Scattering Length ◽  
Analytical Formula ◽  
Finite Size ◽  
Bose Gas ◽  
Finite Size Effects ◽  
First Order ◽  
Power Law Exponent

We investigate the critical temperature of an interacting Bose gas confined in a trap described by a generic isotropic power-law potential. We compare the results with respect to the non-interacting case. In particular, we derive an analytical formula for the shift of the critical temperature holding to first order in the scattering length. We show that this shift scales as Nn/3(n+2), where N is the number of Bosons and n is the exponent of the power-law potential. Moreover, the sign of the shift critically depends on the power-law exponent n. Finally, we find that the shift of the critical temperature due to finite-size effects vanishes as N-2n/3(n+2).

scholarly journals Finite-size effects in metallic superlattice systems

1995 ◽  
Vol 73 (9-10) ◽  
pp. 545-553
Author(s):  
J. Chen ◽  
R. Kobes ◽  
J. Wang
Keyword(s):  
Critical Temperature ◽  
Simple Model ◽  
Proximity Effect ◽  
Size Effects ◽  
Finite Size ◽  
Cooper Pairs ◽  
Superconducting Layer ◽  
Finite Size Effects ◽  
Realistic Form ◽  
Pair Amplitude

Clean metallic superlattice systems composed of alternating layers of superconducting and normal materials are considered, particularly aspects of the proximity effect as it affects the critical temperature. A simple model is used to address the question of when a finite–sized system theoretically approximates well a true infinite superlattice. The methods used in the analysis afford some tests of the approximation used that the pair amplitude of the Cooper pairs is constant over a superconducting region. We also use these methods to construct a model of a single superconducting layer which intends to incorporate a more realistic form of the pair amplitude than a simple constant.

scholarly journals Finite-size effects in disordered λφ4 model

2016 ◽  
Vol 30 (30) ◽  
pp. 1650207 ◽  
Author(s):  
R. Acosta Diaz ◽  
N. F. Svaiter
Keyword(s):  
Phase Transition ◽  
Long Range ◽  
Power Law ◽  
Order Phase Transition ◽  
Size Effects ◽  
Finite Size ◽  
Second Order ◽  
Finite Size Effects ◽  
Power Law Decay ◽  
Second Order Phase Transition

We discuss finite-size effects in one disordered [Formula: see text] model defined in a [Formula: see text]-dimensional Euclidean space. We consider that the scalar field satisfies periodic boundary conditions in one dimension and it is coupled with a quenched random field. In order to obtain the average value of the free energy of the system, we use the replica method. We first discuss finite-size effects in the one-loop approximation in [Formula: see text] and [Formula: see text]. We show that in both cases, there is a critical length where the system develop a second-order phase transition, when the system presents long-range correlations with power-law decay. Next, we improve the above result studying the gap equation for the size-dependent squared mass, using the composite field operator method. We obtain again that the system present a second-order phase transition with long-range correlation with power-law decay.

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