Bec in Nonextensive Statistical Mechanics

We investigate within density functional theory various physical properties of the zero-temperature unitary Fermi gas which critically depend on the presence of a dispersive gradient term in the equation of state. First, we consider the unitary Fermi superfluid gas confined to a semi-infinite domain and calculate analytically its density profile and surface tension. Then we study the quadrupole modes of the superfluid system under harmonic confinement finding a reliable analytical formula for the oscillation frequency, which reduces to the familiar Thomas-Fermi one in the limit of a large number of atoms. Finally, we discuss the formation and propagation of dispersive shock waves in the collision between two resonant fermionic clouds, and compare our findings with recent experimental results

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“…The numerical results of the figure can quite well be captured by a time-dependent Gaussian variational approach [39]. We set…”

Section: Quadrupole Oscillationsmentioning

confidence: 97%

“…From this effective Lagrangian we calculate analytically the small oscillations around the equilibrium configuration, following the procedure described in Ref. [39]. In this way we get the following formula for the frequency of the quadrupole mode:…”

Section: Quadrupole Oscillationsmentioning

confidence: 99%

Dispersive Effects in the Unitary Fermi Gas

2012

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“…12 Recently, we have also afforded the study of the thermodynamics of interacting Bose gases in harmonic potential. 13,14 In this paper, we investigate the thermal properties of both Bose and Fermi ideal gases in a generic confining external potential. All the calculations are performed by assuming a D-dimensional space.…”

Section: Introductionmentioning

confidence: 99%

Ideal quantum gases in D-dimensional space and power-law potentials

Salasnich

2000

Journal of Mathematical Physics

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We investigate ideal quantum gases in D-dimensional space and confined in a generic external potential by using the semiclassical approximation. In particular, we derive density of states, density profiles and critical temperatures for Fermions and Bosons trapped in isotropic power-law potentials. From such results, one can easily obtain those of quantum gases in a rigid box and in a harmonic trap. Finally, we show that the Bose-Einstein condensation can set up in a confining power-law potential if and only if D/2 + D/n >1, where D is the space dimension and n is the power-law exponent

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“…Figs. 15 shows the temperature dependence of the inversed susceptibility 1/χ calculated by the IA and FA for q = 0.8, 1.0 and 1.2. The Curie temperature T C , which is realized at 1/χ = 0, is monotonously decreased with increasing q in the IA, which is different from its q dependence in the FA, as shown in Fig.…”

Section: Spin Susceptibilitymentioning

confidence: 99%

“…(1 − q)(n + 1)x] −q) = [e −x q ] (n+1) in Eqs (15). and(21)except for q = 1.0. f IA q (ǫ, β) given by Eqs.…”

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confidence: 99%

The interpolation approach to nonextensive quantum statistics

Hasegawa

2010

Physica A: Statistical Mechanics and its Applications

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a b s t r a c tRecently it has been shown by the present author [H. Hasegawa, Phys. Rev. E 80 (2009) 011126] that the interpolation approximation (IA) to the generalized Bose-Einstein and Fermi-Dirac distributions yields good results in agreement with the exact ones within the O(q − 1) and in high-and low-temperature limits, where (q − 1) expresses the nonextensivity: the case of q = 1 corresponding to the conventional quantal distributions. This paper reports applications of the IA to four nonextensive quantum subjects: (i) the blackbody radiation, (ii) the Bose-Einstein condensation, (iii) the BCS superconductivity and (iv) itinerant-electron (metallic) ferromagnetism. Effects of the nonextensivity on physical quantities in these nonextensive quantum systems have been investigated. Comparisons between the calculated results and available observed data are made for the subjects (ii) and (iii). It has been pointed out that the factorization approximation (FA) which has been so far applied to many nonextensive systems, overestimates the nonextensivity and that it leads to inappropriate results for fermion systems like the subjects (iii) and (iv).

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Bec in Nonextensive Statistical Mechanics

Cited by 25 publications

References 12 publications

Dispersive Effects in the Unitary Fermi Gas

Dispersive Effects in the Unitary Fermi Gas

Ideal quantum gases in D-dimensional space and power-law potentials

The interpolation approach to nonextensive quantum statistics

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