900 research outputs found
Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space
Based on the Bogoliubov non-ideal gas model, we discuss the energy spectrum
and phase transition of the superfluid Fermi gas of atoms with a weak
attractive interaction on the canonical noncommutative space. Because the
interaction of a BCS-type superfluid Fermi gas originates from a pair of
Fermionic quasi-particles with opposite momenta and spins, the Hamiltonian of
the Fermi gas on the noncommutative space can be described in terms of the
ordinary creation and annihilation operators related to the commutative space,
while the noncommutative effect appears only in the coefficients of the
interacting Hamiltonian. As a result, we can rigorously solve the energy
spectrum of the Fermi gas on the noncommutative space exactly following the way
adopted on the commutative space without the use of perturbation theory. In
particular, different from the previous results on the noncommutative
degenerate electron gas and superconductor where only the first order
corrections of the ground state energy level and energy gap were derived, we
obtain the nonperturbative energy spectrum for the noncommutative superfluid
Fermi gas, and find that each energy level contains a corrected factor of
cosine function of noncommutative parameters. In addition, our result shows
that the energy gap becomes narrow and the critical temperature of phase
transition from a superfluid state to an ordinary fluid state decreases when
compared with that in the commutative case
Microscopic structures and thermal stability of black holes conformally coupled to scalar fields in five dimensions
Completely from the thermodynamic point of view, we explore the microscopic
character of a hairy black hole of Einstein's theory conformally coupled to a
scalar field in five dimensions by means of the Ruppeiner thermodynamic
geometry. We demonstrate that the scalar hairy black hole has rich microscopic
structures in different parameter spaces. Moreover, we analyze the thermal
stability of this black hole in detail.Comment: v1: 15 pages, 1 figure; v2: 19 pages, clarifications and references
added; v3: clarifications and references added; v4: 21 pages, clarifications
added; v5: minor clarifications and one reference added, final version to
appear in Nuclear Physics
Thermodynamics of the Schwarzschild-AdS black hole with a minimal length
Using the mass-smeared scheme of black holes, we study the thermodynamics of
black holes. Two interesting models are considered. One is the self-regular
Schwarzschild-AdS black hole whose mass density is given by the analogue to
probability densities of quantum hydrogen atoms. The other model is the same
black hole but whose mass density is chosen to be a rational fractional
function of radial coordinates. Both mass densities are in fact analytic
expressions of the -function. We analyze the phase structures of the
two models by investigating the heat capacity at constant pressure and the
Gibbs free energy in an isothermal-isobaric ensemble. Both models fail to decay
into the pure thermal radiation even with the positive Gibbs free energy due to
the existence of a minimal length. Furthermore, we extend our analysis to a
general mass-smeared form that is also associated with the -function,
and indicate the similar thermodynamic properties for various possible
mass-smeared forms based on the -function.Comment: v1: 25 pages, 14 figures; v2: 26 pages, 15 figures; v3: minor
revisions, final version to appear in Adv. High Energy Phy
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