scholarly journals THERMODYNAMICAL PROPERTIES OF A TRAPPED INTERACTING BOSE GAS

2012 ◽  
Vol 26 (08) ◽  
pp. 1250053 ◽  
Author(s):  
SHI-JIE YANG ◽  
YUECHAN LIU ◽  
SHIPING FENG
Keyword(s):  
Chemical Potential ◽  
Mean Field ◽  
Interaction Strength ◽  
Field Potential ◽  
Ideal Gas ◽  
Mean Field Approximation ◽  
Pitaevskii Equation ◽  
Condensation Temperature ◽  
Universal Relation ◽  
Thermodynamical Properties

The thermodynamical properties of interacting Bose atoms in a harmonic potential are studied within the mean-field approximation. For weak interactions, the quantum statistics is equivalent to an ideal gas in an effective mean-field potential. The eigenvalue of the Gross–Pitaevskii equation is identified as the chemical potential of the ideal gas. The condensation temperature and density profile of atoms are calculated. It is found that the critical temperature Tc decreases as the interactions increase. Below the critical point, the condensation fraction exhibits a universal relation of N0/N = 1-(T/Tc)γ, with the index γ ≈ 2.3 independent of the interaction strength, the chemical potential, as well as the frequency of the confining potential.

CRITICAL TEMPERATURE OF A WEAKLY INTERACTING BOSE GAS IN A POWER-LAW POTENTIAL

2003 ◽  
Vol 17 (12) ◽  
pp. 2439-2446 ◽  
Author(s):  
HIDENORI SUZUKI ◽  
MASUO SUZUKI
Keyword(s):  
Critical Temperature ◽  
Chemical Potential ◽  
Particle Density ◽  
Dimensional Space ◽  
Mean Field ◽  
Bose Gas ◽  
Ideal Gas ◽  
Mean Field Approximation ◽  
Weakly Interacting ◽  
The Mean

The critical temperature T c of a weakly interacting Bose gas in an isotropic power-low potential is investigated in the mean-field approximation by taking into account the fact that the particle density distribution function appearing in the mean-field depends on the chemical potential. We derive the general formula of the shift of T c from that of the ideal gas to the lowest order of an interaction. In three-dimensional space, we show that the shift of T c changes its sign from a negative value for n < 3 to a positive one for n > 3, where n is the exponent of the power-low potential.

scholarly journals Locating the critical end point using the linear sigma model coupled to quarks.

2018 ◽  
Vol 172 ◽  
pp. 02003
Author(s):  
Alejandro Ayala ◽  
J. A. Flores ◽  
L. A. Hernández ◽  
S. Hernández-Ortiz
Keyword(s):  
Sigma Model ◽  
Chemical Potential ◽  
Potential Temperature ◽  
Mean Field ◽  
Field Approximation ◽  
Baryon Density ◽  
Linear Sigma Model ◽  
Mean Field Approximation ◽  
End Point ◽  
The Mean

We use the linear sigma model coupled to quarks to compute the effective potential beyond the mean field approximation, including the contribution of the ring diagrams at finite temperature and baryon density. We determine the model couplings and use them to study the phase diagram in the baryon chemical potential-temperature plane and to locate the Critical End Point.

scholarly journals SU(3) Polyakov linear-sigma model with finite isospin asymmetry: QCD phase diagram

2019 ◽  
Vol 34 (31) ◽  
pp. 1950199 ◽  
Author(s):  
Abdel Nasser Tawfik ◽  
Abdel Magied Diab ◽  
M. T. Ghoneim ◽  
H. Anwer
Keyword(s):  
Phase Structure ◽  
Sigma Model ◽  
Chemical Potential ◽  
Mean Field ◽  
Field Approximation ◽  
Linear Sigma Model ◽  
Dense Medium ◽  
Mean Field Approximation ◽  
Isospin Asymmetry ◽  
Qcd Phase Diagram

The SU(3) Polyakov linear-sigma model (PLSM) in mean-field approximation is utilized in analyzing the chiral condensates [Formula: see text], [Formula: see text], [Formula: see text] and the deconfinement order parameters [Formula: see text], [Formula: see text], at finite isospin asymmetry. The bulk thermodynamics including pressure density, interaction measure, susceptibility and second-order correlations with baryon, strange and electric charge quantum numbers are studied in thermal and dense medium. The PLSM results are confronted to the available lattice quantum chromodynamics (QCD) calculations. The excellent agreement obtained strengthens the reliability of fixing the PLSM parameters and therefore supports further predictions even beyond the scope of the lattice QCD numerical applicability. From the QCD phase structure at finite isospin chemical potential [Formula: see text], we find that the pseudocritical temperatures decrease with the increase in [Formula: see text]. We conclude that the QCD phase structure in [Formula: see text] plane seems to extend the one in [Formula: see text] plane.

THE ROLE OF ANTIKAON CONDENSATES IN THE EQUATION OF STATE OF NEUTRON STARS

2010 ◽  
Vol 19 (08n10) ◽  
pp. 1545-1548 ◽  
Author(s):  
F. FERNÁNDEZ ◽  
A. MESQUITA ◽  
M. RAZEIRA ◽  
C. A. Z. VASCONCELLOS
Keyword(s):  
Neutron Stars ◽  
Electric Charge ◽  
Chemical Potential ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Charge Neutrality ◽  
The Mean ◽  
Nucleon Matter

We study the consequences of the presence of a negative electric charge condensate of antikaons in neutron stars using an effective model with derivative couplings. In our formalism, nucleons interact through the exchange of σ, ω and ϱ mesons, in the presence of electrons and muons, to accomplish electric charge neutrality and beta equilibrium. The phase transition to the antikaon condensate was implemented through the Gibbs conditions combined with the mean-field approximation, giving rise to a mixed phase of coexistence between nucleon matter and the antikaon condensate. Assuming neutrino-free matter, we observe a rapid decrease of the electron chemical potential produced by the gradual substitution of electrons by kaons to accomplish electric charge neutrality. The exotic composition of matter in neutron star including antikaon condensation and nucleons can yield a maximum mass of about M ns ~ 1.76 M ⊙.

scholarly journals VECTOR-LIKE CONTRIBUTIONS FROM OPTIMIZED PERTURBATION IN THE ABELIAN NAMBU–JONA-LASINIO MODEL FOR COLD AND DENSE QUARK MATTER

2012 ◽  
Vol 21 (03) ◽  
pp. 1250017 ◽  
Author(s):  
JEAN-LOÏC KNEUR ◽  
MARCUS BENGHI PINTO ◽  
RUDNEI O. RAMOS ◽  
EDERSON STAUDT
Keyword(s):  
Chemical Potential ◽  
Percent Level ◽  
Mean Field ◽  
Physical Nature ◽  
Temperature Limit ◽  
Field Approximation ◽  
Scalar Coupling ◽  
Mean Field Approximation ◽  
Vector Coupling ◽  
Hartree Fock

Two-loop corrections for the standard Abelian Nambu–Jona-Lasinio model are obtained with the optimized perturbation theory (OPT) method. These contributions improve the usual mean-field and Hartree–Fock results by generating a 1/Nc suppressed term, which only contributes at finite chemical potential. We take the zero temperature limit observing that, within the OPT, chiral symmetry is restored at a higher chemical potential μ, while the resulting equation of state is stiffer than the one obtained when mean-field is applied to the standard version of the model. In order to understand the physical nature of these finite Nc contributions, we perform a numerical analysis to show that the OPT quantum corrections mimic effective repulsive vector–vector interaction contributions. We also derive a simple analytical approximation for the mass gap, accurate at the percent level, matching the mean-field approximation extended by an extra vector channel to OPT. For μ ≳ μc the effective vector coupling matching OPT is numerically close (for the Abelian model) to the Fierz-induced Hartree–Fock value G/(2Nc), where G is the scalar coupling, and then increases with μ in a well-determined manner.

ANALYSIS OF THE TWO-DIMENSIONAL NEGATIVE-U HUBBARD MODEL BY COMPOSITE OPERATOR METHOD

1996 ◽  
Vol 10 (22) ◽  
pp. 2745-2756 ◽  
Author(s):  
T. DI MATTEO ◽  
F. MANCINI ◽  
S. MARRA ◽  
H. MATSUMOTO
Keyword(s):  
Hubbard Model ◽  
Chemical Potential ◽  
Particle Density ◽  
Mean Field ◽  
Finite Size ◽  
Operator Method ◽  
Field Approximation ◽  
Composite Operator ◽  
Mean Field Approximation ◽  
Two Dimensional

The two-dimensional negative-U Hubbard model is studied by means of the composite operator approach. In a generalized mean-field approximation we calculate different quantities, as the chemical potential, the double occupancy, the static uniform spin magnetic susceptibility and the density of states for various values of the particle density, attractive on-site interaction and temperature. Comparison with the results obtained by numerical analysis on finite size lattices shows a good agreement.

THE ROLE OF SCALAR-ISOVECTOR MESONS AND ANTIKAONS IN NEUTRON STARS

2010 ◽  
Vol 19 (08n10) ◽  
pp. 1549-1552 ◽  
Author(s):  
A. MESQUITA ◽  
M. RAZEIRA ◽  
C. A. Z. VASCONCELLOS ◽  
F. FERNÁNDEZ
Keyword(s):  
Phase Transition ◽  
Electric Charge ◽  
Optical Potential ◽  
Chemical Potential ◽  
Mean Field ◽  
Field Approximation ◽  
Hadronic Matter ◽  
Mean Field Approximation ◽  
Charge Neutrality ◽  
Nucleon Matter

We study the effects of the scalar-isovector meson δ and those of a new light scalar-isovector resonance ς on the phase transition of hadronic matter to hadronic matter with a condensate of antikaons, using an effective model with derivative couplings. In our formalism, nucleons interact through the exchange of σ, ω, ϱ, δ, and ς mesons in the presence of electrons and muons to accomplish electric charge neutrality and beta equilibrium. The phase-transition to the antikaon condensate was implemented through the Gibbs conditions combined with the mean-field approximation, giving rise to a mixed phase of coexistence between nucleon matter and the condensed antikaons. Scalar-isovector mesons operate for restoring isospin symmetry and reduce this way the value of the effective nucleon mass, independent of the depth of the optical potential for antikaons. Moreover, as expected we found that an increase of the depth of optical potential favors the population of antikaons. Finally, assuming neutrino-free matter, we observe a rapid decrease of the electron chemical potential produced by the gradual substitution of electrons by kaons to accomplish electric charge neutrality.

scholarly journals Non-Hermitian BCS-BEC crossover of Dirac fermions

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Takuya Kanazawa
Keyword(s):  
Chiral Symmetry ◽  
Chemical Potential ◽  
Chiral Symmetry Breaking ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Dirac Fermions ◽  
Coupling Constant ◽  
Dynamical Mass ◽  
The Mean

Abstract We investigate chiral symmetry breaking in a model of Dirac fermions with a complexified coupling constant whose imaginary part represents dissipation. We introduce a chiral chemical potential and observe that for real coupling a relativistic BCS-BEC crossover is realized. We solve the model in the mean-field approximation and construct the phase diagram as a function of the complex coupling. It is found that the dynamical mass increases under dissipation, although the chiral symmetry gets restored if dissipation exceeds a threshold.

scholarly journals Impurities in a one-dimensional Bose gas: the flow equation approach

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Fabian Brauneis ◽  
Hans-Werner Hammer ◽  
Mikhail Lemeshko ◽  
Artem Volosniev
Keyword(s):  
Mean Field ◽  
Interaction Strength ◽  
Field Approximation ◽  
Flow Equation ◽  
Mean Field Approximation ◽  
Bose Gases ◽  
One Dimensional ◽  
Flow Equations ◽  
Impurity Interaction ◽  
The Mean

A few years ago, flow equations were introduced as a technique for calculating the ground-state energies of cold Bose gases with and without impurities[1,2]. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the densities, and phase fluctuations of one-dimensional Bose gases with one and two impurities. For a single mobile impurity, we use flow equations to validate the mean-field results obtained upon the Lee-Low-Pines transformation. We show that the mean-field approximation is accurate for all values of the boson-impurity interaction strength as long as the phase coherence length is much larger than the healing length of the condensate. For two static impurities, we calculate impurity-impurity interactions induced by the Bose gas. We find that leading order perturbation theory fails when boson-impurity interactions are stronger than boson-boson interactions. The mean-field approximation reproduces the flow equation results for all values of the boson-impurity interaction strength as long as boson-boson interactions are weak.

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