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.

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 ⊙.

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.

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 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.

scholarly journals Susceptibilities and critical exponents within the Nambu–Jona-Lasinio model

2015 ◽  
Vol 30 (34) ◽  
pp. 1550199 ◽  
Author(s):  
Yi-Lun Du ◽  
Ya Lu ◽  
Shu-Sheng Xu ◽  
Zhu-Fang Cui ◽  
Chao Shi ◽  
...  
Keyword(s):  
Critical Exponents ◽  
Chemical Potential ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Coupled Equations ◽  
Theoretical Predictions ◽  
The Mean ◽  
Chiral Susceptibility ◽  
Quark Number Susceptibility

In the mean field approximation of (2 + 1)-flavor Nambu–Jona-Lasinio model, we strictly derive several sets of coupled equations for the chiral susceptibility, the quark number susceptibility, etc. at finite temperature and quark chemical potential. The critical exponents of these susceptibilities in the vicinity of the QCD critical end point (CEP) are presented in SU(2) and SU(3) cases, respectively. It is found that these various susceptibilities share almost the same critical behavior near the CEP. The comparisons between the critical exponents for the order parameters and the theoretical predictions are also included.

Critical phenomena: General considerations. Mean-field theory (MFT)

2021 ◽  
pp. 324-356
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Critical Temperature ◽  
Critical Phenomena ◽  
Correlation Length ◽  
Particle Physics ◽  
Mean Field ◽  
Lattice Models ◽  
Field Approximation ◽  
Phase Region ◽  
Mean Field Approximation ◽  
The Mean

This chapter is devoted to a brief review of general properties of phase transitions in macroscopic physics and, in particular in lattice models. Some of these lattice models actually appear as lattice regularizations of Euclidean (imaginary time) quantum physics theory (QFT). Most of the transitions considered in this work have the following character: spins on the lattice, or macroscopic particles in the continuum, interact through short-range forces, assumed, for simplicity, to decay exponentially. For simple systems, it is possible to find a local observable, called order parameter, whose expectation values depend on the phase in the several phase region, for example, the spin in ferromagnetic systems. In the disordered phase, the connected two-point function decreases exponentially at large distance, at a rate characterized by the correlation length (the inverse of the smallest physical mass in particle physics). In continuous transitions, the correlation length diverges at the critical temperature. Within the mean-field approximation (consistent with Landau's theory of critical phenomena), it can be shown that the singular behaviour of thermodynamic quantities at the critical temperature is universal. These properties can also be reproduced by calculating correlation functions with a perturbed Gaussian measure. It is then shown that the leading corrections to the mean-field approximation, in Ising-like systems, diverge at the critical temperature for dimensions smaller than or equal to $4$.

scholarly journals DAMPING IN TWO-COMPONENT BOSE GAS

2014 ◽  
Vol 28 (04) ◽  
pp. 1450029 ◽  
Author(s):  
ARANYA B. BHATTACHERJEE
Keyword(s):  
Mean Field ◽  
Field Approximation ◽  
Bose Gas ◽  
The Other ◽  
Mean Field Approximation ◽  
Collective Modes ◽  
Elementary Excitations ◽  
Two Component ◽  
Atom Interaction ◽  
The Mean

In this paper, we investigate the Landau and Baliaev damping of the collective modes in a two-component Bose gas using the mean-field approximation. We show that due to the two body atom–atom interaction, oscillations of each component is coupled to the thermal excitations of the other component which gives rise to creation or destruction of the elementary excitations that can take place in the two separate components. In addition, we find that the damping is also enhanced due to inter-component coupling.

Sign in / Sign up

Export Citation Format

Share Document