scholarly journals THERMODYNAMIC PROPERTIES OF AN INTERACTING HARD-SPHERE BOSE GAS IN A TRAP USING THE STATIC FLUCTUATION APPROXIMATION

2010 ◽  
Vol 24 (24) ◽  
pp. 4779-4809 ◽  
Author(s):  
SALEEM I. QASHOU ◽  
MOHAMED K. AL-SUGHEIR ◽  
ASAAD R. SAKHEL ◽  
HUMAM B. GHASSIB
Keyword(s):  
Thermodynamic Properties ◽  
Hard Sphere ◽  
Occupation Number ◽  
Interaction Strength ◽  
Bose Gas ◽  
Weakly Interacting ◽  
Oscillator Wave Function ◽  
Static Fluctuation Approximation ◽  
Static Fluctuation ◽  
Number Of Particles

A hard-sphere (HS) Bose gas in a trap is investigated at finite temperatures in the weakly interacting regime and its thermodynamic properties are evaluated using the static fluctuation approximation. The energies are calculated with a second-quantized many-body Hamiltonian and a harmonic oscillator wave function. The specific heat capacity, internal energy, pressure, entropy, and the Bose–Einstein occupation number of the system are determined as functions of temperature and for various values of interaction strength and number of particles. It is found that the number of particles plays a more profound role in the determination of the thermodynamic properties of the system than the HS diameter characterizing the interaction, that the critical temperature drops with the increase of the repulsion between the bosons, and that the fluctuations in the energy are much smaller than the energy itself in the weakly interacting regime.

scholarly journals Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas

2021 ◽  
Vol 60 (3) ◽  
Author(s):  
Phan Thành Nam ◽  
Marcin Napiórkowski
Keyword(s):  
Density Matrix ◽  
Ground State ◽  
Mean Field ◽  
Interaction Strength ◽  
Bose Gas ◽  
Body Density ◽  
The Mean ◽  
The One ◽  
Mean Field Regime ◽  
Number Of Particles

AbstractWe consider the homogeneous Bose gas on a unit torus in the mean-field regime when the interaction strength is proportional to the inverse of the particle number. In the limit when the number of particles becomes large, we derive a two-term expansion of the one-body density matrix of the ground state. The proof is based on a cubic correction to Bogoliubov’s approximation of the ground state energy and the ground state.

scholarly journals Harmonically trapped one-dimensional Fermi gas using the static fluctuation approximation

2016 ◽  
Vol 94 (1) ◽  
pp. 47-57 ◽  
Author(s):  
H.A. Al-Khzon ◽  
H.B. Ghassib ◽  
Mohamed K. Al-Sugheir
Keyword(s):  
Magnetic Field ◽  
Heat Capacity ◽  
Chemical Potential ◽  
Attractive Potential ◽  
Large N ◽  
Static Fluctuation Approximation ◽  
Trapped Fermions ◽  
Static Fluctuation ◽  
The Magnetic Field ◽  
Number Of Particles

A system of a finite number of harmonically trapped fermions in one dimension, in the presence of a static magnetic field, is studied within the framework of the static fluctuation approximation, for different repulsive and attractive potential strengths. Specifically, the thermodynamic properties of the system (the chemical potential, total energy, heat capacity, and entropy), as well as its magnetic properties (the magnetization and susceptibility), are calculated. It is observed that the system remains in an ordered phase for a small number of particles N, even at high temperatures T. Disorder sets in for large N, even at low T. The effect of the potential strength on the heat capacity is particularly tangible in the region bordering the quantum and classical regimes. The effect of the temperature (representing disorder) is directly opposite to that of the magnetic field (representing order), as expected on basic physical grounds. These features are consistent with experimental results.

Thermodynamic properties of spin-imbalance harmonically trapped one-dimensional attractive 6Li atomic gas

2021 ◽  
Vol 35 (04) ◽  
pp. 2150059
Author(s):  
H. A. Al-Khzon ◽  
M. K. Al-Sugheir
Keyword(s):  
Thermodynamic Properties ◽  
Spin Polarization ◽  
Mean Field ◽  
Interaction Strength ◽  
Fflo State ◽  
Contact Potential ◽  
Gas System ◽  
Atomic Gas ◽  
Spin Populations ◽  
Static Fluctuation

The thermodynamic properties of 6Li atomic gas system, with imbalanced spin populations trapped in one-dimension, were systematically investigated using the Static Fluctuation Approximation. The two-body interaction used is an attractive contact potential. The effects of gas parameter [Formula: see text] and spin polarization [Formula: see text], on the thermodynamic properties and effective magnetic field were investigated. We observed a decrease in [Formula: see text] and an enhancement in [Formula: see text] and [Formula: see text] with increasing [Formula: see text]. At strong interaction and at [Formula: see text], the behavior of entropy with [Formula: see text] indicated two different phases. At small spin polarization [Formula: see text], the system could be in Fulde–Ferrell–Larkin Ovchinnikov (FFLO) state, while above [Formula: see text], the system might be in normal state. In addition, we found a clear decrease in both [Formula: see text] and [Formula: see text] and an enhancement in [Formula: see text] with the increase of the interaction strength. Our results are consistent with the reported results obtained by the mean-field Bogoliubov–de Gennes method, the Bardeen–Cooper–Schrieffer (BCS) approximation and Nozieres–Schmitt–Rink (NSR) theory.

scholarly journals Thermodynamic properties of graphene using the static fluctuation approximation (SFA)

2017 ◽  
Vol 95 (3) ◽  
pp. 211-219 ◽  
Author(s):  
Mustafa M. Hawamdeh ◽  
Mohamed K. Al-Sugheir ◽  
Ayman S. Sandouqa ◽  
Humam B. Ghassib
Keyword(s):  
Thermodynamic Properties ◽  
Statistical Mechanics ◽  
Ideal Gas ◽  
Two Dimensional ◽  
Nonextensive Statistical Mechanics ◽  
Static Fluctuation Approximation ◽  
Entropy Parameter ◽  
The Mean ◽  
Static Fluctuation ◽  
Good Agreement

The thermodynamic properties of two-dimensional graphene nanosystems are investigated using the static fluctuation approximation (SFA). These properties are analyzed using both extensive and nonextensive statistical mechanics. It is found that these properties are less sensitive to temperature when using nonextensive — in contrast to extensive — statistical mechanics. It is also noted that the mean internal energy and the specific heat behave as a power law, Tα, at T < 8 eV; whereas they go to the classical limit for the two-dimensional ideal gas at T > 8 eV. The results are presented in a set of figures and one table. The roles played by the number of particles and the entropy parameter q are underlined. Whenever possible, comparisons are made to previous studies. It is concluded that Boltzmann–Gibbs statistics are not valid for some cases, and that SFA results are in good agreement with those obtained within other formalisms.

A microscopic study of neon and argon gases within the static fluctuation approximation (SFA)

2018 ◽  
Vol 32 (16) ◽  
pp. 1850203
Author(s):  
H. B. Ghassib ◽  
A. S. Sandouqa ◽  
B. R. Joudeh ◽  
I. F. Al-Maaitah ◽  
A. N. Akour ◽  
...  
Keyword(s):  
Experimental Data ◽  
Monte Carlo ◽  
Thermodynamic Properties ◽  
Specific Heat ◽  
Internal Energy ◽  
Microscopic Study ◽  
Ideal Gas ◽  
Static Fluctuation Approximation ◽  
Static Fluctuation ◽  
The Ideal

The thermodynamic properties of neon and argon gases are studied within the static fluctuation approximation (SFA). These properties include the total internal energy, pressure, entropy, compressibility and specific heat. The results are compared with those recently obtained within the Galitskii–Migdal–Feynman (GMF) formalism. The overall agreement is very good. An exception, however, is the specific-heat results for neon. While SFA gives results rather similar to those of the ideal gas, the corresponding GMF results are quite different. It is argued that the discrepancy seems to have arisen from quantum effects in conformity with very recent Monte Carlo computations. Whenever possible, our SFA results are compared to experimental data.

On the range of validity of the static fluctuation approximation (SFA) in the description of a 1D trapped Bose gas

2013 ◽  
Vol 425 ◽  
pp. 105-111 ◽  
Author(s):  
Saleem I. Qashou ◽  
Asaad R. Sakhel ◽  
Roger R. Sakhel ◽  
Humam B. Ghassib
Keyword(s):  
Bose Gas ◽  
Static Fluctuation Approximation ◽  
Static Fluctuation
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