Applications of Mellin transforms to the statistical mechanics of ideal quantum gases

1981 ◽  
Vol 49 (6) ◽  
pp. 570-578 ◽  
Author(s):  
W. T. Grandy ◽  
S. Goulart Rosa
Keyword(s):  
Statistical Mechanics ◽  
Quantum Gases ◽  
Mellin Transforms ◽  
Ideal Quantum

scholarly journals Performance Analysis and Optimization for Irreversible Combined Carnot Heat Engine Working with Ideal Quantum Gases

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 536
Author(s):  
Lingen Chen ◽  
Zewei Meng ◽  
Yanlin Ge ◽  
Feng Wu
Keyword(s):  
Power Output ◽  
Thermal Efficiency ◽  
Combined Cycle ◽  
Quantum Gases ◽  
Carnot Cycle ◽  
Leakage Loss ◽  
Optimal Power ◽  
Heat Leakage ◽  
Working Medium ◽  
Ideal Quantum

An irreversible combined Carnot cycle model using ideal quantum gases as a working medium was studied by using finite-time thermodynamics. The combined cycle consisted of two Carnot sub-cycles in a cascade mode. Considering thermal resistance, internal irreversibility, and heat leakage losses, the power output and thermal efficiency of the irreversible combined Carnot cycle were derived by utilizing the quantum gas state equation. The temperature effect of the working medium on power output and thermal efficiency is analyzed by numerical method, the optimal relationship between power output and thermal efficiency is solved by the Euler-Lagrange equation, and the effects of different working mediums on the optimal power and thermal efficiency performance are also focused. The results show that there is a set of working medium temperatures that makes the power output of the combined cycle be maximum. When there is no heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are parabolic-like ones, and the internal irreversibility makes both power output and efficiency decrease. When there is heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are loop-shaped ones, and the heat leakage loss only affects the thermal efficiency of the combined Carnot cycle. Comparing the power output of combined heat engines with four types of working mediums, the two-stage combined Carnot cycle using ideal Fermi-Bose gas as working medium obtains the highest power output.

scholarly journals D-DIMENSIONAL IDEAL QUANTUM GASES IN A Arn+Br-n POTENTIAL

2003 ◽  
Vol 17 (25) ◽  
pp. 1321-1330 ◽  
Author(s):  
AHMED JELLAL ◽  
MOHAMMED DAOUD
Keyword(s):  
Semiclassical Approximation ◽  
Quantum Gases ◽  
Einstein Condensation ◽  
Density Profiles ◽  
Ideal Gases ◽  
Power Law Exponent ◽  
Ideal Quantum ◽  
Bose Einstein ◽  
Physical Quantities ◽  
Number Of Particles

This paper is concerned with thermostatistics of both D-dimensional Bose and Fermi ideal gases in a confining potential of type Arn+Br-n, where A, B are strictly positive constants and n is the power-law exponent. The investigation is performed in the framework of the semiclassical approximation. Some physical quantities for such systems are derived, like the density of states, density profiles and the number of particles. Bose–Einstein condensation (BEC) is discussed in the high and low temperature limits corresponding to T→∞ and T→0, respectively.

scholarly journals Heat kernel approach for confined quantum gas

2020 ◽  
Vol 35 (13) ◽  
pp. 2050100
Author(s):  
Ping Zhang ◽  
Tong Liu
Keyword(s):  
Heat Kernel ◽  
Equations Of State ◽  
Dimensional Space ◽  
Quantum Gases ◽  
Thermodynamic Quantities ◽  
Quantum Gas ◽  
Confined Space ◽  
Kernel Approach ◽  
Ideal Quantum ◽  
The One

In this paper, based on the heat kernel technique, we calculate equations of state and thermodynamic quantities for ideal quantum gases in confined space with external potential. Concretely, we provide expressions for equations of state and thermodynamic quantities by means of heat kernel coefficients for ideal quantum gases. Especially, using an analytic continuation treatment, we discuss the application of the heat kernel technique to Fermi gases in which the expansion diverges when the fugacity [Formula: see text]. In order to calculate the modification of heat kernel coefficients caused by external potentials, we suggest an approach for calculating the expansion of the global heat kernel of the operator [Formula: see text] based on an approximate method of the calculation of spectrum in quantum mechanics. We discuss the properties of quantum gases under the condition of weak and complete degeneration, respectively. Moreover, we give an expansion of the one-loop effective action in D-dimensional space.

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