THERMOSTATISTIC PROPERTIES OF A RELATIVISTIC FERMI GAS

2010 ◽  
Vol 24 (29) ◽  
pp. 5783-5792 ◽  
Author(s):  
SHUKUAN CAI ◽  
GUOZHEN SU ◽  
JINCAN CHEN
Keyword(s):  
Heat Capacity ◽  
Pair Production ◽  
Low Temperatures ◽  
Chemical Potential ◽  
Dimensional Space ◽  
Average Distance ◽  
Relativistic Effects ◽  
Fermi Gas ◽  
Compton Wavelength ◽  
Relativistic Fermi

Thermodynamic properties of a relativistic Fermi gas in any dimensional space are studied, in which the influence of particle–antiparticle pair production is taken into account. It is shown that relativistic effects cannot be ignored even at very low temperatures for the system with the Compton wavelength of a particle comparable with the average distance between particles. The pair production results in some novel characteristics, which include the asymptotic behavior of the chemical potential and the rapid increase in the heat capacity with temperature in the high temperature regions, etc.

STATISTICAL PROPERTIES OF A TRAPPED RELATIVISTIC FERMI GAS WITH PAIR PRODUCTION

2013 ◽  
Vol 27 (24) ◽  
pp. 1350177 ◽  
Author(s):  
GUOZHEN SU ◽  
LIWEI CHEN ◽  
JINCAN CHEN
Keyword(s):  
Pair Production ◽  
Low Temperatures ◽  
Relativistic Effect ◽  
Chemical Potential ◽  
Fermi Gas ◽  
Ideal Gas ◽  
Statistical Properties ◽  
High Temperature Region ◽  
Rest Energy ◽  
Relativistic Fermi

Statistical properties of an ideal gas of relativistic fermions trapped in a D-dimensional power-law potential are studied, in which the effect of particle–antiparticle pair production is taken into account. It is shown that the relativistic effect is considerable even at very low temperatures for the system with Fermi energy comparable with the rest energy of a particle. In contrast, the effect of pair production is significant at high temperatures, but negligible at low temperatures. Moreover, it is found that the pair production results in several novel characteristics, such as the asymptotic behavior of chemical potential and rapid increase of heat capacity in the high temperature region.

RELATIVISTIC EFFECTS IN POLYTROPIC COMPACT STARS

2007 ◽  
Vol 16 (09) ◽  
pp. 2834-2837 ◽  
Author(s):  
L. FERRARI ◽  
G. ESTRELA ◽  
M. MALHEIRO
Keyword(s):  
Equation Of State ◽  
Relativistic Effects ◽  
Fermi Gas ◽  
Matter Density ◽  
Compact Stars ◽  
Polytropic Index ◽  
First Order ◽  
Polytropic Equation ◽  
Relativistic Fermi ◽  
First Order Differential Equations

We solve numerically the two first order differential equations obtained by Tooper for polytropic compact stars. These equations depend on the polytropic index n related to the adiabatic index Γ = 1 + 1/n and on a parameter σ that manifests the relativistic content of the polytropic equation of state (EOS). In this work we investigate the effect of increasing σ for two polytropic EOS: the case of a nonrelativistic Fermi gas (n = 1.5) and the relativistic one (n = 3.0). We show that for large values of σ, where the sound velocity is not small in comparison to the velocity of light, the matter density is more concentrated in the center of the star and as a consequence the star mass also is: this effect is quite strong in the case of the relativistic fermi gas.

scholarly journals ON THE DERIVATION OF THERMODYNAMIC QUANTITIES OF IDEAL FERMI GAS IN HARMONIC TRAP

2017 ◽  
Vol 126 (1B) ◽  
Author(s):  
PHẠM NGUYỄN THÀNH VINH
Keyword(s):  
Heat Capacity ◽  
Total Energy ◽  
Chemical Potential ◽  
Three Dimensional ◽  
Fermi Gas ◽  
Integral Function ◽  
Harmonic Trap ◽  
Thermodynamic Quantities ◽  
Comprehensive Study ◽  
The Ideal

In this paper, we provide comprehensive study of the thermodynamic quantities of the ideal Fermi gas confined in a three-dimensional harmonic trap by using the properties of Fermi – Dirac integral function both analytically and numerically. The dependences of the chemical potential, total energy and heat capacity on the temperature are obtained via the appropriately approximated analytic formulae. Afterwards, the results are compared with the exact numerical ones in order to evaluate the applicability of these formulae.

scholarly journals ON THE DERIVATION OF THERMODYNAMIC QUANTITIES OF IDEAL FERMI GAS IN HARMONIC TRAP

2017 ◽  
Vol 126 (1B) ◽  
pp. 117 ◽  
Author(s):  
Pham Nguyen Thanh Vinh
Keyword(s):  
Heat Capacity ◽  
Total Energy ◽  
Chemical Potential ◽  
Three Dimensional ◽  
Fermi Gas ◽  
Integral Function ◽  
Harmonic Trap ◽  
Thermodynamic Quantities ◽  
Comprehensive Study ◽  
The Ideal

In this paper, we provide comprehensive study of the thermodynamic quantities of the ideal Fermi gas confined in a three-dimensional harmonic trap by using the properties of Fermi – Dirac integral function both analytically and numerically. The dependences of the chemical potential, total energy and heat capacity on the temperature are obtained via the appropriately approximated analytic formulae. Afterwards, the results are compared with the exact numerical ones in order to evaluate the applicability of these formulae.

ChemInform Abstract: THE HEAT CAPACITY OF MANGANESE AND ZINC HEXAFLUOROSILICATES AT LOW TEMPERATURES

1985 ◽  
Vol 16 (46) ◽  
Author(s):  
K. E. HALSTEAD ◽  
D. J. SEDDON ◽  
L. A. K. STAVELEY ◽  
R. D. WEIR
Keyword(s):  
Heat Capacity ◽  
Low Temperatures

scholarly journals Thermal Properties of Stabilized Zirconia at Low Temperatures

1985 ◽  
Vol 38 (4) ◽  
pp. 617 ◽  
Author(s):  
JG Collins ◽  
SJ Collocott ◽  
GK White
Keyword(s):  
Heat Capacity ◽  
Thermal Expansion ◽  
Thermal Properties ◽  
Thermal Expansion Coefficient ◽  
Expansion Coefficient ◽  
Low Temperatures ◽  
Linear Thermal Expansion Coefficient ◽  
Linear Thermal Expansion ◽  
Stabilized Zirconia ◽  
Elastic Data

The linear thermal expansion coefficient a from 2 to 100 K and heat capacity per gram cp from 0�3 to 30 K are reported for fully-stabilized zirconia containing a nominal 16 wt.% (9 mol.%) of yttria. The heat capacity below 7 K has been analysed into a linear (tunnelling?) term, a Schottky term centred at 1�2 K, a Debye term (e~ = 540 K), and a small T5 contribution. The expansion coefficient is roughly proportional to T from 5 to 20 K and gives a limiting lattice Griineisen parameter 'Yo ::::: 5, which agrees with that calculated from elastic data.

Heat Capacity of ThU Alloys at Low Temperatures

1974 ◽  
pp. 585-589 ◽  
Author(s):  
C. A. Luengo ◽  
J. M. Cotignola ◽  
J. Sereni ◽  
A. R. Sweedler ◽  
M. B. Maple
Keyword(s):  
Heat Capacity ◽  
Low Temperatures

scholarly journals Extension of mathematical background for Nearest Neighbour Analysis in three-dimensional space

2013 ◽  
Vol 11 ◽  
pp. 25-36
Author(s):  
Eva Stopková
Keyword(s):  
Dimensional Space ◽  
Average Distance ◽  
Three Dimensional ◽  
Nearest Neighbour ◽  
Mathematical Background ◽  
Area Of Interest ◽  
Nearest Neighbours ◽  
Anisotropic Function ◽  
Neighbour Analysis ◽  
Three Dimensional Space

Proceeding deals with development and testing of the module for GRASS GIS [1], based on Nearest Neighbour Analysis. This method can be useful for assessing whether points located in area of interest are distributed randomly, in clusters or separately. The main principle of the method consists of comparing observed average distance between the nearest neighbours r A to average distance between the nearest neighbours r E that is expected in case of randomly distributed points. The result should be statistically tested. The method for two- or three-dimensional space differs in way how to compute r E . Proceeding also describes extension of mathematical background deriving standard deviation of r E , needed in statistical test of analysis result. As disposition of phenomena (e.g. distribution of birds’ nests or plant species) and test results suggest, anisotropic function would repre- sent relationships between points in three-dimensional space better than isotropic function that was used in this work.

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