Polylogarithmic analysis of chemical potential and fluctuations in a D‐dimensional free Fermi gas at low temperatures

1995 ◽  
Vol 36 (3) ◽  
pp. 1217-1231 ◽  
Author(s):  
M. Howard Lee
Keyword(s):  
Low Temperatures ◽  
Chemical Potential ◽  
Fermi Gas ◽  
Free Fermi

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.

scholarly journals Bose-Einstein Condensation of Confined Atomic Gases at Ultra Low Temperatures

2017 ◽  
Vol 9 (5) ◽  
pp. 96
Author(s):  
M. Serhan
Keyword(s):  
Low Temperatures ◽  
Chemical Potential ◽  
Scattering Length ◽  
Einstein Condensation ◽  
Pitaevskii Equation ◽  
Atomic Gases ◽  
Bose Einstein Condensation ◽  
Gaussian Type ◽  
Negative Scattering Length ◽  
Bose Einstein

In this work I solve the Gross-Pitaevskii equation describing an atomic gas confined in an isotropic harmonic trap by introducing a variational wavefunction of Gaussian type. The chemical potential of the system is calculated and the solutions are discussed in the weakly and strongly interacting regimes. For the attractive system with negative scattering length the maximum number of atoms that can be put in the condensate without collapse begins is calculated.

scholarly journals Thermodynamics of Low-Dimensional Trapped Fermi Gases

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Francisco J. Sevilla
Keyword(s):  
Isothermal Compressibility ◽  
Chemical Potential ◽  
Particle Density ◽  
Fermi Gas ◽  
Fermi Gases ◽  
Nonmonotonic Dependence ◽  
Characteristic Temperatures ◽  
Low Dimensionality ◽  
Thermodynamic Regime ◽  
Low Dimensional

The effects of low dimensionality on the thermodynamics of a Fermi gas trapped by isotropic power-law potentials are analyzed. Particular attention is given to different characteristic temperatures that emerge, at low dimensionality, in the thermodynamic functions of state and in the thermodynamic susceptibilities (isothermal compressibility and specific heat). An energy-entropy argument that physically favors the relevance of one of these characteristic temperatures, namely, the nonvanishing temperature at which the chemical potential reaches the Fermi energy value, is presented. Such an argument allows interpreting the nonmonotonic dependence of the chemical potential on temperature, as an indicator of the appearance of a thermodynamic regime, where the equilibrium states of a trapped Fermi gas are characterized by larger fluctuations in energy and particle density as is revealed in the corresponding thermodynamics susceptibilities.

scholarly journals Modified Josephson Relation

2003 ◽  
Vol 17 (18n20) ◽  
pp. 3407-3410
Author(s):  
Jan Koláček ◽  
Pavel Lipavský
Keyword(s):  
Electric Field ◽  
Low Temperatures ◽  
Ohmic Contacts ◽  
Chemical Potential ◽  
Electrochemical Potential ◽  
Type Ii ◽  
Type Ii Superconductors ◽  
Effective Electric Field

For type II superconductors, Josephson has shown that vortices moving with velocity v L create an effective electric field E′= -v L ×B V . By definition the effective electric field is gradient of the electrochemical potential, what is the quantity corresponding to voltage observed with the use of Ohmic contacts. It relates to the true electric field E via the local chemical potential μ as E′=E-∇μ/e. We argue that at low temperatures the true electric field in the bulk can be approximated by a modified Josephson relation E=(v S -v L )×B V , where v S is the condensate velocity.

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