Analytical approximations for the Fermi energy of an ideal Fermi gas obeying a nonparabolic dispersion relation

1991 ◽  
Vol 70 (9) ◽  
pp. 5156-5158 ◽  
Author(s):  
R. Beresford
Keyword(s):  
Dispersion Relation ◽  
Fermi Energy ◽  
Fermi Gas ◽  
Analytical Approximations

Fermi–Dirac Statistics

2019 ◽  
pp. 386-403
Author(s):  
Robert H. Swendsen
Keyword(s):  
High Temperature ◽  
Low Temperature ◽  
Specific Heat ◽  
Fermi Energy ◽  
Fermi Gas ◽  
Main Application ◽  
Densities Of States ◽  
Low Temperature Specific Heat ◽  
Very High ◽  
The Ideal

The main application of Fermi–Dirac Statistics is to calculate the properties of electrons. This chapter explains how the properties of fermions account for the behavior of metals. The Fermi energy is introduced and shown to correspond to a very high temperature, so that most properties can be obtained from low-temperature expansions. Both discrete and continuous densities of states are discussed. The Sommerfeld expansion is derived explicitly. The low-temperature specific heat and compressibility are derived. The most important fermions are electrons, and understanding the properties of electrons is central to understanding the properties of all materials. In this chapter we will study the ideal Fermi gas, which turns out to explain many of the properties of electrons in metals.

Analytic approximations for the Fermi energy of an ideal Fermi gas

1977 ◽  
Vol 31 (5) ◽  
pp. 354-356 ◽  
Author(s):  
W. B. Joyce ◽  
R. W. Dixon
Keyword(s):  
Fermi Energy ◽  
Fermi Gas ◽  
Analytic Approximations

scholarly journals The asymptotic theory of dispersion relations containing Bessel functions of imaginary order

2012 ◽  
Vol 468 (2148) ◽  
pp. 4008-4023 ◽  
Author(s):  
C. J. Chapman
Keyword(s):  
Dispersion Relation ◽  
Asymptotic Theory ◽  
Bessel Functions ◽  
Removable Singularity ◽  
Wave Theory ◽  
Dispersion Relations ◽  
Dynamical Problem ◽  
Physical Processes ◽  
Analytical Approximations ◽  
Wide Range

This paper presents a method of analysing wave-field dispersion relations in which Bessel functions of imaginary order occur. Such dispersion relations arise in applied studies in oceanography and astronomy, for example. The method involves the asymptotic theory developed by Dunster in 1990, and leads to simple analytical approximations containing only trigonometric and exponential functions. Comparisons with accurate numerical calculations show that the resulting approximations to the dispersion relation are highly accurate. In particular, the approximations are powerful enough to reveal the fine structure in the dispersion relation and so identify different wave regimes corresponding to different balances of physical processes. Details of the method are presented for the fluid-dynamical problem that stimulated this analysis, namely the dynamics of an internal ocean wave in the presence of an aerated surface layer; the method identifies and gives different approximations for the subcritical, supercritical and critical regimes. The method is potentially useful in a wide range of problems in wave theory and stability theory. A mathematical theme of the paper is that of the removable singularity.

Dispersion relation of excitation mode in spin-polarized Fermi gas

2012 ◽  
Vol 21 (3) ◽  
pp. 030309
Author(s):  
Ke Liu ◽  
Ji-Sheng Chen
Keyword(s):  
Dispersion Relation ◽  
Fermi Gas ◽  
Excitation Mode ◽  
Spin Polarized

scholarly journals A note on the Fermi energy of an ideal Fermi gas trapped under a generic power law potential in d -dimension

2015 ◽  
Vol 36 (5) ◽  
pp. 058003 ◽  
Author(s):  
Mir Mehedi Faruk
Keyword(s):  
Power Law ◽  
Fermi Energy ◽  
Fermi Gas

scholarly journals Analytical approximations of the dispersion relation of a linear chain of metal nanoparticles

2011 ◽  
Vol 284 (7) ◽  
pp. 1822-1827 ◽  
Author(s):  
Massimiliano Guasoni ◽  
Costantino De Angelis
Keyword(s):  
Dispersion Relation ◽  
Metal Nanoparticles ◽  
Linear Chain ◽  
Analytical Approximations

Two-Dimensional Fermi Gas at Half Filling is a Luttinger Liquid

1995 ◽  
Vol 5 (11) ◽  
pp. 1481-1486
Author(s):  
E. Batkilin
Keyword(s):  
Luttinger Liquid ◽  
Fermi Gas ◽  
Two Dimensional ◽  
Half Filling

NON-EQUILIBRIUM NUCLEON EMISSION AROUND THE FERMI ENERGY REGION

1986 ◽  
Vol 47 (C4) ◽  
pp. C4-77-C4-82
Author(s):  
J. N. DE ◽  
S. K. SAMADDAR
Keyword(s):  
Fermi Energy ◽  
Energy Region ◽  
Nucleon Emission ◽  
Non Equilibrium

A New Condition of Formation and Stablity of All Crystalline Systems in a Good Agreement with Experimental Data

2015 ◽  
Vol 11 (3) ◽  
pp. 3224-3228
Author(s):  
Tarek El-Ashram
Keyword(s):  
Experimental Data ◽  
Brillouin Zone ◽  
Electron Concentration ◽  
Free Electron ◽  
Lattice Point ◽  
Valence Electron ◽  
Fermi Gas ◽  
Valence Electron Concentration ◽  
Fermi Sphere ◽  
Good Agreement

In this paper we derived a new condition of formation and stability of all crystalline systems and we checked its validity andit is found to be in a good agreement with experimental data. This condition is derived directly from the quantum conditionson the free electron Fermi gas inside the crystal. The new condition relates both the volume of Fermi sphere VF andvolume of Brillouin zone VB by the valence electron concentration VEC as ;𝑽𝑭𝑽𝑩= 𝒏𝑽𝑬𝑪𝟐for all crystalline systems (wheren is the number of atoms per lattice point).

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