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انجمن اپتیک و فوتونیک ایران

Two-dimensional free massless Fermi theory at finite chemical potential in the Thermo-field Dynamics approach

Marjan Jafari

Published Mar 15, 2015• 0 citations
OpenAlex

Abstract

A free massless fermion field at finite chemical potential and time varying temperature are considered and in thermo-field dynamics the expectation value of 2n-point functions as the thermodynamic average are computed. It was observed that the Fermi fields under consideration, was able to factorize the chemical potential dependence of the two-point functions in to an exponential pre-factor.

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A free massless fermion field at finite chemical potential and time varying temperature are considered and in thermo-field dynamics the expectation value of 2n-point functions as the thermodynamic average are computed. It was observed that the Fermi fields under consideration, was able to factorize the chemical potential dependence of the two-point functions in to an exponential pre-factor.
The chemical potential of a D-dimensional free Fermi gas at low temperatures has been obtained using some ideas due to Barker and Blankenbechler [J. Math. Phys. 97, 302 (1986); Am. J. Phys. 25, 279 (1957)]. There is an interesting even–odd-dimensional effect in the behavior of the chemical potential, also observed in other properties of a free Fermi gas, such as the susceptibility. For D=2, it is possible to give a closed form expression, thus valid both in the high- and low-temperature regions, probably not possible in any other even or odd dimensions.
The partition function of system with finite number of particles is derived is derived by using partition function of a weakly interacting Fermi gas trapped in weak magnetic field.Based on the derived expressions,the analytical expressions of thermodynamic quantities of a weakly interacting Fermi gas for finite particle number are solved by using statistical average method and the thermodynamic properties under different temperature conditions are given.It is shown that each thermodynamic quantity has a correctional term due to effects of a finite number of particles.The particle number has a direct effect on correction of chemical potential but has no direct effects on corrections of total energy and heat capacity except T=0.Furthermore,effects of a finite number of particles always reduce chemical potential,thereby zero point of chemical potential shifts towards low temperatures.The increase of particle number weakens the effect,but the repulsive interactions between particles strengthen the effect.
In this paper, the chemical potential of two-dimensional (2D) and quasi-one-dimensional (Q1D) multisubband charged Fermi gases is evaluated. We start with a rather general formula for the thermodynamic potential of an ideal quantum statistical system with arbitrary occupation-number to calculate, as a particular case, the chemical potential of the multisubband 2D Fermi gas described by a quadratic energy spectrum. The chemical potential is also studied in the case of a low-dimensional Fermi gas in the presence of a quantizing magnetic field. The same approach is used to study the chemical potential of a multisubband Q1D Fermi gas. The influence of temperature is considered. We found interesting analytical results for special limits as well as numerical results that may be important for the description of both the thermodynamic and kinetic properties of Fermi systems in low dimensionality.
We have studied here the critical behaviors in a simple model from the point of view of the renormalization group at finite temperature utilizing the Stochastic field theoretic approach towards a finite temperature field theory. To this end, thermofield dynamics has been formulated in terms of Stochastic fields in the external and internal space and the thermal average of the two-point correlation function of the internal field functions is related with the order parameter. The thermodynamical functions and the critical phenomena are then studied constructing the generating functionals involving Stochastic fields.
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.