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Progress of Theoretical and Experimental Physics

Virial theorem and generalization of the Fermi-liquid theory for the homogeneous degenerate electron system

Viktor Borisovich Bobrov, S. A. Trigger, Anatolij G. Zagorodny

Published Feb 4, 2013• 1 citation
Publisher

Abstract

Using the general thermodynamic equalities and the virial theorem, it is shown that the ground state energy of the homogeneous electron liquid is uniquely defined by the one-particle electron distribution function over momenta and spin quantum numbers. On this basis, taking into account the results of quantum field theory for the one-particle Green’s function, we state that the ground state energy of the homogeneous electron liquid is a functional of the one-particle distribution function.

DOI
10.1093/ptep/pts090

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Using the general thermodynamic equalities and the virial theorem, it is shown that the ground state energy of the homogeneous electron liquid is uniquely defined by the one-particle electron distribution function over momenta and spin quantum numbers. On this basis, taking into account the results of quantum field theory for the one-particle Green’s function, we state that the ground state energy of the homogeneous electron liquid is a functional of the one-particle distribution function.
It is shown by dimensional analysis that Pauli's ground-state-energy theorem, which expresses the ground-state energy in the form of a coupling-constant integration of the potential energy, and the virial theorem are equivalent for a many-particle system interacting with a homogeneous interparticle potential ($\ensuremath{\propto}{r}^{l}$) in arbitrary (ddd) dimensions. The finite-temperature case is also discussed.
Abstract A new formalism of the statistical description of the electron liquid is proposed. The renormalized statistical perturbation theory is formulated in terms of n‐particle correlation functions of some simpler model system, called the reference system. The functional representations of the partition function, free energy, ground state energy, and two‐particle correlation function are obtained for quantum systems on the basis of the method of collective variables. The approach under consideration describes, in particular, the strongly coupled electron liquid, it is general enough and can be generalized to the case of superconducting electron systems, systems in external fields, and also Bose systems.
The set of equations for the two-particle Green's functions in a nonequilibrium medium is derived in the diffusive approximation. Both the two- and single-particle Green's functions are calculated when matter is in the ground state. It is shown that the Landau Fermi-liquid consideration is correct when the interaction between particles in matter is rather weak or when matter is not too dense. In the opposite cases the energy spectrum of the particles is rearranged so that the step in the momentum distribution of the particles disappears. The applicability of the Landau Fermi-liquid theory is established in the general case.