Quasiparticle parametrization of mean fields, Galilei invariance, and universal conserving response functions

Abstract

The general possible form of mean-field parametrization in a running frame in terms of current, energy, and density functionals is examined under the restrictions of Galilean invariance. It is found that only two density-dependent parameters remain which are usually condensed in a position-dependent effective mass and the self-energy formed by current and mass. The position-dependent mass induces a position-dependent local current, which is identified for different nonlinear frames. In a second step the response to an external perturbation and relaxation towards a local equilibrium is investigated. The response function is found to be universal in the sense that the actual parametrization of the local equilibrium does not matter and is eliminated from the theory due to the conservation laws. The explicit form of the response with respect to density, momentum, and energy is derived. The compressibility sum rule as well as the sum rule by first- and third-order frequency moments are proved analytically to be fulfilled simultaneously. The results are presented for Bose or Fermi systems in one, two, and three dimensions.

Kinetic theory of spin-polarized systems in electric and magnetic fields with spin-orbit coupling. I. Kinetic equation and anomalous Hall and spin-Hall effects

“…Though the selfconsistent Fermi functions and the selfconsistent precession both contain an involved spin-orbit coupling separately, they cancel each other in the polarization in quasi two dimensions and for Rashba or Dresselhaus coupling. It remains to show that this observation is consistent with the general expression for the linearized result (85). With the help of (87) one obtains in fact just (91)…”

“…In this way the density is conserved in the response function which could be extended to included more conservation laws 85,118 . If we consider only density conservation but no polarization conservation, of course, we can restrict ourselves to the ∂ µ f 0 terms.…”

“…With the aim to derive the RPA response we concentrate on the correct mean-field formulation and restrict ourselves to a relaxation-time approximation of the collision integral as a first step. This relaxation time will be understood with respect to a local equilibrium which accounts for local conservation laws [81][82][83][84][85] . Though it can be derived from Boltzmann collision integrals, this relaxation time approximation omits quantum interference effects such as weak localization due to disorder, for an adequate treatment of these effects see, e.g., 86 .…”

Kinetic theory of spin-polarized systems in electric and magnetic fields with spin-orbit coupling. II. RPA response functions and collective modes

“…In this way the density is conserved in the response function which could be extended to include more conservation laws 76,77 . If we consider only the density conservation but not the polarization conservation, we can restrict ourselves to the ∂ µ f 0 term.…”

“…The 1/τ terms come from the Mermin conserving relaxation-time approximation which means a relaxation towards a local equilibrium specified such that local conservation laws are obbeyed 74,75,77 .…”