Quasiparticle parameterization of meanfields, Galilei invariance and universal conserving response functions

TL;DR

This paper analyzes meanfield parameterizations under Galilean invariance, deriving universal response functions that satisfy key sum rules for Bose and Fermi systems across various dimensions.

Contribution

It introduces a universal form of response functions independent of local equilibrium parameterizations, ensuring conservation laws are satisfied.

Findings

Response functions are universal and independent of local equilibrium details.

Explicit forms of response functions for density, momentum, and energy are derived.

Sum rules like compressibility and frequency moments are analytically proven to hold.

Abstract

The general possible form of meanfield parameterization in a running frame in terms of current, energy and density functionals are 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 selfenergy 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 parameterization 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.