Collective excitations of trapped Fermi or Bose gases

TL;DR

This paper introduces a hydrodynamic method to calculate all excitations in trapped quantum gases at zero temperature, applicable to both Fermi and Bose gases with arbitrary equations of state and trapping potentials.

Contribution

It develops a general hydrodynamic framework with a natural scalar product, ensuring hermiticity and orthogonality of mode functions, and verifies the exactness of Kohn-modes for harmonic traps.

Findings

Calculated fermionic excitations in the BCS-BEC transition region.

Established hermitian wave operator and orthogonal mode functions.

Confirmed Kohn-modes are exact in harmonic traps.

Abstract

A new method is developed to calculate all excitations of trapped gases using hydrodynamics at zero temperature for any equation of state $\mu=\mu(n)$ and for any trapping potential. It is shown that a natural scalar product can be defined for the mode functions, by which the wave operator is hermitian and the mode functions are orthogonal. It is also shown that the Kohn-modes are exact for harmonic trapping in hydrodynamic theory. Excitations for fermions are calculated in the BCS-BEC transition region using the equation of state of the mean-field Leggett-model for isotrop harmonic trap potential.