Abstract
The phase theory of two interacting one-dimensional degenerate Fermi gases confined to different harmonic traps is developed based on the concept of bosonization. The excitation spectra of mass and composition waves are calculated and stability boundaries as function of interaction strength and frequency detuning of the traps are found. The experimentally accessible non-local mobilities and their relation to the excitation frequencies are also studied. The problem of the Kohn mode within phase theory is discussed and a solution is proposed. As an example of the simplicity and effectiveness of the new approach the propagation of a composition perturbation across the Fermi seas is calculated analytically.
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