Orbital Dynamics of Anisotropic Superfluid: Microscopic TDGL Approach near the Absolute Zero

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Abstract
The basic equations of orbital motions of ABM state at low frequency and long wave length are derived near the absolute zero of temperature within the Gor'kov approximation. The equations in the TDGL region are equivalent to the phenomenological theory proposed by Leggett and Takagi. Two orbital modes with linear dispersion are obtained. The transverse mode is strongly coupled with the Bogoliubov-Anderson mode in contrast with the longitudinal mode.