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arXiv · 1710.10439

Generalized Josephson relation for conserved charges in multi-component bosons

Yi-Cai Zhang
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Abstract

The Josephson relation is generalized for conserved charges in multi-component bosons. With linear response theory, a formula for derivation of generalized superfluid density is given. When there are several conserved charges, the superfluid density is generally a second order tensor in internal spin space. When the rank of Green's function matrix is one, Josephson relation is given explicitly with phase operator method. For two-component bosons, with quantum field theory, we show a generalized Hugenholtz-Pines relation hold and existence of two gapless phonons. When the interactions are $U(2)$ invariant, we show there is a gapless quadratic dispersion excitation no matter how strong the interactions are. The corresponding generalized Josephson relation is expressed with Green's function matrix elements.

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Yi-Cai Zhang. 2017-10-28. Generalized Josephson relation for conserved charges in multi-component bosons. https://doi.org/10.1103/physreva.98.033611

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