Generalized Josephson relation for conserved charges in multi-component bosons

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.

14 pages 3 figures

References in corpus (6)

• Superfluid Density of a Spin-orbit Coupled Bose Gas
• Diffused vorticity and moment of inertia of a spin-orbit coupled Bose-Einstein condensate
• The Josephson relation for the superfluid density in the BCS-BEC crossover
• Tunneling properties of Bogoliubov mode and spin wave modes in supercurrent states of a spin-1 ferromagnetic spinor Bose-Einstein condensate
• Landau's criterion for an anisotropic Bose-Einstein condensate
• Josephson relation for disordered superfluids

Cited by in corpus (5)

• Superfluid density and collective modes of fermion superfluid in dice lattice
• Superfluidity of a Raman spin-orbit-coupled Bose gas at finite temperature
• Two-fluid theory for superfluid system with anisotropic effective masses
• Superfluid density, Josephson relation and pairing fluctuations in a multi-component fermion superfluid
• Hydrodynamic equations for a U(N) invariant superfluid