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We initiate the investigation of the zero temperature holographic superfluids with two competing orders, where besides the vacuum phase, two one band superfluid phases, the coexistent superfluid phase has also been found in the AdS soliton background for the first time. We construct the complete phase diagram in the $e-mu$ plane by numerics, which is consistent with our qualitative analysis. Furthermore, we calculate the corresponding optical conductivity and sound speed by the linear response theory. The onset of pole of optical conductivity at $omega=0$ indicates that the spontaneous breaking phase always represents the superfluid phase, and the residue of pole is increased with the chemical potential, which is consistent with the fact that the particle density is essentially the superfluid density for zero temperature superfluids. In addition, the resulting sound speed demonstrates the non-smoothness at the critical points as the order parameter of condensate, which indicates that the phase transitions can also be identified by the behavior of sound speed. Moreover, as expected from the boundary conformal field theory, the sound speed saturates to $frac{1}{sqrt{2}}$ at the large chemical potential limit for our two band holographic superfluid model.
We investigate the dynamical stability of the holographic system with two order parameters, which exhibits competition and coexistence of condensations. In the linear regime, we have developed the gauge dependent formalism to calculate the quasi-norm
We study the pole-skipping phenomenon of the scalar retarded Greens function in the rotating BTZ black hole background. In the static case, the pole-skipping points are typically located at negative imaginary Matsubara frequencies $omega=-(2pi T)ni$
We study dissipation in holographic superfluids at finite temperature and zero chemical potential. The zero overlap with the heat current allows us to isolate the physics of the conserved current corresponding to the broken global $U(1)$. By using an
We study the anisotropic properties of dynamical quantities: direct current (DC) conductivity and butterfly velocity. The anisotropy plays a crucial role in determining the phase structure of the two-lattice system. Even a small deviation from isotro
Solitons are important nonperturbative excitations in superfluids. For holographic superfluids, we numerically construct dark solitons that have the symmetry-restored phase at their core. A central point is that we include the gravitational back-reac