By utilizing the $\mathrm{AdS}/\mathrm{CFT}$ correspondence, we explore the dynamics of strongly coupled superfluid vortices in a disk with constant angular velocity at a finite temperature. Each vortex in the vortex lattice is quantized with vorticity $n=1$ by the direct inspection of their phases. As the angular velocity of the disk is greater than a critical value, the first vortex will be excited as expected from theoretical predictions. Subsequent vortices are also generated by increasing the rotation of the disk, resulting in remarkable step transitions of the angular velocity which excite each individual vortex. When the vortex number is large enough, the density of vortices is found to be linearly proportional to the angular velocity, which matches the Feynman relation very well. We also find that varying the temperature does not alter this Feynman relation.

Formation and evolution of topological defects in course of non-equilibrium symmetry breaking phase transitions is of wide interest in many areas of physics, from cosmology through condensed matter to low temperature physics. Its study in strongly coupled systems, in absence of quasiparticles, is especially challenging. We investigate breaking of U(1) symmetry and the resulting spontaneous formation of vortices in a (2 + 1)-dimensional holographic superconductor employing gauge/gravity duality, a ‘first-principles’ approach to study strongly coupled systems. Magnetic fluxons with quantized fluxes are seen emerging in the post-transition superconducting phase. As expected in type II superconductors, they are trapped in the cores of the order parameter vortices. The dependence of the density of these topological defects on the quench time, the dispersion of the typical winding numbers, and the vortex-vortex correlations are consistent with predictions of the Kibble-Zurek mechanism.

Vortices are topological defects associated with superfluids and superconductors, which, when mobile, dissipate energy destroying the dissipationless nature of the superfluid. The nature of this “quantum dissipation” is rooted in the quantum physical nature of the problem, which has been the subject of an extensive literature. However, this has mostly been focused on the measures applicable in weakly interacting systems wherein they are tractable via conventional methods. Recently, it became possible to address such dynamical quantum thermalization problems in very strongly interacting systems using the holographic duality discovered in string theory, mapping the quantum problem on a gravitational problem in one higher dimension, having as benefit offering a more general view on how dissipation emerges from such intricate quantum physical circumstances. We study here the elementary problem of a single vortex in two space dimensions, set in motion by a sudden quench in the background superflow formed in a finite-density Reissner-Nordstrom holographic superfluid. This reveals a number of surprising outcomes addressing questions of principle. By fitting the trajectories unambiguously to the Hall-Vinen-Iordanskii phenomenological equation of motion we find that these are characterized by a large inertial mass at low temperature that, however, diminishes upon raising temperature. For a weak drive the drag is found to increase when temperature is lowered, which reveals a simple shear drag associated with the viscous metallic vortex cores, supplemented by a conventional normal fluid component at higher temperatures. For a strong drive we discover a unique dynamical phenomenon: the core of the vortex deforms accompanied by a large increase of the drag force.

At finite temperature, the stable equilibrium states of coupled two-component Bose Einstein condensations (BECs) with the same conformal mass in both non-rotating and rotating condition can be obtained by studying its real dynamics via holography. The equilibrium state is the state where the free energy reaches the minimum and does not change any more. In the case of no rotation, the spatial phase separated states of the two components become more stable than the miscible condensates state when the direct repulsive inter-component coupling constant $$\eta>\eta _c>0$$η > η c > 0 . Under rotation, the quantum fluid reveals four equilibrium structures of vortex states by varying the $$\eta $$η from the miscible region to the phase separated region. Among the four structures, the vortex sheet solution is the most exotic one that appears in the phase separated region.

We studied the dynamics of the order parameter and the winding numbers $W$ formation of a quenched normal-to-superconductor state phase transition in a finite size holographic superconducting ring. There is a critical circumference $\tilde{C}$ below which no winding number will be formed; then, $\tilde{C}$ can be treated as the Kibble-Zurek mechanism (KZM) correlation length $\xi$, which is proportional to the fourth root of its quench rate ${\tau }_Q$, which is also the average size of independent pieces formed after a quench. When the circumference $C\ge 10\xi$, the key KZM scaling between the average value of absolute winding number and the quench rate $⟨|W|⟩\propto {\tau }_Q^{-1/8}$ is observed. At smaller sizes, the universal scaling will be modified; there are two regions. The middle size $5\xi <C<10\xi$ result $⟨|W|⟩\propto {\tau }_Q^{-1/5}$ agrees with a finite size experiment observation, while at $\xi <C\le 5\xi$, the average value of absolute winding number equals the variance of winding number, and there is no exponential relationship between the quench rate and the average value of absolute winding number. The winding number statistics can be derived from a trinomial distribution with $\tilde{N}=C/(f\xi )$ trials, and $f\simeq 5$ is the average number of adjacent pieces that are effectively correlated.

We study the nonlinear dynamical evolution of spinodal decomposition in a first-order superfluid phase transition using a simple holographic model in the probe limit. We first confirm the linear stability analysis based on quasinormal modes and verify the existence of a critical length scale related to a gradient instability — negative speed of sound squared — of the superfluid sound mode, which is a consequence of a negative thermodynamic charge susceptibility. We present a comparison between our case and the standard Cahn-Hilliard equation for spinodal instability, in which a critical length scale can be also derived based on a diffusive instability. We then perform several numerical tests which include the nonlinear time evolution directly from an unstable state and fast quenches from a stable to an unstable state in the spinodal region. Our numerical results provide a real time description of spinodal decomposition and phase separation in one and two spatial dimensions. We reveal the existence of four different stages in the dynamical evolution, and characterize their main properties. Finally, we investigate the strength of dynamical heterogeneity using the spatial variance of the local chemical potential and we correlate the latter to other features of the dynamical evolution.