[Paper Review] Landau Instability and soliton formation

Shan-quan Lan, Hong Liu+2 more|arXiv (Cornell University)|Oct 13, 2020

Quantum, superfluid, helium dynamics1 references4 citations

TL;DR

This paper investigates the dynamical instability of a finite-temperature superfluid beyond the Landau critical velocity using holographic duality. It demonstrates that the system evolves into a stable, homogeneous superfluid state with a final velocity below the critical value through spontaneous soliton nucleation, with a universal relation linking the final velocity to the number of solitons formed.

ABSTRACT

Consider at a finite temperature $T$ a superfluid moving with a velocity $v$ relative to the thermal bath or its normal component. From Landau's argument there exists a critical $v_c (T)$ beyond which excitations can be spontaneously generated and the system becomes unstable. Identifying the final state induced by such an instability has been an outstanding open question. Using holographic duality we perform dynamical simulations of evolutions from initial unstable states, and find that the system settles to a homogenous superfluid state with a final velocity below the critical velocity. The dynamical evolution process appears to be highly chaotic, exhibiting transient turbulence. Nevertheless we are able to identify from the simulations a universal physical mechanism for the reduction of superfluid velocity, in terms of spontaneous nucleation of solitons. We also derive a simple analytic formula which relates the final velocity to the number of solitons nucleated during the evolution.

Motivation & Objective

• To resolve the long-standing open question of the final state of a superfluid flowing above the Landau critical velocity at finite temperature.
• To investigate the dynamical evolution from an unstable supercritical state to a stable final state, particularly focusing on non-equilibrium quantum dynamics.
• To identify a universal physical mechanism for velocity reduction in superfluids beyond the critical velocity, independent of microscopic details.
• To test the feasibility of this mechanism in cold atomic systems and explore its broader physical implications.

Proposed method

• Employing holographic duality to map the strongly correlated superfluid system to a classical gravitational system in a (3+1)-dimensional asymptotically AdS black hole spacetime.
• Using an Abelian-Higgs model with a complex scalar field Ψ and U(1) gauge field Aa to describe the superfluid phase and its hydrodynamic response.
• Performing nonlinear numerical simulations via a pseudo-spectral method with 28 Chebyshev modes in the z-direction and 121 Fourier modes in the x-direction, using fourth-order Runge-Kutta time integration.
• Deriving the boundary stress-energy tensor and current from the renormalized on-shell action to compute physical observables like charge density and order parameter.
• Analyzing linearized perturbations around the superflow background to identify the onset of Landau instability via quasinormal mode analysis.
• Implementing periodic boundary conditions in the x-direction and fixing total charge to maintain consistency in the dynamical evolution.

Experimental results

Research questions

• RQ1 What is the final state of a superfluid flowing above the Landau critical velocity at finite temperature?
• RQ2 How does the superfluid velocity evolve dynamically from an unstable supercritical state to a stable configuration?
• RQ3 Is there a universal physical mechanism underlying the reduction of superfluid velocity in such systems?
• RQ4 Can the final velocity be predicted from the number of solitons nucleated during the relaxation process?
• RQ5 To what extent is the soliton nucleation mechanism independent of specific system details, and can it be tested experimentally?

Key findings

• The system evolves from an unstable supercritical state to a stable, homogeneous superfluid state with a final velocity below the Landau critical velocity.
• The dynamical relaxation process exhibits transient turbulence and chaotic behavior, indicating strong non-equilibrium dynamics.
• The final superfluid velocity is universally determined by the number of solitons nucleated during the evolution, with a derived analytic formula linking the two.
• Soliton nucleation is identified as the dominant physical mechanism responsible for reducing the superfluid velocity below the critical threshold.
• The holographic framework enables first-principles simulation of real-time, far-from-equilibrium dynamics in strongly correlated superfluids.
• The mechanism is universal and robust, suggesting testability in cold atomic systems and applicability to diverse superfluid and superconducting systems.