Dissipative Dynamics of Superfluid Vortices at Nonzero Temperatures

Abstract

We consider the evolution and dissipation of vortex rings in a condensate at non-zero temperature, in the context of the classical field approximation, based on the defocusing nonlinear Schrödinger equation. The temperature in such a system is fully determined by the total number density and the number density of the condensate. A vortex ring is introduced into a condensate in a state of thermal equilibrium, and interacts with non-condensed particles. These interactions lead to a gradual decrease in the vortex line density, until the vortex ring completely disappears. We show that the square of the vortex line length changes linearly with time, and obtain the corresponding universal decay law. We relate this to mutual friction coefficients in the fundamental equation of vortex motion in superfluids.PACS numbers: 03.65. Sq, 03.75.Kk, 05.65.+b, 67.40.Vs, 67.57.De The processes of self-organization, formation of largescale coherent localized structures and interactions of these structures with small-scale fluctuations are at the heart of nonlinear sciences, ranging from classical turbulence, superfluids, ultracold gases and Bose-Einstein Condensates (BECs), to the formation of the early Universe. Turbulence is characterised by the co-existence of motions with many length and time scales described by many degrees of freedom. The key to our understanding of turbulence is to elucidate physics of interactions between large scales (eg. large eddies) and small scales (eg. turbulent fluctuations), and to develop mathematical models that account for the effects of small scales without actually solving for them. According to the Landau description, superfluid 4 He consists of the ground state and the excitations -quasiparticles drifting on top of the ground state. In the language of relativistic quantum fields this corresponds to vacuum and matter (eg. gravity waves interacting with a vacuum). Indeed, there is a close relationship between superfluid hydrodynamics and quantum gravity, so that at some level of hierarchy of parameters the interactions of the quantum vacuum and matter can be described by the defocusing nonlinear Schrödinger (NLS) equation [1]. The dynamics of Bose condensates depends on the energy exchange between the condensed and non-condensed parts of the gas. Again, the NLS equation (reformulated as the Gross-Pitaevskii (GP) equation [2]) describes equilibrium and dynamical properties of BEC as well as the formation of BEC from a strongly degenerate gas of weakly interacting bosons [3,4]. The formation of the large-scale coherent localized ground state (condensate) from a non-equilibrium initial state has been studied in a number of papers addressing different stages of the formation. Weak turbulence theory has been used to predict the self-similar evolution of the field in the regime of random phases of Fourier amplitudes [5,6], the transition from the regime of weak turbulence to superfluid turbulence via states of strong turbulence in the long-wavelength region of energy space [7], and the final stage...

Relaxation of superfluid turbulence in highly oblate Bose-Einstein condensates

“…We have characterized the relaxation of the turbulent condensate with the one-body and two-body decay rates of the vortex number. Our measurement results on the decay rates should provide a quantitative test on finite-temperature theories for vortex dynamics [29][30][31]. One interesting extension of this work would be exploring the crossover regime from 3D to 2D by increasing the axial confinement [17,35].…”

“…The local vortex dynamics in a homogeneous system is governed by the temperature T and the chemical potential µ of the system: at finite temperature, a vortex experiences a friction force caused by collisional exchange of atoms between the condensate and the thermal cloud [29][30][31], and the chemical potential determines the vortex core size ξ ∝ µ −1/2 , providing a characteristic length scale in the vortex dynamics. In this subsection, we present the measurement results of the decay rates of the vortex number for various sample conditions.…”

Vortex Dynamics in Trapped Bose-Einstein Condensate

“…The generation, dynamics and decay of simple vortex configurations have been observed and described [1,2,3]. At finite temperatures, the interaction of the condensate with the thermal cloud damps the motion of structures (collective modes, solitons, vortices) [4,5,6]. Current investigations of atomic Bose-Einstein condensates are concerned with this damping [7,8,9,10,11,12].…”

Vortex reconnections in atomic condensates at finite temperature

“…The velocity of the curve at the point s is v L = v si − αs × v si , where v si is the self-induced velocity (determined by a Biot-Savart integral over the entire vortex configuration), s ≡ ds /dς is the unit tangent vector at s, and α is a dimensionless temperature dependent friction parameter. In the full expression v L there is a second friction parameter, α , which we have neglected here since it is much smaller than α [23,44,45]. In superfluid helium, outside the phase transition region (less than 1 percent from T c ), α is less than unity and positive [23,44].…”

“…In the full expression v L there is a second friction parameter, α , which we have neglected here since it is much smaller than α [23,44,45]. In superfluid helium, outside the phase transition region (less than 1 percent from T c ), α is less than unity and positive [23,44]. In atomic condensates, numerical sim-ulations of vortex motion based on the ZNG model have shown that [23] α < 0.03 for T /T c < 0.8.…”