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Register a new userEmergent Non-Eulerian Hydrodynamics of Quantum Vortices in Two Dimensions
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We develop a coarse-grained description of the point-vortex model, finding that a large number of planar vortices and antivortices behave as an inviscid non-Eulerian fluid at large scales. The emergent binary vortex fluid is subject to anomalous stresses absent from Eulers equation, caused by the singular nature of quantum vortices. The binary vortex fluid is compressible, and has an asymmetric Cauchy stress tensor allowing orbital angular momentum exchange with the vorticity and vortex density. An analytic solution for vortex shear flow driven by anomalous stresses is in excellent agreement with numerical simulations of the point-vortex model.
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Generic short-range interacting quantum systems with a conserved quantity exhibit universal diffusive transport at late times. We employ non-equilibrium quantum field theory and semi-classical phase-space simulations to show how this universality is replaced by a more general transport process in a long-range XY spin chain at infinite temperature with couplings decaying algebraically with distance as $r^{-alpha}$. While diffusion is recovered for $alpha>1.5$, longer-ranged couplings with $0.5<alphaleq 1.5 $ give rise to effective classical Levy flights; a random walk with step sizes drawn from a distribution with algebraic tails. We find that the space-time dependent spin density profiles are self-similar, with scaling functions given by the stable symmetric distributions. As a consequence, for $0.5<alphaleq1.5$ autocorrelations show hydrodynamic tails decaying in time as $t^{-1/(2alpha-1)}$ and linear-response theory breaks down. Our findings can be readily verified with current trapped ion experiments.
Despite the prominence of Onsagers point-vortex model as a statistical description of 2D classical turbulence, a first-principles development of the model for a realistic superfluid has remained an open problem. Here we develop a mapping of a system of quantum vortices described by the homogeneous 2D Gross-Pitaevskii equation (GPE) to the point-vortex model, enabling Monte-Carlo sampling of the vortex microcanonical ensemble. We use this approach to survey the full range of vortex states in a 2D superfluid, from the vortex-dipole gas at positive temperature to negative-temperature states exhibiting both macroscopic vortex clustering and kinetic energy condensation, which we term an Onsager-Kraichnan condensate (OKC). Damped GPE simulations reveal that such OKC states can emerge dynamically, via aggregation of small-scale clusters into giant OKC-clusters, as the end states of decaying 2D quantum turbulence in a compressible, finite-temperature superfluid. These statistical equilibrium states should be accessible in atomic Bose-Einstein condensate experiments.
Adding energy to a system through transient stirring usually leads to more disorder. In contrast, point-like vortices in a bounded two-dimensional fluid are predicted to reorder above a certain energy, forming persistent vortex clusters. Here we realize experimentally these vortex clusters in a planar superfluid: a $^{87}$Rb Bose-Einstein condensate confined to an elliptical geometry. We demonstrate that the clusters persist for long times, maintaining the superfluid system in a high energy state far from global equilibrium. Our experiments explore a regime of vortex matter at negative absolute temperatures, and have relevance to the dynamics of topological defects, two-dimensional turbulence, and systems such as helium films, nonlinear optical materials, fermion superfluids, and quark-gluon plasmas.
A tremendous amount of recent attention has focused on characterizing the dynamical properties of periodically driven many-body systems. Here, we use a novel numerical tool termed `density matrix truncation (DMT) to investigate the late-time dynamics of large-scale Floquet systems. We find that DMT accurately captures two essential pieces of Floquet physics, namely, prethermalization and late-time heating to infinite temperature. Moreover, by implementing a spatially inhomogeneous drive, we demonstrate that an interplay between Floquet heating and diffusive transport is crucial to understanding the systems dynamics. Finally, we show that DMT also provides a powerful method for quantitatively capturing the emergence of hydrodynamics in static (un-driven) Hamiltonians; in particular, by simulating the dynamics of generic, large-scale quantum spin chains (up to L = 100), we are able to directly extract the energy diffusion coefficient.
Artificial phoretic particles swim using self-generated gradients in chemical species (self-diffusiophoresis) or charges and currents (self-electrophoresis). These particles can be used to study the physics of collective motion in active matter and might have promising applications in bioengineering. In the case of self-diffusiophoresis, the classical physical model relies on a steady solution of the diffusion equation, from which chemical gradients, phoretic flows and ultimately the swimming velocity, may be derived. Motivated by disk-shaped particles in thin films and under confinement, we examine the extension to two dimensions. Because the two-dimensional diffusion equation lacks a steady state with the correct boundary conditions, Laplace transforms must be used to study the long-time behavior of the problem and determine the swimming velocity. For fixed chemical fluxes on the particle surface, we find that the swimming velocity ultimately always decays logarithmically in time. In the case of finite Peclet numbers, we solve the full advection-diffusion equation numerically and show that this decay can be avoided by the particle moving to regions of unconsumed reactant. Finite advection thus regularizes the two-dimensional phoretic problem.
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