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Physica A Statistical Mechanics and its Applications

Dynamical pair correlations of classical and quantum fluids perturbed with weak long-range forces

Johan S. Høye

Published Dec 17, 2009• 6 citations
Publisher
DOI
10.1016/j.physa.2009.12.003

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The Landau criterion, a cornerstone of quantum fluid dynamics, dictates that dissipation is forbidden for uniform motion below a critical velocity. Yet, the fundamental question of how acceleration reshapes the principles of quantum friction has remained open since Landau and Pitaevskii's seminal works. Here, we establish a theoretical framework for the quantum tribology of non-inertial motion, describing a probe particle undergoing composite translation and rotation within a weakly interacting Bose condensate. Using the nonlinear Gross-Pitaevskii equation, we show that centripetal acceleration fundamentally modifies the energy-momentum constraints on elementary excitations. This leads to a finite drag force in the subsonic regime of the probe particle motion, and a characteristic quantum stick-slip behaviour in the deeply supersonic regime -- a direct generalization of the classical Landau-Pitaevskii picture. Beyond this dissipative response, we uncover a fundamentally distinct mechanism: the nonlinearity of the quantum fluid, combined with the broken symmetry of the trajectory, gives rise to a non-dissipative anomalous transverse force. This quantum Magnus-like response, emerging from the second-order density perturbation, performs no work and is rooted in the geometric asymmetry of the dynamically induced flow. Our findings lay the foundation for a universal program in quantum tribology of accelerated motion, establishing a direct and experimentally testable connection among non-inertial dynamics, nonlinear response, and topological symmetry breaking across platforms ranging from ultracold atoms and exciton-polariton condensates to cosmological analog systems.
We report a direct experimental detection of the frictional-superfluid transition in the flow of a fluid of light past a weakly perturbing localized obstacle in a bulk nonlinear crystal. In our cavityless all-optical system, we extract on the one hand a direct optical analog of the drag force experienced by the obstacle and measure on the other hand the associated obstacle displacement. We observe a superfluid regime characterized by a suppression of long-range radiation from the obstacle, which is, as expected, associated to the cancellation of the drag force and the absence of displacement of the obstacle.
Correlations in a system with a weak, long-ranged attractive potential are studied. Using a natural small parameter, the asymptotic orders of all correlations are established. Explicit leading order solutions are obtained for all correlations when the system is away from phase change As it approaches transition, It is shown that the many-body correlations, even though still small, develop very long range and that they are shown extremely slowly varying functions over space. As a results all the correlations contribut equally significantly to the computation of the pair correlation. In an asymptotic ragion near transition, a hierarchy is derived in which each corelation is expressed in terms of its immediate predecessor, its immediate successor and the pair correlation. The pair potential does not appear in these equations. Instead the correlations are expressed in terms of a Yukawa potential whose strength and range are related to the density and other parameters but not to the detailed form of the potential. In the leading approximation, the pair correlation is proportional to this Yukawa function.