Quantum Fluid Dynamics from Path Integrals

Sagnik Ghosh, Swapan Kumar Ghosh

Terrebce Reese, Bruce N. Miller

Walter Dittrich, M. Reuter

Jeffrey Yepez

Riccardo Fantoni

We solve numerically exactly a simple toy model to quantum general relativity or more properly to path integral on a curved space. We consider the thermal equilibrium of a quantum many body problem on the sphere, the surface of constant positive curvature. We use path integral Monte Carlo to measure the kinetic energy, the internal energy and the static structure of a bosons, fermions and anyons fluid at low temperatures on the sphere. For bosons we also measure the superfluid fraction and compare its behavior at the critical temperature with the universal jump predicted by Nelson and Kosterlitz in flat space in the thermodynamic limit at the superfluid phase transition. For fermions and anyons it is necessary to use the restricted path integral recipe in order to overcome the sign problem. Even if this recipe is exact for the non interacting fluid it reduces to just an approximation for an interacting system. And we make the example of the electron gas at low temperature. Snapshots of the many body path configuration during the evolution of the computer experiment show that the ``speed'' of the single particle path near the poles slows down as a consequence of the ``hairy ball theorem'' of Poincaré. The influence of curvature on the thermodynamic and structural properties of the many body fluid is also studied.

Frank Schneider, P. Nielaba

We study the quantum dynamics of a generic model fluid with internal quantum states and classical translational degrees of freedom in two spatial dimensions. The path integral Monte Carlo data for the imaginary time correlation functions are presented and analyzed by the maximum entropy method. A comparison of the frequency distribution with those of a mean field approximation and virial expansion shows good agreement at high and low densities, respectively. \textcopyright{} 1996 The American Physical Society.