Analogue stochastic gravity in strongly-interacting Bose-Einstein condensates

作者：Keser Aydin Cem^*; Galitski Victor

来源：Annals of Physics, 2018, 395: 84-111.

DOI：10.1016/j.aop.2018.05.009

• Collective modes
• Quantum fluids
• General relativity
• Stochastic dynamics

Collective modes propagating in a moving superfluid are known to satisfy wave equations in a curved space-time, with a metric determined by the underlying superflow. We use the Keldysh technique in a curved space-time to develop a quantum geometric theory of fluctuations in superfluid hydrodynamics. This theory relies on a "quantized" generalization of the : two-fluid description of Landau and Khalatnikov, where the superfluid component is viewed as a quasi-classical field coupled to a normal component - the collective modes/phonons representing a quantum bath. This relates the problem in the hydrodynamic limit to the "quantum friction" problem of Caldeira-Leggett type, By integrating out the phonons, we derive stochastic Langevin equations describing a coupling between the superfluid component and phonons. These equations have the form of Euler equations with additional source terms expressed through a fluctuating stress-energy tensor of phonons. Conceptually, this result is similar to stochastic Einstein equations that arise in the theory of stochastic gravity. We formulate the fluctuation-dissipation theorem in this geometric language and discuss possible physical consequences of this theory.

• 出版日期2018-8