Efimkin Dmitry K, Hofmann Johannes, Galitski Victor
Joint Quantum Institute and Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA.
Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom.
Phys Rev Lett. 2016 Jun 3;116(22):225301. doi: 10.1103/PhysRevLett.116.225301. Epub 2016 May 31.
We explore the quantum dynamics of a bright matter-wave soliton in a quasi-one-dimensional bosonic superfluid with attractive interactions. Specifically, we focus on the dissipative forces experienced by the soliton due to its interaction with Bogoliubov excitations. Using the collective coordinate approach and the Keldysh formalism, a Langevin equation of motion for the soliton is derived from first principles. The equation contains a stochastic Langevin force (associated with quantum noise) and a nonlocal in time dissipative force, which appears due to inelastic scattering of Bogoliubov quasiparticles off of the moving soliton. It is shown that Ohmic friction (i.e., a term proportional to the soliton's velocity) is absent in the integrable setup. However, the Markovian approximation gives rise to the Abraham-Lorentz force (i.e., a term proportional to the derivative of the soliton's acceleration), which is known from classical electrodynamics of a charged particle interacting with its own radiation. These Abraham-Lorentz equations famously contain a fundamental causality paradox, where the soliton (particle) interacts with excitations (radiation) originating from future events. We show, however, that the causality paradox is an artifact of the Markovian approximation, and our exact non-Markovian dissipative equations give rise to physical trajectories. We argue that the quantum friction discussed here should be observable in current quantum gas experiments.
我们研究了具有吸引相互作用的准一维玻色超流体中亮物质波孤子的量子动力学。具体而言，我们关注孤子与博戈留波夫激发相互作用时所经历的耗散力。利用集体坐标方法和凯尔迪什形式，从第一性原理推导出了孤子的朗之万运动方程。该方程包含一个随机朗之万力（与量子噪声相关）和一个时间非局部耗散力，后者源于博戈留波夫准粒子在移动孤子上的非弹性散射。结果表明，在可积设置中不存在欧姆摩擦（即与孤子速度成正比的项）。然而，马尔可夫近似产生了亚伯拉罕 - 洛伦兹力（即与孤子加速度导数成正比的项），这在带电粒子与其自身辐射相互作用的经典电动力学中是已知的。这些亚伯拉罕 - 洛伦兹方程著名地包含一个基本的因果性悖论，即孤子（粒子）与源自未来事件的激发（辐射）相互作用。然而，我们表明因果性悖论是马尔可夫近似的产物，我们精确的非马尔可夫耗散方程产生了物理轨迹。我们认为这里讨论的量子摩擦在当前的量子气体实验中应该是可观测的。
