漂移量子扩散与爱因斯坦关系I
Quantum Diffusion with Drift and the Einstein Relation I
摘要：
研究了在恒定外力驱动下，量子粒子在简单立方晶格上跳跃的动力学。它被耦合到一个相同的，独立的热库阵列组成的自由，无质量的玻色场，一个在每个网站的晶格。当粒子访问晶格的位置x时，它可以发射或吸收x处的库的场量子。在假设粒子和储层之间的耦合和驱动力足够小的情况下，我们建立了以下结果：粒子状态随时间的遍历平均接近非平衡稳态（NESS），描述了粒子的非零平均漂移。它围绕平均漂移的运动是扩散的，扩散常数和漂移速度通过爱因斯坦关系相互关联。
英文摘要：
We study the dynamics of a quantum particle hopping on a simple cubic lattice and driven by a constant external force. It is coupled to an array of identical, independent thermal reservoirs consisting of free, massless Bose fields, one at each site of the lattice. When the particle visits a site x of the lattice it can emit or absorb field quanta of the reservoir at x. Under the assumption that the coupling between the particle and the reservoirs and the driving force are sufficiently small, we establish the following results: The ergodic average over time of the state of the particle approaches a non-equilibrium steady state (NESS) describing a non-zero mean drift of the particle. Its motion around the mean drift is diffusive, and the diffusion constant and the drift velocity are related to one another by the Einstein relation.
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