量子热浴的朗之万方程
The Langevin Equation for a Quantum Heat Bath
摘要：
我们计算了量子朗之万方程（或量子随机微分方程），它表示处于热平衡的量子热浴对简单量子系统的作用。这些方程是通过对给定密度矩阵态下光子序列与重复量子相互作用的哈密顿描述取连续极限而得到的。特别是，我们专门这些方程的情况下，热平衡状态。在这个过程中，出现了新的量子噪声：热量子噪声。我们讨论了这些热量子噪声的数学性质。我们计算的Lindblad发电机与行动的热浴上的小系统。我们展示了典型的Lindblad生成器，它提供了一个给定的量子系统的热化。
英文摘要：
We compute the quantum Langevin equation (or quantum stochastic differential equation) representing the action of a quantum heat bath at thermal equilibrium on a simple quantum system. These equations are obtained by taking the continuous limit of the Hamiltonian description for repeated quantum interactions with a sequence of photons at a given density matrix state. In particular we specialise these equations to the case of thermal equilibrium states. In the process, new quantum noises are appearing: thermal quantum noises. We discuss the mathematical properties of these thermal quantum noises. We compute the Lindblad generator associated with the action of the heat bath on the small system. We exhibit the typical Lindblad generator that provides thermalization of a given quantum system.
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