A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics
A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics
复制标题
DOI：
10.1140/epjst/e2009-00962-3
复制
发表时间：
2009-02
期刊：
影响因子：
--
通讯作者：
H. Schoeller
中科院分区：
文献类型：
--
作者：
H. Schoeller
我们研究耗散量子力学的一个通用问题，一个小的局部量子系统与离散状态耦合在一个任意的方式（即不一定是线性的），以几个无限大的粒子或热源。对于玻色子或费米子水库，我们开发了一个量子场论的图形配方在刘维尔空间系统地扩大在量子系统耦合和集成的水库自由度。结果得到了量子系统约化密度矩阵的动力学方程。基于这种形式主义，我们提出了一种形式上精确的微扰重整化群（RG）方法，从该方法可以计算该动力学方程的核。它演示了如何非平衡稳态（由几个水库保持在不同的化学势或温度引起的），任意可观的，如运输电流，和时间演化到稳态可以计算。最重要的是，我们展示了如何RG方程的松弛和失相率可以推导出，以及他们如何切断一般的RG流的顶点。该方法是基于以前推导的实时RG技术[1-4]，但在这里在拉普拉斯空间中制定，并推广到任意耦合系统。此外，对于具有平坦态密度的费米子库，我们使用了最近引入的虚频轴上的截止方案[5]，该方案具有几个技术优势。除了正式成立的RG方程的一般问题的耗散量子力学，我们证明了该方法，将其应用到非平衡各向同性近藤模型。我们提出了一个系统的方法来解决RG方程的弱耦合极限解析，并提供了一个展望的适用性强耦合的情况下。
We study a generic problem of dissipative quantum mechanics, a small local quantum system with discrete states coupled in an arbitrary way (i.e. not necessarily linear) to several infinitely large particle or heat reservoirs. For both bosonic or fermionic reservoirs we develop a quantum field-theoretical diagrammatic formulation in Liouville space by expanding systematically in the reservoir-system coupling and integrating out the reservoir degrees of freedom. As a result we obtain a kinetic equation for the reduced density matrix of the quantum system. Based on this formalism, we present a formally exact perturbative renormalization group (RG) method from which the kernel of this kinetic equation can be calculated. It is demonstrated how the nonequilibrium stationary state (induced by several reservoirs kept at different chemical potentials or temperatures), arbitrary observables such as the transport current, and the time evolution into the stationary state can be calculated. Most importantly, we show how RG equations for the relaxation and dephasing rates can be derived and how they cut off generically the RG flow of the vertices. The method is based on a previously derived real-time RG technique [1-4] but formulated here in Laplace space and generalized to arbitrary reservoir-system couplings. Furthermore, for fermionic reservoirs with flat density of states, we make use of a recently introduced cutoff scheme on the imaginary frequency axis [5] which has several technical advantages. Besides the formal set-up of the RG equations for generic problems of dissipative quantum mechanics, we demonstrate the method by applying it to the nonequilibrium isotropic Kondo model. We present a systematic way to solve the RG equations analytically in the weak-coupling limit and provide an outlook of the applicability to the strong-coupling case.