Santos Jader P, Landi Gabriel T
Universidade Federal do ABC, 09210-580 Santo André, Brazil.
Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil.
Phys Rev E. 2016 Dec;94(6-1):062143. doi: 10.1103/PhysRevE.94.062143. Epub 2016 Dec 28.
Quantum master equations form an important tool in the description of transport problems in open quantum systems. However, they suffer from the difficulty that the shape of the Lindblad dissipator depends sensibly on the system Hamiltonian. Consequently, most of the work done in this field has focused on phenomenological dissipators which act locally on different parts of the system. In this paper we show how to construct Lindblad dissipators to model a one-dimensional bosonic tight-binding chain connected to two baths at the first and last site, kept at different temperatures and chemical potentials. We show that even though the bath coupling is local, the effective Lindblad dissipator stemming from this interaction is inherently nonlocal, affecting all normal modes of the system. We then use this formalism to study the current of particles and energy through the system and find that they have the structure of Landauer's formula, with the bath spectral density playing the role of the transfer integral. Finally, we consider infinitesimal temperature and chemical potential gradients and show that the currents satisfy Onsager's reciprocal relations, which is a consequence of the fact that the microscopic quantum dynamics obeys detailed balance.
量子主方程是描述开放量子系统中输运问题的重要工具。然而，它们存在一个困难，即林德布拉德耗散算符的形式强烈依赖于系统哈密顿量。因此，该领域的大部分工作都集中在对系统不同部分局部起作用的唯象耗散算符上。在本文中，我们展示了如何构建林德布拉德耗散算符，以对一个一维玻色子紧束缚链进行建模，该链在第一个和最后一个格点处连接到两个处于不同温度和化学势的浴场。我们表明，尽管浴场耦合是局部的，但源于这种相互作用的有效林德布拉德耗散算符本质上是非局部的，会影响系统的所有正则模。然后，我们使用这种形式体系来研究通过该系统的粒子流和能量流，发现它们具有朗道尔公式的结构，其中浴场谱密度起到转移积分的作用。最后，我们考虑无穷小的温度和化学势梯度，并表明电流满足昂萨格互易关系，这是微观量子动力学服从细致平衡这一事实的结果。
