论文标题
热力学极限中马尔可夫进化的发生器的光谱：从非铁分子到完全进化，通过三角形laurent矩阵
Spectra of generators of Markovian evolution in the thermodynamic limit: From non-Hermitian to full evolution via tridiagonal Laurent matrices
论文作者
论文摘要
我们确定无限线上单粒子翻译不变的lindblad操作员的光谱。如果离散的Laplacian和Lindblad运营商给出了哈密顿量的情况，则是等级$ r $，有限范围并彼此翻译，我们获得了Lindbladian的代表，是有限范围Bi-Infinite Laurent Laurent Laurent Matrices与等级$ r $ r $ - Pertertrestations的直接组成部分。通过分析直接积分，我们严格确定一般情况下的光谱，并针对几种类型的耗散（例如\ dephasing和cooherent Hopping）进行明确计算。我们进一步使用有关频谱的详细信息来证明无处不在，缺乏残留光谱以及有限体积光谱与无限体积对应物收敛的条件。我们最终将讨论扩展到了安德森·哈密顿（Anderson Hamiltonian）的案例，这使我们能够研究与开放量子系统中本地化相关的lindbladian。
We determine spectra of single-particle translation-invariant Lindblad operators on the infinite line. In the case where the Hamiltonian is given by the discrete Laplacian and the Lindblad operators are rank $r$, finite range and translates of each other, we obtain a representation of the Lindbladian as a direct integral of finite range bi-infinite Laurent matrices with rank-$r$-perturbations. By analyzing the direct integral we rigorously determine the spectra in the general case and calculate it explicitly for several types of dissipation e.g.\ dephasing, and coherent hopping. We further use the detailed information about the spectrum to prove gaplessness, absence of residual spectrum and a condition for convergence of finite volume spectra to their infinite volume counterparts. We finally extend the discussion to the case of the Anderson Hamiltonian, which enables us to study a Lindbladian recently associated with localization in open quantum systems.
