Dynamics in Open Quantum Systems: strong Dissipation and Integrability

处于和不处于平衡状态的量子系统具有截然不同的性质。在系统经历受控耗散的非平衡环境中，时间演化变得非么正，动力学不可逆。通常，长时间的演化会使量子系统进入一种具有与时间无关的性质的状态，即所谓的非平衡稳态(Ness)。定态性质对于时间初始条件和沿途的附带微扰都是稳健的，从而打开了耗散量子系统作为量子态工程的一条有吸引力的道路。此外，Ness的性质通常与Gibbs系综的性质完全不同，例如，量子自旋链的Ness可以携带宏观稳定的电流，并伴随着长程关联，或者对链边缘的边界条件出人意料地敏感。因此，相干动力学和耗散动力学之间的相互作用使得新的量子态变得可达，否则在通常的么正动力学中是无法到达的。我们的目标是研究最近在冷原子系统中实验制备的量子磁体中的手性态。我们想要了解这些自旋-螺旋型态的稳定性，并对它们的耗散产生感兴趣。这些态具有不同寻常的物理性质，比如强自旋流，我们将用解析和数值方法来计算。在解析上，我们将利用最近发现的“幻影”Bethe态的结构。我们计划展示如何利用耗散只在边缘局部作用来产生手性态的混合物，并通过所谓的矩阵乘积态(MPS)来构造各自的Ness。在耗散背景下，MPS是由矩形Lax矩阵构造的，这与平衡物理中出现的MPS有本质的不同。在Zeno极限中，我们将利用可积开放Heisenberg和Hubbard类系统所支配的有效Zeno动力学的可积性来计算Ness及其性质。

Quantum systems in and out of equilibrium have drastically different properties. In a non-equilibrium setting in which the system experiences a controlled dissipation, the time evolution becomes non-unitary and the dynamics irreversible. Usually the long-time evolution then brings the quantum system into a state with properties that do not depend on time, the so-called non-equilibrium steady state (NESS). The steady state properties are robust with respect to temporal initial conditions and incidental perturbations along the way, thus opening dissipative quantum systems as an attractive path to quantum states engineering. Furthermore, the properties of a NESS are usually completely different from those of a Gibbs ensemble of states, e.g. the NESS of a quantum spin chain can carry macroscopic stationary currents accompanied by long-range correlations, or be unexpectedly sensitive to boundary conditions at the edges of the chain. The interplay between coherent and dissipative dynamics thus renders novel quantum states accessible which are otherwise unreachable in the usual unitary dynamics. Our objective is the study of chiral states in quantum magnets as they have recently been experimentally prepared in systems of cold atoms. We want to understand the stability of these states of spin-helix type and are interested in their dissipative generation. These states have unusual physical properties like strong spin currents which we are going to compute by analytical and numerical means. Analytically we will make use of the recently discovered structure of "phantom'' Bethe states. We plan to show how to dissipatively generate mixtures of chiral states using dissipation acting just locally at the edges and to construct the respective NESS via so-called matrix product states (MPS). In the dissipative setting the MPS are constructed from rectangular Lax matrices which is qualitatively different from the MPS appearing in equilibrium physics. In the Zeno limit we will compute NESS and its properties using the integrability of effective Zeno dynamics governed by integrable open Heisenberg and Hubbard type systems.