Decay, scattering, and decoherence in many-body quanum systems

在Forschergruppe的特殊散射视角下，我们专注于粒子-粒子相互作用产生复杂动力学的系统。特别是，我们将研究光学晶格中相互作用玻色子的范例和三体库仑问题。这两种情况都表现出开放量子系统的特征，例如粒子损失到多粒子连续体，与探测粒子的能量交换或相互作用诱导的退相干。我们为这些现象寻找微观理论。在项目的第一部分，我们将研究被困在光学晶格中的相互作用玻色子的衰变，这种相互作用的玻色子可能通过隧穿到多体连续统而逃逸出晶格。为此，我们将寻求一个近似的主方程ansatz，但也依赖于精确的数值技术，如复数膨胀，因为我们已经将其应用于三体库仑问题。在第二部分，我们将研究限制在小晶格中的玻色-爱因斯坦凝聚体(BEC)的非弹性散射，目的是在不破坏凝聚体的情况下，探测散射粒子对BEC的散射。特别是，我们想要了解BEC量子动力学中规则的、混合的或混沌的相空间结构是如何反映在散射过程中的，并探索随机矩阵理论建模的可能性。在项目的第三部分，我们将研究倾斜光学晶格上原子Bloch振荡的相互作用诱导的衰减，重点关注多体能级统计是混沌的区域。具体地说，我们想了解这些光谱特性是如何控制相干性损失的。

Under the specific scattering perspective of the Forschergruppe, we focus on systems where complex dynamics result from particle-particle interactions. In particular, we will study the paradigmatic cases of interacting bosons in optical lattices and the three-body Coulomb problem. Both these cases exhibit characteristic features of open quantum systems, such as the loss of particles to the multi-particle continuum, the exchange of energy with a probe particle or interaction-induced decoherence. We seek a microscopic theory for these phenomena.In the first part of the project, we will examine the decay of interacting bosons trapped inside an optical lattice, which may escape from the lattice by tunneling to the many-body continuum. For this purpose, we will pursue an approximate master-equation ansatz, but also rely on exact numerical techniques such as complex dilation, as we have already applied it to the three-body Coulomb problem.In the second part, we will study inelastic scattering from Bose-Einstein condensates (BECs) confined in small lattices, with the purpose of probing the BEC by a scattering particle without destroying the condensate. In particular, we want to understand how the regular, mixed, or chaotic phase-space structure underlying the BEC’s quantum dynamics is reflected in the scattering process and explore the possibility of a random matrix theory modeling.In the third part of the project, we will investigate the interaction-induced decay of atomic Bloch oscillations on tilted optical lattices, focusing on that regime where the many-body level statistics is chaotic. Specifically, we want to understand how these spectral properties control the loss of coherence.