Data for Figures 1 to 4 of Conference Proceeding

The Lindblad master equation is a frequently used Markovian approach to describe open quantum systems in terms of the temporal evolution of a reduced density matrix. Here, the thermal environment is traced out to obtain an expression to describe the evolution of what is called a system: one particle or a chain of interacting particles, which is/are surrounded by a thermal heat bath. In this work, we investigate the formation of non-relativistic bound states, involving the Pöschl-Teller potential, in order to discuss the formation time and the thermal equilibrium, applying scales from nuclear physics. This problem is borrowed from the field of heavy-ion collisions, where the deuteron is a probe which is measured at temperature regimes around the chemical freeze out temperature, while the deuteron itself has a binding energy which is much lower. This is known and often described as a ``snowball in hell". We use a reformulated Lindblad equation, in terms of a diffusion-advection equation with sources and therefore provide a hydrodynamical formulation of a dissipative quantum master equation.

林德布拉德主方程（Lindblad master equation）是描述开放量子系统的常用马尔可夫方法，其基于约化密度矩阵（reduced density matrix）的时间演化展开。该方法通过对热环境求迹，得到用于描述系统演化的表达式：这里的系统指被热浴包围的单粒子或相互作用粒子链。本研究依托核物理尺度，探讨涉及珀施尔-泰勒势（Pöschl-Teller potential）的非相对论束缚态的形成过程，以分析其形成时间与热平衡特性。该问题源自重离子碰撞领域：其中氘核作为探针，在接近化学冻结温度的温度区间内被观测，而氘核自身的结合能极低。这一现象常被称为“地狱中的雪球”。我们采用带源项的扩散-平流方程对林德布拉德主方程进行了重构，由此给出了耗散量子主方程的流体动力学表述。