Bound state formation within the Lindblad approach
- URL: http://arxiv.org/abs/2503.07402v1
- Date: Mon, 10 Mar 2025 14:52:15 GMT
- Title: Bound state formation within the Lindblad approach
- Authors: Jan Rais, Hendrik van Hees, Carsten Greiner,
- Abstract summary: We investigate the formation of non-relativistic bound states, involving the P"oschl-Teller potential, in order to discuss the formation time and the thermal equilibrium.<n>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.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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 P\"oschl-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.
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