Bound state formation within the Lindblad approach
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910867475398656 |
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| author | Rais, Jan van Hees, Hendrik Greiner, Carsten |
| author_facet | Rais, Jan van Hees, Hendrik Greiner, Carsten |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_07402 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bound state formation within the Lindblad approach Rais, Jan van Hees, Hendrik Greiner, Carsten Nuclear Theory Quantum Physics 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. |
| title | Bound state formation within the Lindblad approach |
| topic | Nuclear Theory Quantum Physics |
| url | https://arxiv.org/abs/2503.07402 |