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arXiv · 2412.08154

Effective description of open quantum dynamics in relativistic scattering

Kaito Kashiwagi·Akira Matsumura
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Abstract

The open dynamics of quantum particles in relativistic scattering is investigated. In particular, we consider the scattering process of quantum particles coupled to an environment initially in a vacuum state. Tracing out the environment and using the unitarity of S-operator, we find the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) generator describing the evolution of the particles. The GKSL generator is exemplified by focusing on the concrete processes: one is the decay of scalar particle ($ϕ\rightarrow χχ$), and the others are the pair annihilation and the $2\rightarrow 2$ scattering of scalar particles ($ϕϕ\rightarrow χχ$ and $ϕϕ\rightarrow ϕϕ$). The GKSL generator for $ϕ\rightarrow χχ$ has a parameter with the coupling between $ϕ$ and $χ$ and the mass of both fields. The GKSL generator associated with $ϕϕ\rightarrow χχ$ is characterized by a Lorentz-invariant function of initial momenta. Especially, in the pair annihilation process, we show that the probability of pair annihilation varies depending on the superposition state of incident scalar $ϕ$ particles. Furthermore, we observe that the GKSL generators derived in this paper have Poincaré symmetry. This means that the description by the GKSL generator with Poincaré symmetry is effective for the asymptotic behavior of open quantum dynamics in the long-term processes of interest.

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Kaito Kashiwagi, Akira Matsumura. 2024-12-11. Effective description of open quantum dynamics in relativistic scattering. https://arxiv.org/abs/2412.08154

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