Classical-quantum oscillators as diffusive processes in phase space

• URL: http://arxiv.org/abs/2510.07402v1
• Date: Wed, 08 Oct 2025 18:01:02 GMT
• Title: Classical-quantum oscillators as diffusive processes in phase space
• Authors: Emanuele Panella,
• Abstract summary: We show that for any initial state, the dynamics flows to a unique (non-equilibrium) steady state, which we compute explicitly.<n>We make use of a useful mapping between hybrid and classical diffusive dynamics, which we characterise in detail in the master equation formalism.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The dynamics of hybrid systems -- i.e. ones in which classical and quantum degrees of freedom co-exist and interact -- feature both diffusion in the classical sector and decoherence in the quantum state. In this article, we will consider the simple setup of a classical damped oscillator interacting with its quantum counterpart and show that, for any initial state, the dynamics flows to a unique (non-equilibrium) steady state, which we compute explicitly. To do so, we make use of a useful mapping between hybrid and classical diffusive dynamics, which we characterise in detail in the master equation formalism.

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