On dynamical semigroup for damped driven Jaynes-Cummings equations

• URL: http://arxiv.org/abs/2603.17553v1
• Date: Wed, 18 Mar 2026 10:01:49 GMT
• Title: On dynamical semigroup for damped driven Jaynes-Cummings equations
• Abstract summary: The article addresses the damped driven Jaynes-Cummings for quantised one-mode Maxwell field coupled to a two-level molecule.<n>We consider a broad class of pumping which are damping in the creation and Hilbert-Schmidt operators.<n>All trajectories of the semigroup are generalised solutions to the Jaynes-Cummings equations.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The article addresses the damped driven Jaynes-Cummings for quantised one-mode Maxwell field coupled to a two-level molecule. We consider a broad class of damping and pumping which are polynomial in the creation and annihilation operators. Our main result is the construction of a contraction dynamical semigroup in the Hilbert space of Hermitian Hilbert-Schmidt operators in the case of a nonpositive dissipation operator and time-independent pumping. All trajectories of the semigroup are generalised solutions to the Jaynes-Cummings equations. As a key example, we prove nonpositivity for the basic dissipation operator of Quantum Optics.

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