Egorov-Type Semiclassical Limits for Open Quantum Systems with a Bi-Lindblad Structure

• URL: http://arxiv.org/abs/2601.03041v1
• Date: Tue, 06 Jan 2026 14:21:29 GMT
• Title: Egorov-Type Semiclassical Limits for Open Quantum Systems with a Bi-Lindblad Structure
• Authors: Leonardo Colombo, Asier López-Gordón,
• Abstract summary: Bi-Hamiltonian structures of Poisson-Lie type, contact Hamiltonian dynamics, and the Gorini-Kossakowski-Sudarshan-Lindblad formalism are studied.<n>On the classical side, we consider bi-Hamiltonian systems defined by a Poisson pencil with non-trivial invariants.<n>On the quantum side, we introduce a class of contact-compatible Lindblad generators.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper develops a bridge between bi-Hamiltonian structures of Poisson-Lie type, contact Hamiltonian dynamics, and the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) formalism for quantum open systems. On the classical side, we consider bi-Hamiltonian systems defined by a Poisson pencil with non-trivial invariants. Using an exact symplectic realization, these invariants are lifted and projected onto a contact manifold, yielding a completely integrable contact Hamiltonian system in terms of dissipated quantities and a Jacobi-commutative algebra of observables. On the quantum side, we introduce a class of contact-compatible Lindblad generators: GKSL evolutions whose dissipative part preserves a commutative $C^\ast$-subalgebra generated by the quantizations of the classical dissipated quantities, and whose Hamiltonian part admits an Egorov-type semiclassical limit to the contact dynamics. This construction provides a mathematical mechanism compatible with the semiclassical limit for pure dephasing, compatible with integrability and contact dissipation. An explicit Euler-top-type Poisson-Lie pencil, inspired by deformed Euler top models, is developed as a fully worked-out example illustrating the resulting bi-Lindblad structure and its semiclassical behavior.

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