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

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 open quantum 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 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 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.

44 pages. Final version as appearing in the journal

Mathematical Physics (math-ph); Differential Geometry (math.DG); Symplectic Geometry (math.SG); Quantum Physics (quant-ph)

arXiv:2601.03041 [math-ph]

(or arXiv:2601.03041v3 [math-ph] for this version)

https://doi.org/10.48550/arXiv.2601.03041 Focus to learn more arXiv-issued DOI via DataCite

Anal. Math. Phys. 16 (118), 2026

https://doi.org/10.1007/s13324-026-01265-9 Focus to learn more DOI(s) linking to related resources

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