Egorov-Type Semiclassical Limits for Open Quantum Systems with a Bi-Lindblad Structure
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arXiv
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| Formato: | Preprint |
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2026
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| _version_ | 1866911436389744640 |
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| author | Colombo, Leonardo López-Gordón, Asier |
| author_facet | Colombo, Leonardo López-Gordón, Asier |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03041 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Egorov-Type Semiclassical Limits for Open Quantum Systems with a Bi-Lindblad Structure Colombo, Leonardo López-Gordón, Asier Mathematical Physics Differential Geometry Symplectic Geometry Quantum Physics 81S22 (primary), 37J35, 37J55, 46L60, 53Z05, 81Q70, 81R12, 81S10 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. |
| title | Egorov-Type Semiclassical Limits for Open Quantum Systems with a Bi-Lindblad Structure |
| topic | Mathematical Physics Differential Geometry Symplectic Geometry Quantum Physics 81S22 (primary), 37J35, 37J55, 46L60, 53Z05, 81Q70, 81R12, 81S10 |
| url | https://arxiv.org/abs/2601.03041 |