Contact manifolds and dissipation, classical and quantum

Motivated by a geometric decomposition of the vector field associated with the Gorini–Kossakowski–Lindblad–Sudarshan (GKLS) equation for finite-level open quantum systems, we propose a generalization of the recently introduced contact Hamiltonian systems for the description of dissipative-like dynam...

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Bibliographic Details
Published in:Annals of physics 2018-11, Vol.398, p.159-179
Main Authors: Ciaglia, F.M., Cruz, H., Marmo, G.
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Contact manifold
Dissipation
DYNAMICAL SYSTEMS
General linear group
GKLS equation
Hamiltonian mechanics
HAMILTONIANS
LAGRANGIAN FUNCTION
Lagrangian mechanics
NONLINEAR PROBLEMS
Nonlinear Schrödinger equation
PURE STATES
QUANTUM MECHANICS
QUANTUM SYSTEMS
VECTOR FIELDS
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Summary:Motivated by a geometric decomposition of the vector field associated with the Gorini–Kossakowski–Lindblad–Sudarshan (GKLS) equation for finite-level open quantum systems, we propose a generalization of the recently introduced contact Hamiltonian systems for the description of dissipative-like dynamical systems in the context of (non-necessarily exact) contact manifolds. In particular, we show how this class of dynamical systems naturally emerges in the context of Lagrangian Mechanics and in the case of nonlinear evolutions on the space of pure states of a finite-level quantum system.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2018.09.012