Contact manifolds and dissipation, classical and quantum Articles uri icon

publication date

  • November 2018

volume

  • 398

International Standard Serial Number (ISSN)

  • 0003-4916

Electronic International Standard Serial Number (EISSN)

  • 1096-035X

abstract

  • (copyright) 2018 Elsevier Inc.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.

keywords

  • contact manifold; dissipation; general linear group; gkls equation; hamiltonian mechanics; lagrangian mechanics; nonlinear schrödinger equation