A canonical formulation of dissipative mechanics using complex-valued hamiltonians

We show that a large class of dissipative systems can be brought to a canonical form by introducing complex co-ordinates in phase space and a complex-valued hamiltonian. A naive canonical quantization of these systems lead to non-hermitean hamiltonian operators. The excited states are unstable and d...

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Veröffentlicht in:Annals of physics 2007-07, Vol.322 (7), p.1541-1555
1. Verfasser: Rajeev, S.G.
Format: Artikel
Sprache:eng
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Zusammenfassung:We show that a large class of dissipative systems can be brought to a canonical form by introducing complex co-ordinates in phase space and a complex-valued hamiltonian. A naive canonical quantization of these systems lead to non-hermitean hamiltonian operators. The excited states are unstable and decay to the ground state. We also compute the tunneling amplitude across a potential barrier by solving the dissipative version of the Schrödinger equation. We then generalize the formalism to cases where the configuration space is a curved Riemannian manifold.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2007.02.004