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Dissipative Mechanics Using Complex-Valued Hamiltonians

S. G. Rajeev
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Abstract

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.

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S. G. Rajeev. 2007-01-19. Dissipative Mechanics Using Complex-Valued Hamiltonians. https://arxiv.org/abs/quant-ph/0701141

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