Dissipative Mechanics Using Complex-Valued Hamiltonians
Quantum Physics
2007-05-23 v1 Statistical Mechanics
High Energy Physics - Theory
Mathematical Physics
Dynamical Systems
math.MP
Symplectic Geometry
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.
Keywords
Cite
@article{arxiv.quant-ph/0701141,
title = {Dissipative Mechanics Using Complex-Valued Hamiltonians},
author = {S. G. Rajeev},
journal= {arXiv preprint arXiv:quant-ph/0701141},
year = {2007}
}