Waves in Open Systems via Bi-orthogonal Basis

Details Waves in Open Systems via Bi-orthogonal Basis Waves in Open Systems via Bi-orthogonal Basis

1999-03-08

arxiv.org/abs/math-ph/9903016v1

Physics

Mathematical Physics

Published in Phys. Rev. E

Scientific paper

Dissipative quantum systems are sometimes phenomenologically described in terms of a non-hermitian hamiltonian $H$, with different left and right eigenvectors forming a bi-orthogonal basis. It is shown that the dynamics of waves in open systems can be cast exactly into this form, thus providing a well-founded realization of the phenomenological description and at the same time placing these open systems into a well-known framework. The formalism leads to a generalization of norms and inner products for open systems, which in contrast to earlier works is finite without the need for regularization. The inner product allows transcription of much of the formalism for conservative systems, including perturbation theory and second-quantization.

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