1999/03/08 by P. T. Leung, Leung, P. T., W. -M. Suen +6
Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Mechanical and Optical Resonators #Quantum chaos and dynamical systems #Spectroscopy and Quantum Chemical Studies #gr-qc #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/9903016
Published in Phys. Rev. E
arxiv created 1999/03/08 · openalex publication_date 1999/03/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.