Non-unitary operator equivalence classes, the PT-symmetric brachistochrone problem and Lorentz boosts
Year: 2007
Type: preprint
Abstract: The PT-symmetric (PTS) quantum brachistochrone problem is reanalyzed as quantum system consisting of a non-Hermitian PTS component and a purely Hermitian component simultaneously. Interpreting this specific setup as subsystem of a larger Hermitian system, we find non-unitary operator equivalence classes (conjugacy classes) as natural ingredient which contain at least one Dirac-Hermitian representative. With the help of a geometric analysis the compatibility of the vanishing passage time solution of a PTS brachistochrone with the Anandan-Aharonov lower bound for passage times of Hermitian brachistochrones is demonstrated.
Source: arXiv (Cornell University)
Authors: Uwe Guenther, B. F. Samsonov
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2964286648