On the construction of pseudo-hermitian quantum system with a pre-determined metric in the Hilbert space
Abstract
A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum system in terms of operators those are hermitian with respect to a pre-determined positive definite metric in the Hilbert space. Appropriate combinations of these operators result in a large number of pseudo-hermitian quantum systems admitting entirely real spectra and unitary time evolution. The examples considered include simple harmonic oscillators with complex angular frequencies, Stark(Zeeman) effect with complex electric(magnetic) field, non-hermitian general quadratic form of N boson(fermion) operators, symmetric and asymmetric XXZ spin-chain in complex magnetic field, non-hermitian Haldane-Shastry spin-chain and Lipkin-Meshkov-Glick model.
Keywords
Cite
@article{arxiv.0908.1321,
title = {On the construction of pseudo-hermitian quantum system with a pre-determined metric in the Hilbert space},
author = {Pijush K. Ghosh},
journal= {arXiv preprint arXiv:0908.1321},
year = {2010}
}
Comments
29 pages, revtex, minor changes, version to appear in Journal of Physics A(v3)