December 2010
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Day December 7, 2010

Constructing Exactly Solvable Pseudo-hermitian Many-particle Quantum Systems by Isospectral Deformation

Pijush K. Ghosh

A class of non-Dirac-hermitian many-particle quantum systems admitting entirely real spectra and unitary time-evolution is presented. These quantum models are isospectral with Dirac-hermitian systems and are exactly solvable. 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. Examples of a pseudo-hermitian rational Calogero model and XXZ spin-chain are considered.

http://arxiv.org/abs/1012.0907
Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph)

Matrix Algebras in Non-Hermitian Quantum Mechanics

Alessandro Sergi

Non-Hermitian quantum dynamics can be defined by giving a more fundamental role either to the Heisenberg’s or to the Schr\”odinger’s picture of quantum dynamics. In both cases, it is shown how to map the algebra of commutators, defining time evolution in terms of a non-Hermitian Hamiltonian, onto a non-Hamiltonian algebra with a Hermitian Hamiltonian. The results and discussions are of interest to methods for simulating open quantum systems dynamics in terms of non-Hermitian time evolution.

http://arxiv.org/abs/1012.0906
Quantum Physics (quant-ph)