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The quantum brachistochrone problem for non-Hermitian Hamiltonians

Assis, P. E. G. and Fring, A. (2008). The quantum brachistochrone problem for non-Hermitian Hamiltonians. Journal of Physics A: Mathematical and Theoretical, 41(24), doi: 10.1088/1751-8113/41/24/244002

Abstract

Recently Bender, Brody, Jones and Meister found that in the quantum brachistochrone problem the passage time needed for the evolution of certain initial states into specified final states can be made arbitrarily small, when the time-evolution operator is taken to be non-Hermitian but PT-symmetric. Here we demonstrate that such phenomena can also be obtained for non-Hermitian Hamiltonians for which PT-symmetry is completely broken, i.e. dissipative systems. We observe that the effect of a tunable passage time can be achieved by projecting between orthogonal eigenstates by means of a time-evolution operator associated with a non-Hermitian Hamiltonian. It is not essential that this Hamiltonian is PT-symmetric.

Publication Type: Article
Publisher Keywords: PSEUDO-HERMITICITY, PT-SYMMETRY, SPECTRUM, SYSTEMS, STATES
Subjects: Q Science > QC Physics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/779
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