Assis, P. E. G. & Fring, A. (2008). The quantum brachistochrone problem for nonHermitian Hamiltonians. Journal of Physics A: Mathematical and Theoretical, 41(24), doi: 10.1088/17518113/41/24/244002

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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 timeevolution operator is taken to be nonHermitian but PTsymmetric. Here we demonstrate that such phenomena can also be obtained for nonHermitian Hamiltonians for which PTsymmetry 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 timeevolution operator associated with a nonHermitian Hamiltonian. It is not essential that this Hamiltonian is PTsymmetric.
Item Type:  Article 

Uncontrolled Keywords:  PSEUDOHERMITICITY, PTSYMMETRY, SPECTRUM, SYSTEMS, STATES 
Subjects:  Q Science > QC Physics 
Divisions:  School of Engineering & Mathematical Sciences > Department of Mathematical Science 
URI:  http://openaccess.city.ac.uk/id/eprint/779 
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