2007/03/31 by Paulo E G Assis, Paulo E. G. Assis, Andreas Fring · 26 citations
Mathematics · Physics and Astronomy · #Dissipative operator #Dissipative system #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Ladder operator #Operator (biology) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #Quantum chaos and dynamical systems #Quantum system #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/41/24/244002
published in Journal of Physics A Mathematical and Theoretical 41(24), 244002 (Institute of Physics) · 7 pages Latex, 2 figures
arxiv created 2007/10/04 · openalex publication_date 2008/06/03 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 -symmetric. Here we demonstrate that such phenomena can also be obtained for non-Hermitian Hamiltonians for which -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 -symmetric.