Abstract
Resonances are defined as the poles of the scattering matrix. The poles are associated with the complex eigenvalues of the Hamiltonian which are embedded in the lower half of the complex plane. The asymptotes of the corresponding eigenfunctions are exponentially diverged. Therefore, the resonance eigenfunctions are not embedded in the Hermitian domain of the Hamiltonian. The time asymmetric problem is discussed for these types of non-Hermitian Hamiltonians and several solutions of this problem are proposed.
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References
Bohm, A., Harshman, N. L., and Walther, H. (2002). Physical Review A 66, 012107.
Csoto, A., Gyarmati, B., Kruppa, A. T., Pal, K. F., and Moiseyev, N. (1990). Physical Review A 41, 3469.
Fermi, E. (1932). Reviews of Modern Physics 4, 87.
Fogedby, H. C., Eriksson, A. B., and Mikheev, L. V. (1995). Physical Review Letters 75, 1883.
Hatano, N. and Nelson, D. R. (1996). Physical Review Letters 77, 5706.
Hatano, N. and Nelson, D. R. (1997). Physical Review B 56, 8651.
Hatano, N. and Nelson, D. R. (1998).58, 8384.
Kadanoff, L. P. and Swift, J. (1968). Physical Review 165, 310.
Kim, D. (1995). Physical Review E 52, 3512.
Lieb, E. H. and Wu, F. Y. (1972). In Phase Transitions and Critical Phenomena, Vol. 1, Domb, C. and Green, M. S. (eds). Academic, London, p. 331.
McCoy, B. M. and Wu, T. T. (1968). Nuovo Cimento, B 56, 311.
Moiseyev, N. (1998a). Physics Reports 302, 211.
Moiseyev, N. (1998b). Journal of Physics B: Atomic, Molecular and Optical Physics 31, 1431
Narevicius, E. and Moiseyev, N. (1998). Physical Review Letters 81, 2221.
Narevicius, E. and Moiseyev, N. (2000). Physical Review Letters 84, 1681.
Nicolaides, C. A. and Beck, D. R. (1977a). Physical Review Letters 38, 683.
Nicolaides, C. A. and Beck, D. R. (1977b).38, 1037.
Peskin, U. and Moiseyev, N. (1993a). International Journal of Quantum Chemistry 46, 343.
Peskin, U. and Moiseyev, N. (1993b). Journal of Chemical Physics 99, 4590.
Peskin, U. and Moiseyev, N. (1994). Physical Review A 49, 3712.
Reinhardt, W. P. (1982). Annual Review of Physical Chemistry 33, 223.
Riss, U. V. and Meyer, H-D. (1993). Journal of Physics B: Atomic, Molecular and Optical Physics 26, 4503.
Taylor, J. R. (1972). Scattering Theory: The Quantum Theory of Non-Relativistic Collisions, Wiley, New York.
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Moiseyev, N., Narevich, R. The Resonance Phenomena Associated with the Time Asymmetry in Non-Hermitian Quantum Mechanics. International Journal of Theoretical Physics 42, 2131–2143 (2003). https://doi.org/10.1023/B:IJTP.0000005951.03650.60
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DOI: https://doi.org/10.1023/B:IJTP.0000005951.03650.60