Title: Time-reversal symmetric resolution of unity without background integrals in open quantum systems

We present a new complete set of states for a class of open quantum systems, to be used in expansion of the Greenâ€™s function and the time-evolution operator. A remarkable feature of the complete set is that it observes time-reversal symmetry in the sense that it contains decaying states (resonant states) and growing states (anti-resonant states) parallelly. We can thereby pinpoint the occurrence of the breaking of time-reversal symmetry at the choice of whether we solve SchrĂ¶dinger equation as an initial-condition problem or a terminal-condition problem. Another feature of the complete set is that in the subspace of the central scattering area of the system, it consists of contributions of all states with point spectra but does not contain any background integrals. In computing the time evolution, we can clearly see contribution of which point spectrum produces which time dependence. In the whole infinite state space, the complete set does contain an integral but it is over unperturbed eigenstates of the environmental area of the system and hence can be calculated analytically. We demonstrate the usefulness of the complete set by computing explicitly the survival probability and the escaping probability as well as the dynamics of wave packets. The originmore » of each term of matrix elements is clear in our formulation, particularly, the exponential decays due to the resonance poles.« less

Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro, Tokyo 153-8505 Japan and Department of Physics, Washington University, One Brookings Drive, Saint Louis, Missouri 63130 (United States)

Department of Physics and Astronomy, Butler University Gallahue Hall, 4600 Sunset Ave, Indianapolis, Indiana 46208 (United States)

Publication Date:

OSTI Identifier:

22403064

Resource Type:

Journal Article

Resource Relation:

Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 12; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

Country of Publication:

United States

Language:

English

Subject:

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DECAY; FUNCTIONS; INTEGRALS; MATRIX ELEMENTS; RESOLUTION; SYMMETRY; TIME DEPENDENCE