Time-Reversal Symmetry and Arrow of Time in Quantum Mechanics of Open Systems.
Entropy (Basel)
; 21(4)2019 Apr 08.
Article
em En
| MEDLINE
| ID: mdl-33267094
ABSTRACT
It is one of the most important and long-standing issues of physics to derive the irreversibility out of a time-reversal symmetric equation of motion. The present paper considers the breaking of the time-reversal symmetry in open quantum systems and the emergence of an arrow of time. We claim that the time-reversal symmetric Schrödinger equation can have eigenstates that break the time-reversal symmetry if the system is open in the sense that it has at least a countably infinite number of states. Such eigenstates, namely the resonant and anti-resonant states, have complex eigenvalues. We show that, although these states are often called "unphysical", they observe the probability conservation in a particular way. We also comment that the seemingly Hermitian Hamiltonian is non-Hermitian in the functional space of the resonant and anti-resonant states, and hence there is no contradiction in the fact that it has complex eigenvalues. We finally show how the existence of the states that break the time-reversal symmetry affects the quantum dynamics. The dynamics that starts from a time-reversal symmetric initial state is dominated by the resonant states for t > 0 ; this explains the phenomenon of the arrow of time, in which the decay excels the growth. The time-reversal symmetry holds in that the dynamic ending at a time-reversal symmetric final state is dominated by the anti-resonant states for t < 0 .
Texto completo:
1
Coleções:
01-internacional
Base de dados:
MEDLINE
Idioma:
En
Revista:
Entropy (Basel)
Ano de publicação:
2019
Tipo de documento:
Article
País de afiliação:
Japão