Time-Reversal Symmetry and Arrow of Time in Quantum Mechanics of Open Systems
AbstractIt 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
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Hatano, N.; Ordonez, G. Time-Reversal Symmetry and Arrow of Time in Quantum Mechanics of Open Systems. Entropy 2019, 21, 380.
Hatano N, Ordonez G. Time-Reversal Symmetry and Arrow of Time in Quantum Mechanics of Open Systems. Entropy. 2019; 21(4):380.Chicago/Turabian Style
Hatano, Naomichi; Ordonez, Gonzalo. 2019. "Time-Reversal Symmetry and Arrow of Time in Quantum Mechanics of Open Systems." Entropy 21, no. 4: 380.
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