Paper Info
Title
Time-Reversal Symmetry and Arrow of Time in Quantum Mechanics of Open Systems
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 Schrodinger 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 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.
Year
DOI
Venue
2019
10.3390/e21040380
ENTROPY
Keywords
Field
DocType
open quantum system,time-reversal symmetry,arrow of time,resonant state
Open quantum system,T-symmetry,Quantum,Mathematical optimization,Hamiltonian (quantum mechanics),Mathematical physics,Schrödinger equation,Arrow of time,Hermitian matrix,Quantum dynamics,Mathematics
Journal
Volume
Issue
ISSN
21
4
1099-4300
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
Naomichi Hatano1727.49
Gonzalo Ordonez2281.75