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Open quantum systems are often represented by non-Hermitian effectiveHamiltonians that have complex eigenvalues associated with resonances. Inprevious work we showed that the evolution of tight-binding open systems can berepresented by an explicitly time-reversal symmetric expansion involving allthe discrete eigenstates of the effective Hamiltonian. These eigenstatesinclude complex-conjugate pairs of resonant and anti-resonant states. Aninitially time-reversal-symmetric state contains equal contributions from theresonant and anti-resonant states. Here we show that as the state evolves intime, the symmetry between the resonant and anti-resonant states isautomatically broken, with resonant states becoming dominant for $t>0$ andanti-resonant states becoming dominant for $t<0$. Further, we show that thereis a time-scale for this symmetry-breaking, which we associate with the "Zenotime." We also compare the time-reversal symmetric expansion with an asymmetricexpansion used previously by several researchers. We show how the presenttime-reversal symmetric expansion bypasses the non-Hilbert nature of theresonant and anti-resonant states, which previously introduced exponentialdivergences into the asymmetric expansion.

The arrow of time in open quantum systems and dynamical breaking of the resonance-antiresonance symmetry