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

TL;DR

This paper investigates how the symmetry between resonant and anti-resonant states in open quantum systems is broken over time, revealing a natural arrow of time and addressing divergence issues in previous expansions.

Contribution

It introduces a time-reversal symmetric expansion for open quantum systems that explains the dynamical breaking of resonance-antiresonance symmetry and overcomes divergence problems of earlier methods.

Findings

Resonant states dominate for t>0

Anti-resonant states dominate for t<0

Identifies a Zeno time scale for symmetry breaking

Abstract

Open quantum systems are often represented by non-Hermitian effective Hamiltonians that have complex eigenvalues associated with resonances. In previous work we showed that the evolution of tight-binding open systems can be represented by an explicitly time-reversal symmetric expansion involving all the discrete eigenstates of the effective Hamiltonian. These eigenstates include complex-conjugate pairs of resonant and anti-resonant states. An initially time-reversal-symmetric state contains equal contributions from the resonant and anti-resonant states. Here we show that as the state evolves in time, the symmetry between the resonant and anti-resonant states is automatically broken, with resonant states becoming dominant for $t>0$ and anti-resonant states becoming dominant for $t<0$. Further, we show that there is a time-scale for this symmetry-breaking, which we associate with the "Zeno time." We also compare the time-reversal symmetric expansion with an asymmetric expansion used previously by several researchers. We show how the present time-reversal symmetric expansion bypasses the non-Hilbert nature of the resonant and anti-resonant states, which previously introduced exponential divergences into the asymmetric expansion.