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

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.

17 pages, 12 figures

References in corpus (6)

• Amplification of non-Markovian decay due to bound state absorption into continuum
• Time-reversal symmetric resolution of unity without background integrals in open quantum systems
• Equivalence of the effective Hamiltonian approach and the Siegert boundary condition for resonant states
• Hermitian and non-Hermitian formulations of the time evolution of quantum decay
• Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects
• To the Theory of Unstable States

Cited by in corpus (11)

• Non-Markovian dynamics revealed at the bound state in continuum
• Exact description of coalescing eigenstates in open quantum systems in terms of microscopic Hamiltonian dynamics
• Anomalous-order exceptional point and non-Markovian Purcell effect at threshold in one-dimensional continuum systems
• Resonance-dominant optomechanical entanglement in open quantum systems
• Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model
• Time-Reversal Symmetry and Arrow of Time in Quantum Mechanics of Open Systems
• One-proton emission from the ${}_{\Lambda }^6$Li hypernucleus
• Convergence and completeness for square-well Stark resonant state expansions
• Swanson Hamiltonian: non-PT-symmetry phase
• Weak-coupling bound states in semi-infinite topological waveguide QED
• Characteristic influence of exceptional points in quantum dynamics