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- W2744489927 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." @default.
- W2744489927 created "2017-08-17" @default.
- W2744489927 creator A5014471207 @default.
- W2744489927 creator A5084024265 @default.
- W2744489927 date "2017-09-06" @default.
- W2744489927 modified "2023-10-16" @default.
- W2744489927 title "The arrow of time in open quantum systems and dynamical breaking of the resonance–anti-resonance symmetry" @default.
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- W2744489927 doi "https://doi.org/10.1088/1751-8121/aa85ae" @default.
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