The arrow of time in open quantum systems and dynamical breaking of the resonance-antiresonance symmetry
| Autor: | Ordonez, Gonzalo, Hatano, Naomichi |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | J. Phys. A: Math. Theor. 50 (2017) 405304 (34pp) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8121/aa85ae |
| Popis: | 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. Comment: 17 pages, 12 figures |
| Databáze: | arXiv |
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