| I will talk on the spontaneous breaking of the time-reversal symmetry by resonant states of open quantum systems. Open quantum systems have resonant states as eigenstates of the stationary Schroedinger equation. The resonant states have complex eigenvalues and decay in time. Each resonant eigenstate therefore breaks the time-reversal symmetry spontaneously. The time-reversal symmetry that the Schroedinger equation has is recovered only after each resonant state is paired with the corresponding anti-resonant state, which grows in time. This breaking of the time-reversal symmetry explaines the energy dissipation in nano-structures. Indeed, the Landauer formula tells us that the conductance (the inverse resistance) of a nano-structure is given by a solution of the scattering problem. Here the energy dissipation into particle baths is simulated by the decay of a resonant state. |
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