Localization in chaotic systems with a single-channel opening.
We introduce a single-channel opening in a random Hamiltonian and a quantized chaotic map: localization on the opening occurs as a sensible deviation of the wave-function statistics from the predictions of random matrix theory, even in the semiclassical limit. Increasing the coupling to the open channel in the quantum model, we observe a similar picture to resonance trapping, made of a few fast-decaying states, whose left (right) eigenfunctions are entirely localized on the (preimage of the) opening, and plentiful long-lived states, whose probability density is instead suppressed at the opening. For the latter, we derive and test a linear relation between the wave-function intensities and the decay rates, similar to the Breit-Wigner law. We then analyze the statistics of the eigenfunctions of the corresponding (discretized) classical propagator, finding a similar behavior to the quantum system only in the weak-coupling regime.
Institute for Advanced Study, Tsinghua University, Beijing 100084, China.|Department of Physics, Pusan National University, Busan 609-735, South Korea.
Domenico
D
Lippolis
Department of Physics, Pusan National University, Busan 609-735, South Korea.|School of Electronics Engineering, Kyungpook National University, Daegu 702-701, South Korea.
Jung-Wan
JW
Ryu
Department of Physics Education, Pusan National University, Busan 609-735, South Korea.
Sang Wook
SW
Kim