RESUMO
The chaotic mixing by random two-body interactions of many-electron Fock states in a confined geometry is investigated. Two regimes are distinguished in the dependence of the typical number of Fock states that are mixed into an eigenstate on the interaction strength V, the excitation energy varepsilon, and the level spacing Delta. In both regimes the number is large (indicating delocalization in Fock space). However, only the large- V regime is described by the golden rule (indicating chaotic mixing). The crossover region is characterized by a maximum in a scaling function that becomes more pronounced with increasing excitation energy. The scaling parameter that governs the transition is (varepsilonV/Delta(2))ln(Delta/V).
RESUMO
A recent paper [A. V. Kolesnikov and K. B. Efetov, Phys. Rev. Lett. 83, 3689 (1999)] predicts a two-scale behavior of wave function decay in disordered wires in the crossover regime from preserved to broken time-reversal symmetry. We have tested this prediction by a transmission approach, relying on the Borland conjecture that relates the decay length of the transmittance to the decay length of the wave functions. Our numerical simulations show no indication of two-scale behavior.
RESUMO
The average power spectrum of a pulse reflected by a disordered medium embedded in an N-mode waveguide decays in time with a power law t(-p). We show that the exponent p increases from 3 / 2 to 2 after N2 scattering times, due to the onset of localization. We compare two methods to arrive at this result. The first method involves the analytic continuation to an imaginary absorption rate of a static scattering problem. The second method involves the solution of a Fokker-Planck equation for the frequency dependent reflection matrix, by means of a mapping onto a problem in non-Hermitian quantum mechanics.
