Fingerprints of classical diffusion in open 2 D mesoscopic systems in the metallic regime

– We investigate the distribution of the resonance widths P(Γ) and Wigner delay times P(τW) for scattering from two-dimensional systems in the diffusive regime. We obtain the forms of these distributions (log-normal for large τW and small Γ, and power law in the opposite case) for different symmetry classes and show that they are determined by the underlying diffusive classical dynamics. Our theoretical arguments are supported by extensive numerical calculations. Quantum scattering has been a subject of intensive research activity both in mesoscopic physics and in Quantum Chaos in the last years [1–7]. Among the most interesting quantities for the description of a scattering process are the Wigner delay times and resonance widths. The former quantity captures the time-dependent aspects of quantum scattering. It can be interpreted as the typical time an almost monochromatic wave packet remains in the interaction region. It is related to the energy derivative of the total phase shift Φ(E) = −i ln det S(E) of the scattering matrix S(E), i.e. τ W (E) = dΦ(E) dE. Resonances are defined as poles of the S-matrix occurring at complex energies E n = E n − i 2 Γ n , where E n is the position and Γ n the width of the resonance. They correspond to " eigenstates " of the open system that decay in time due to the coupling to the " outside world ". For chaotic/ballistic systems Random Matrix Theory (RMT) is applicable, and the distributions of resonance widths P(Γ) and Wigner delay times P(τ W) are known [2]. As the disorder increases the system becomes diffusive and the deviations from RMT become increasingly apparent. In the strongly disordered limit where localization dominates, the distribution of resonances P(Γ) [4] and delay times P(τ W) [5] were found recently. At the same time, an attempt to understand systems at critical conditions, was undertaken in [6, 7]. For diffusive mesoscopic samples, however, there is no study of P(Γ) and P(τ W) besides Ref. [3] where the authors have focused on the tails of P(Γ) for a quasi-1D system in the diffusive regime. This study is important for diffusive random lasers, where the knowledge of short resonance width distribution determines the properties of lasing thresholds [8], as well as for various other applications like mesoscopic capacitors [9], microwave cavities [10] and chaotic optical cavities [11] where most of the theoretical treatment is limited by RMT. …