Scattering and Resonances: Classical and Quantum Dynamics

J. M. Combes, Pierre Duclos, Ruedi Seiler

Gürsoy B. Akgüç, L. E. Reichl

Abstract A new type of quantum billiard, the ripple billiard, allows us to use reaction matrix theory to study the effect of dynamic tunneling on scattering processes in systems for which the underlying classical phase space contains a mixture of chaotic and regular orbits. We find that large scattering resonances occur due to dynamic tunneling of the quantum particle into classically forbidden nonlinear resonance regions. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Kunal K. Das, Joshua Garner, Kevin Ruppert

We report on the transport properties of a single-mode quantum pump that operates by the simultaneous translation and oscillation of a potential well. We examine the dynamics comparatively using quantum, classical, and semiclassical simulations. The use of an attractive or well potential is found to present several striking features absent if a barrier potential is used instead, as usually favored. The trapping of particles by the well for variable durations and subsequent release leads to a fractal-like structure in the distribution of the classical scattering trajectories. Interference among them leads to a rich dynamical structure in the quantum current, conspicuously missing in the classical current. Specifically, we observe sharp steps, spikes, and dips in the current as a function of the incident energy of the carriers and determine that a dynamical version of Fano resonance has a role that depends on the direction of incidence and on multiple scattering by the potential.

F. J. Arranz, R. M. Benito, F. Borondo

Marco Merkli

Felipe Barra, Pierre Gaspard

We study the classical limit of quantum mechanics on graphs by introducing a Wigner function for graphs. The classical dynamics is compared to the quantum dynamics obtained from the propagator. In particular, we consider extended open graphs whose classical dynamics generate a diffusion process. The transport properties of the classical system are revealed in the scattering resonances and in the time evolution of the quantum system.