Escaping from a complex maze, by exploring different paths with several decision-making branches in order to reach the exit, has always been a very challenging and fascinating task. Wave field and quantum objects may explore a complex structure in parallel by interference effects, but without necessarily leading to more efficient transport. Here, inspired by recent observations in biological en...

We present a dynamical analysis of the transport through small quantum cavities with large openings. The systematic suppression of shot noise is used to distinguish direct, deterministic from indirect, indeterministic transport processes. The analysis is based on quantum mechanical calculations of S matrices and their poles for quantum billiards with convex boundaries of different shape and two...

We develop the `duality approach', that has been extensively studied for classical models of transport, quantum systems in contact with a thermal `Lindbladian' bath. The method provides (a) mapping original model to simpler one, containing only few particles and (b) shows any dynamic process this kind generic baths may be mapped onto one equilibrium baths. exemplify through study particular mod...

The calculation of quantum canonical time correlation functions is considered in this paper. Transport properties, such as diffusion and reaction rate coefficients, can be determined from time integrals of these correlation functions. Approximate, quantum-classical expressions for correlation functions, which are amenable to simulation, are derived. These expressions incorporate the full quantu...