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Quantum scattering is studied in a system consisting of randomly distributed point scatterers in the strip. The model is continuous yet exactly solvable. Varying the number of scatterers (the sample length) we investigate a transition…

Quantum mechanical scattering theory is studied for time-dependent Schroedinger operators, in particular for particles in a rotating potential. Under various assumptions about the decay rate at infinity we show uniform boundedness in time…

Gas permeation through nanoscale pores is ubiquitous in nature and plays an important role in a plethora of technologies. Because the pore size is typically smaller than the mean free path of gas molecules, their flow is conventionally…

We show that Wronskians between properly chosen linearly independent solutions of the Schr\"odinger equation greatly facilitate the study of quantum scattering in one dimension. They enable one to obtain the necessary relationships between…

By following the trajectories of quantum particles inside a periodic lattice and preserving their classical probabilities for reflection, transmission and absorption at each lattice plane, classical scattering outcomes are obtained.…

Quantum mechanical scattering theory is a subject with a long and winding history. We shall pick out some of the most important concepts and ideas of scattering theory and look at them from the perspective of Bohmian mechanics: Bohmian…

For a substance diffusing on a curved surface, we obtain an explicit relation valid for very small values of the time, between the local concentration, the diffusion coefficient, the intrinsic spatial curvature and the time. We recover the…

We consider the scattering theory for the defocusing energy subcritical wave equations with an inverse square potential. By employing the energy flux method we establish energy flux estimates on the light cone. Then by the characteristic…

We study a quantum particle propagating through a ``quantum mechanically chaotic'' background, described by parametric random matrices with only short range spatial correlations. The particle is found to exhibit turbulent-like diffusion…

A version of scattering theory that was developed many years ago to treat nuclear scattering processes, has provided a powerful tool to study universality in scattering processes involving open quantum systems with underlying classically…

The quantum diffusion of a particle in an initially localized state on a cyclic lattice with N sites is studied. Diffusion and reconstruction time are calculated. Strong differences are found for even or odd number of sites and the limit…

The scattering of free particles constrained to move on a cylindrically symmetric curved surface is studied. The nontrivial geometry of the space contributes to the scattering cross section through the kinetic as well as a possible scalar…

The propagation of a localized wave packet in the conical space-time created by a pointlike massive source in 2+1 dimensional gravity is analyzed. The scattering amplitude is determined and shown to be finite along the classical scattering…

We report on the recent construction of a scattering theory for Maxwell potentials on curved spacetimes.

We give a method of describing thermodynamical transport phenomena, based on a quantum scattering theoretical approach. We consider a quantum system of particles connected to thermodynamical reservoirs by leads. The effects of the…

A finite-time fluctuation theorem for the diffusion-influenced surface reaction A <=> B is investigated for spherical and Janus catalytic particles. The finite-time rates and thermodynamic force are analytically calculated by solving…

Scattering is an important phenomenon which is observed in systems ranging from the micro- to macroscale. In the context of nuclear reaction theory the Heidelberg approach was proposed and later demonstrated to be applicable to many chaotic…

The scattering theory of quantum transport relates transport properties of disordered mesoscopic conductors to their transfer matrix $\bbox{T}$. We introduce a novel approach to the statistics of transport quantities which expresses the…

We describe the bound state and scattering properties of a quantum mechanical particle in a scalar $N$-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy…

Quantum mechanics is sensitive to the geometry of the underlying space. Here, we present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space. When the motion manifold hosts localized…