Related papers: Scattering and delay time for 1D asymmetric potent…
Energetic particles spectra at interplanetary shocks often exhibit a power law within a narrow momentum range softening at higher energy. We introduce a transport equation accounting for particle acceleration and escape with diffusion…
In this work we consider a wide range of energy critical wave equation in 3-dimensional space with radial data. We are interested in exterior scattering phenomenon, in which the asymptotic behaviour of a solutions $u$ to the non-linear wave…
In this master thesis, a new approximation scheme to non-relativistic potential scattering is developed and discussed. The starting points are two exact path integral representations of the T-matrix, which permit the application of the…
The exact two-particle energy eigenstates in a generic asymmetric rectangular box with periodic boundary conditions in all three directions are studied. Their relation with the elastic scattering phases of the two particles in the continuum…
The annealing treatment in the advanced manufacturing process, e.g., laser-assisted manufacturing, determines the final state of glasses which is critical to its thermal, electrical and mechanical properties. Energy barriers analysis based…
We present a systematic treatment of scattering processes for quantum systems whose time evolution is discrete. We define and show some general properties of the scattering operator, in particular the conservation of quasi-energy which is…
On the base of a 1D Shr\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a…
The scattering potential of the defects on Ge(001) surfaces is investigated by first-principles methods. The standing wave in the spatial map of the local density of states obtained by wave function matching is compared to the image of the…
Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long…
We present a minimal model to analyze the capacitive response of a biological membrane subjected to a step voltage via blocking electrodes. Through a perturbative analysis of the underlying electrolyte transport equations, we show that the…
We apply the asymptotic iteration method (AIM) [J. Phys. A: Math. Gen. 36, 11807 (2003)] to solve new classes of second-order homogeneous linear differential equation. In particular, solutions are found for a general class of eigenvalue…
We consider a free quantum particle in one dimension whose mass profile exhibits jump discontinuities. The corresponding Hamiltonian is a self-adjoint realisation of the kinetic-energy operator, with the specific realisation determined by…
We develop an eigenvalue-based approach for the stability assessment and stabilization of linear systems with multiple delays and periodic coefficient matrices. Delays and period are assumed commensurate numbers, such that the Floquet…
We derive analytic expressions of the recursive solutions to the Schr\"{o}dinger's equation by means of a cutoff potential technique for one-dimensional piecewise constant potentials. These solutions provide a method for accurately…
There is recent interest in the inter and intra element interactions of metamaterial unit cells. To calculate the effects of these interactions which can be substantial, an ab initio general coupled mode equation, in the form of an…
The stationary phase method is applied to diffusion by a potential barrier for an incoming wave packet with energies greater then the barrier height. It is observed that a direct application leads to paradoxical results. The correct…
When a Brownian particle, initially being in the potential well, overcomes the barrier and moves to the absorptive border, it still has a chance to be scattered back to the well by thermal fluctuations. We study this phenomenon carefully…
It was shown using perturbation theory[1] that Thouless energy Ec for a quantum system scales linearly with the conductance of the system. We derive in an alternate way in 1-D that Ec scales with the conductance in a very different way. We…
Representation of the elastic scattering amplitude in the form of the path integral is obtained using the stationary Schroedinger equation. A few methods of evaluation of path integrals for large coupling constants are formulated. The…
The discovery of topological insulators has opened new prospects for robust signal transport for electronic, phononic, and photonic devices. Though transport of topological protected edge states is robust to disorder, large fluctuations and…