Related papers: Quaternionic Diffusion by a Potential Step
Quantum dynamics of a particle confined in a box with time-dependent wall is revisited by considering some unexplored aspects of the problem. In particular, the case of dynamical confinement in a time-dependent box in the presence of purely…
We investigate the diffusive motion of an overdamped classical particle in a 1D random potential using the mean first-passage time formalism and demonstrate the efficiency of this method in the investigation of the large-time dynamics of…
The correspondence principle is investigated in the framework of deterministic predictions for individual systems. Exact analytical results are obtained for the quantum and the Liouvillian dynamics of a nonlinear oscillator coupled to a…
Motivated by a quaternionic formulation of quantum mechanics, we discuss quaternionic and complex linear differential equations. We touch only a few aspects of the mathematical theory, namely the resolution of the second order differential…
An analytical solution for a quantum wave impedance in a case of piesewise constant potential was derived. It is in fact an analytical depiction of a well-known iterative method of a quantum wave impedance determination. The expression for…
The paper contains the proof that the diffusion ensemble of point wise particles with the intensity depending on the grain of spatial resolution serves as the satisfactory approximation of one quantum particle dynamics.
In this paper, we have firstly presented a new quantum theory to study one-dimensional photonic crystals. We give the quantum transform matrix, quantum dispersion relation and quantum transmissivity, and compare them with the classical…
The major conceptual difficulties of quantum mechanics are analyzed. They are: the notion "wave-particle", the probabilistic interpretation of the Schroedinger wave \psi-function and hence the probability amplitude and its phase, long-range…
We consider a discrete time particle model for kinetic transport on the two dimensional integer lattice. The particle can move due to advection in the $x$-direction and due to dispersion. This happens when the particle is free, but it can…
This papers presents a formalism describing the dynamics of a quantum particle in a one-dimensional tilted time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice and provides a…
We study the quantum tunnelling of a very complex object of which only part is coupled to an external potential ( the potential barrier ). We treat this problem as the tunnelling of a particle (part of the system affected by the potential)…
Transport surrounding is full of all kinds of fields, like particle potential, external potential. Under these conditions, how elements work and how position and momentum redistribute in the diffusion? For enriching the Fick law in…
We present a method to extract the phase shift of a scattering process using the real-time evolution in the early and intermediate stages of the collision in order to estimate the time delay of a wave packet. This procedure is convenient…
Propagation in quantum walks is revisited by showing that very general 1D discrete-time quantum walks with time- and space-dependent coefficients can be described, at the continuous limit, by Dirac fermions coupled to electromagnetic…
Measurable quantities that have positive values in classical dynamical systems need not to be positive in quantum theory. For example, consider a free quantum mechanical particle in one dimension. There are quantum states in which the…
We investigate the orgin of ``quantum superarrivals'' in the reflection and transmission probabilities of a Gaussian wave packet for a rectangular potential barrier while it is perturbed by either reducing or increasing its height. There…
We follow the trajectories of phase singularities at nulls of intensity in the speckle pattern of waves transmitted through random media as the frequency of the incident radiation is scanned in microwave experiments and numerical…
We prove that, under the condition of validity of the Fresnel approximation, diffraction and interference for a wave traveling in the z-direction may be described in terms of the spreading in time of the transverse (x,y)-wave packet. The…
After a review of the problems associated with the conventional treatment of particle oscillations, an oscillation formula is derived within the framework of quantum field theory. The oscillating particle is represented by its propagator…
We study the quantum dynamics of a suddenly released beam of particles using a background independent (polymer) quantization scheme. We show that, in the first order of approximation, the low-energy polymer distribution converges to the…