Related papers: On the electrical current distributions for the ge…
In this paper, the power flow in electrical systems is modelled in the time domain by using Geometric Algebra and the Hilbert Transform. The use of this mathematical framework overcomes some of the limitations shown by the existing…
We study the electron transport in open quantum-dot systems described by the interacting resonant-level models with Coulomb interactions. We consider the situation in which the quantum dot is connected to the left and right leads…
A class of generalized Schr\"{o}dinger problems in bounded domain is studied. A complete overview of the set of solutions is provided, depending on the values assumed by parameters involved in the problem. In order to obtain the results, we…
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus…
We present an algorithm for solving inverse problems on graphs analogous to those arising in diffuse optical tomography for continuous media. In particular, we formulate and analyze a discrete version of the inverse Born series, proving…
A recently introduced nonlinear Fokker-Planck equation, derived directly from a master equation, comes out as a very general tool to describe phenomenologically systems presenting complex behavior, like anomalous diffusion, in the presence…
I review the quantum theory of the electron moving in a random environment. First, the quantum mechanics of individual particles scattered on a random potential is discussed. The quantum-mechanical description is extended to many-body…
The porous media equation has been proposed as a phenomenological ``non-extensive'' generalization of classical diffusion. Here, we show that a very similar equation can be derived, in a systematic manner, for a classical fluid by assuming…
We develop a simple systematic method, valid for all strengths of disorder, to obtain analytically for the first time the full distribution of conductance P(g) for a quasi one dimensional wire in the absence of electron-electron…
Using the semiclassical neutral atom theory, we extend to fourth order the modified gradient expansion of the exchange energy of density functional theory. This expansion can be applied both to large atoms and solid-state problems.…
We derive backward and forward fractional Schr\"odinger type of equations for the distribution of functionals of the path of a particle undergoing anomalous diffusion. Fractional substantial derivatives introduced by Friedrich and…
We develop a simple systematic method, valid for all strengths of disorder, to obtain analytically the full distribution of conductances P(g) for a quasi one dimensional wire within the model of non-interacting fermions. The method has been…
A recently proposed analytical solution for the equations of motion of the one-body Green function of the double quantum dot is extended to the out-of-equilibrium situation. By solving a linear system for the density correlators, not only…
The manner in which probability amplitudes of paths sum up to form wave functions of a harmonic oscillator, as well as other, simple 1-dimensional problems, is described. Using known, closed-form, path-based propagators for each problem, an…
The bifurcation theory of ordinary differential equations (ODEs), and its application to deterministic population models, are by now well established. In this article, we begin to develop a complementary theory for diffusion-like…
In this paper, we present the general governing equations of electrodynamics and continuum mechanics that need to be considered while mathematically modelling the behaviour of electromagnetic acoustic transducers (EMATs). We consider the…
Based on the dispersion chain of the Vlasov equations, the paper considers the construction of a new chain of equations of quantum mechanics of high kinematical values. The proposed approach can be applied to consideration of classical and…
An approach which allows to include the corrections from non-orthogonality of electron states in contacts and quantum dots is developed. Comparison of the energy levels and charge distributions of electrons in 1D quantum dot (QD) in…
In this paper, we investigate the boundedness of the imaginary powers of four generalized diffusion operators. This key property, which implies the maximal regularity property, allows us to solve both the linear and semilinear Cauchy…
The flow of a thermoelectric current through a semiconductor of submicron dimensions is analyzed. The rate of surface relaxation of the energy is assumed to be much higher than the rate of electron-electron collisions. Under these…