Related papers: Dispersive analysis of the charge transfer models

In this paper, we study one-dimensional linear Schr\"odinger equations with multiple moving potentials, known as transfer charge models. Focusing on the non-self-adjoint setting that arises in the study of solitons, we systematically…

We continue our study of scattering theory and dispersive properties for one-dimensional charge transfer models, namely linear Schr\"odinger equations with multiple moving potentials. By the discovery of a refined structure of the…

We prove Strichartz estimates (both regular and reversed) for a scattering state to the wave equation with a charge transfer Hamiltonian in $\mathbb{R}^{3}$: \[ \partial_{tt}u-\Delta u+\sum_{j=1}^{m}V_{j}\left(x-\vec{v}_{j}t\right)u=0. \]…

We present a systematic analysis and classification of several models of quantum batteries involving different combinations of two level systems and quantum harmonic oscillators. In particular, we study energy transfer processes from a…

We present a model of electron transport through a random distribution of interacting quantum dots embedded in a dielectric matrix to simulate realistic devices. The method underlying the model depends only on fundamental parameters of the…

We consider the transport of conserved charges in spatially inhomogeneous quantum systems with a discrete lattice symmetry. We analyse the retarded two point functions involving the charge and the associated currents at long wavelengths,…

We prove the optimal endpoint Strichartz estimates for Schr\"{o}dinger equation with charge transfer potentials and a general source term in $\mathbb{R}^n$ for $n\geq3$. The proof is based on using the projection on the scattering states…

We consider the Vlasov-Poisson system with initial data a small, radial, absolutely continuous perturbation of a point charge. We show that the solution is global and disperses to infinity via a modified scattering along trajectories of the…

Molecular conduction operating in dielectric solvent environments are often described using kinetic rates based on Marcus theory of electron transfer at a molecule-metal electrode interface. However, the successive nature of charge transfer…

We developed a theory of charge transport in a system of non-interacting polarons. The theory was conducted to a compact relation through a nonperturbative method based on electron-phonon Hamiltonian. The derived final result represents…

We develop the techniques of \cite{KS1} and \cite{ES1} in order to derive dispersive estimates for a matrix Hamiltonian equation defined by linearizing about a minimal mass soliton solution of a saturated, focussing nonlinear Schr\"odinger…

Several models for the Monte Carlo simulation of Compton scattering on electrons are quantitatively evaluated with respect to a large collection of experimental data retrieved from the literature. Some of these models are currently…

We introduce a nonlinear parity-time-symmetric dispersive coupler which admits Hamiltonian and Lagrangian formulations. We show that, in spite of the gain and dissipation, the model has several conservation laws. The system also supports a…

We examine charged static perfect fluid distributions with a dilaton field in the frame-work of general relativity. We consider the case that the Einstein equations reduce to a non-linear version of Poisson equation. We show that Maxwell…

Simulations of charge transport in amorphous semiconductors are often performed in microscopically sized systems. As a result, charge carrier mobilities become system-size dependent. We propose a simple method for extrapolating a…

We study the Schr\"odinger flow for the SSH model, a class of self-adjoint discrete dimer lattice Hamiltonians on the half-line. Using oscillatory integral techniques, we prove dispersive time-decay estimates, which quantify the spreading…

We have developed a multi-scale self-consistent method to study the charge conductivity of a porous system or a metallic matrix alloyed by randomly distributed nonmetallic grains and vacancies by incorporating Schr\"{o}dinger's equation and…

We consider a family of models having an arbitrary positive amount of mass on each site and randomly exchanging an arbitrary amount of mass with nearest neighbor sites. We restrict to the case of diffusive models. We identify a class of…

Fluctuating-charge models are computationally efficient methods of treating polarization and charge-transfer phenomena in molecular mechanics and classical molecular dynamics simulations. They are also theoretically appealing as they are…

Soliton solutions are studied for paraxial wave propagation with intensity-dependent dispersion. Although the corresponding Lagrangian density has a singularity, analytical solutions, derived by the pseudo-potential method and the…