Related papers: Dispersive analysis of the charge transfer models
In this paper, we will prove a very general result of stability for perturbations of linear integrable Hamiltonian systems, and we will construct an example of instability showing that both our result and our example are optimal. Moreover,…
In the framework of perturbation theory the reality of the perturbed eigenvalues of a class of $\PT$symmetric Hamiltonians is proved using stability techniques. We apply this method to $\PT$symmetric unperturbed Hamiltonians perturbed by…
We consider the class of non-Hamiltonian and dissipative statistical systems with distributions that are determined by the Hamiltonian. The distributions are derived analytically as stationary solutions of the Liouville equation for…
The relation between relaxation and diffusion is investigated in a Hamiltonian system of globally coupled rotators. Diffusion is anomalous if and only if the system is going towards equilibrium. The anomaly in diffusion is not anomalous…
An analytical approach to the one-dimensional spinless Holstein model is proposed, which is valid at finite charge-carrier concentrations. Spectral functions of charge carriers are computed on the basis of self-energy calculations. A…
Many-polaron systems with finite charge-carrier density are often encountered experimentally. However, until recently, no satisfactory theoretical description of these systems was available even in the framework of simple models such as the…
The theory of linear dispersive equations predicts that waves should spread out and disperse over time. However, it is a remarkable phenomenon, observed both in theory and practice, that once nonlinear effects are taken into account,…
We have studied properties of nonlinear waves in a mathematical model of a predator-prey system with pursuit and evasion. We demonstrate a new type of propagating wave in this system. The mechanism of propagation of these waves essentially…
We discuss the analysis and stability of a family of cross-diffusion boundary value problems with nonlinear diffusion and drift terms. We assume that these systems are close, in a suitable sense, to a set of decoupled and linear problems.…
Complex systems are often non-stationary, typical indicators are continuously changing statistical properties of time series. In particular, the correlations between different time series fluctuate. Models that describe the multivariate…
The semi-inclusive properties of the system of neutral and charged particles with net charge equal to zero are considered in the grand canonical, canonical and micro-canonical ensembles as well as in micro-canonical ensemble with scaling…
We study Bayes procedures for the problem of nonparametric drift estimation for one-dimensional, ergodic diffusion models from discrete-time, low-frequency data. We give conditions for posterior consistency and verify these conditions for…
This work presents a hierarchical model for solute transport in bounded layered porous media with random permeability. The model generalizes the Taylor-Aris dispersion theory to stochastic transport in random layered porous media with a…
In this paper, we demonstrate through the use of matrix calculus a transparent analysis of fractional inhomogeneous Markov models for life insurance where transition matrices commute. The resulting formulae are intuitive matrix…
We present a practical method to detect, diagnose and engineer higher order Van Hove singularities in multiband systems, with no restrictions on the number of bands and hopping terms. The method allows us to directly compute the Taylor…
The multilayer multiconfiguration time-dependent Hartree method is employed to study vibrationally coupled charge transport in models of single molecule junctions. To increase the efficiency of the simulation method, a representation of the…
We present a self-consistent theory for sound propagation in a simple model of a disordered solid. The solid is modeled as a collection of randomly distributed particles connected by harmonic springs with strengths that depend on the…
We present a complete analytical derivation of the equations used for stationary and nonstationary wave systems regarding resonant sound transmission and reflection described by the phenomenological Coupled-Mode Theory. We calculate the…
We consider a large class of harmonic systems, each defined as a quasi-free dynamics on the Weyl algebra over $\ell^2(\mathbb{Z}^d)$. In contrast to recently obtained, short-time locality estimates, known as Lieb-Robinson bounds, we prove a…
In this paper, we study small perturbations of a class of non-convex integrable Hamiltonians with two degrees of freedom, and we prove a result of diffusion for an open and dense set of perturbations, with an optimal time of diffusion which…