相关论文: Homogenization of the Schrodinger equation with a …

Consistent quantum formalism based on the localized basis of the Wannirer functions in Heisenberg and Schrodinger pictures to describe propagation of electromagnetic field in a three dimensional media including diffraction is presented. In…

The Schroedinger equation with an energy-dependent complex absorbing potential, associated with a scattering system, can be reduced for a special choice of the energy-dependence to a harmonic inversion problem of a discrete pseudo-time…

In this article we have developed a formalism to obtain the Schr$\ddot{\rm{o}}$dinger equation for a particle in a frame undergoing an uniform acceleration in an otherwise flat Minkowski space-time geometry. We have presented an exact…

The linear Schr\"odinger equation with piecewise constant potential in one spatial dimension is a well-studied textbook problem. It is one of only a few solvable models in quantum mechanics and shares many qualitative features with…

We use the density matrix renormalization group method to study the properties of the one-dimensional Kondo-Heisenberg model doped with Kondo holes. We find that the perturbation of the Kondo holes to the local hybridization exhibits…

A new mathematical model for the description of three electron quantum dots in 2D space is created, and ground states of this system in external magnetic field is investigated. The Schrodinger equation for three two-dimensional electrons is…

We consider time-dependent Schroedinger equations in one dimension with double well potential and an external nonlinear perturbation. If the initial state belongs to the eigenspace spanned by the eigenvectors associated to the two lowest…

Convergence conditions for quantum annealing are derived for optimization problems represented by the Ising model of a general form. Quantum fluctuations are introduced as a transverse field and/or transverse ferromagnetic interactions, and…

The focus of our work is dispersive, second-order effective model describing the low-frequency wave motion in heterogeneous (e.g.~functionally-graded) media endowed with periodic microstructure. For this class of quasi-periodic medium…

This work develops a dynamic homogenization approach for metamaterials. It finds an approximate macroscopic homogenized equation with constant coefficients posed in space and time; however, the resulting homogenized equation is higher order…

A model quantum wire embedded in a matrix permeable to electron waves is investigated in terms of electronic states. The wire is assumed to have a 1D crystal structure. Through electron waves propagating in its surroundings, lateral modes…

We study Bloch wave homogenization of periodically heterogeneous media with fourth order singular perturbations. We recover different homogenization regimes depending on the relative strength of the singular perturbation and length scale of…

We examine time dependent Schrodinger equation with oscillating boundary condition. More specifically, we use separation of variable technique to construct time dependent rationally extended Poschl-Teller potential (whose solutions are…

In this paper, we study the decoherence of a wave described by the solution to a Schroedinger equation with a time-dependent random potential. The random potential is assumed to have slowly decaying correlations. The main tool to analyze…

Open systems that are weakly coupled to a thermal environment and driven by fast, periodically oscillating fields are commonly assumed to approach an equilibrium-like steady state with respect to a truncated Floquet-Magnus Hamiltonian.…

Quantum mechanics take the sum of first finite order approximate solutions of time-dependent perturbation to substitute the exact solution. From the point of mathematics, it may be correct only in the convergent region of the time-dependent…

By minimizing the difference between the left- and the right-hand sides of the many-body time-dependent Schr\"{o}dinger equation with the Slater-determinant wave-function, we derive a non-adiabatic and self-interaction free time-dependent…

A novel unified Hamiltonian approach is proposed to solve Maxwell-Schrodinger equation for modeling the interaction between classical electromagnetic (EM) fields and particles. Based on the Hamiltonian of electromagnetics and quantum…

We propose a new semiclassical approach based on the dynamical mean field theory to treat the interactions of electrons with local lattice fluctuations. In this approach the classical (static) phonon modes are treated exactly whereas the…

We derive an exact single-body decomposition of the time-dependent Schroedinger equation for N pairwise-interacting fermions. Each fermion obeys a stochastic time-dependent norm-preserving wave equation. As a first test of the method we…