相关论文: Convergence to SPDE of the Schrodinger equation wi…

We study the behavior of solutions to a Schr{\"o}dinger equation with large, rapidly oscillating, mean zero, random potential with Gaussian distribution. We show that in high dimension $d>\mathfrak{m}$, where $\mathfrak{m}$ is the order of…

We consider the perturbation of parabolic operators of the form $\partial_t+P(x,D)$ by large-amplitude highly oscillatory spatially dependent potentials modeled as Gaussian random fields. The amplitude of the potential is chosen so that the…

In this paper we study the asymptotic phase space energy distribution of solution of the Schr\"{o}dinger equation with a time-dependent random potential. The random potential is assumed to be with slowly decaying correlations. We show that…

We study the effective approximation for a nonlocal stochastic Schrodinger equation with a rapidly oscillating, periodically time-dependent potential. We use the natural diffusive scaling of heterogeneous system and study the limit…

We investigate the global well-posedness and modified scattering for the one-dimensional Schr\"odinger equation with gauge-invariant polynomial nonlinearity. For small localized initial data of finite energy in a low-regularity class, we…

We analyze the weak-coupling limit of the random Schr\"odinger equation with low frequency initial data and a slowly decorrelating random potential. For the probing signal with a sufficiently long wavelength, we prove a homogenization…

We study the long-time mixing behavior of the stochastic nonlinear Schr\"odinger equation in $\mathbb{R}^d$, $d\le 3$. It is well known that, under a sufficiently strong damping force, the system admits unique ergodicity, although the rate…

In this paper we obtain a stabilization result for the Schr\"odinger equation under generic assumptions on the potential. Then we consider the Schr\"odinger equation with a potential which has a random time-dependent amplitude. We show that…

We study the local behavior of solutions of the stationary Schr\" od\-inger equation with singular potentials, establishing a local decomposition into a homogeneous harmonic polynomial and a lower order term. Combining a corollary to this…

For the first time, a nonlinear Schr\"odinger equation of the general form is considered, depending on time and two spatial variables, the potential and dispersion of which are specified by two arbitrary functions. This equation naturally…

In this paper, we consider the convergence problem of Schr\"odinger equation. Firstly, we show the almost everywhere pointwise convergence of Schr\"odinger equation in Fourier-Lebesgue spaces…

The discrete one-dimensional Schr\"odinger operator is studied in the finite interval of length $N=2 M$ with the Dirichlet boundary conditions and an arbitrary potential even with respect to the spacial reflections. It is shown, that the…

We consider the defocusing nonlinear Schr{\"o}dinger equation in several space dimensions, in the presence of an external potential depending on only one space vari-able. This potential is bounded from below, and may grow arbitrarily fast…

This paper is devoted to the study of the large-time asymptotics of the small solutions to the matrix nonlinear Schr\"{o}dinger equation with a potential on the half-line and with general selfadjoint boundary condition, and on the line with…

We study the convergence of 1D Schr\"odinger ope\-rators $H_\varepsilon$ with the potentials which are regularizations of a class of pseudo-potentials having in particular the form $$ \alpha \delta'(x)+\beta…

We study the large-time behavior of the solutions to the Schr\"odinger equation associated with a quickly decaying potential in dimension three. We establish the resolvent expansions at threshold zero and near positive resonances. The…

We study the reducibility of a Linear Schr\"odinger equation subject to a small unbounded almost-periodic perturbation which is analytic in time and space. Under appropriate assumptions on the smallness, analiticity and on the frequency of…

We offer several perspectives on the behavior at infinity of solutions of discrete Schroedinger equations. First we study pairs of discrete Schroedinger equations whose potential functions differ by a quantity that can be considered small…

Let H be a Schr\"odinger operator defined on an unbounded domain D in R^d with Dirichlet boundary conditions (D may equal R^d in particular). Let u(x,E) be a solution of the Schr\"odinger equation (H-E)u(x,E)=0, and let B_R denote a ball of…

We investigate the existence and local uniqueness of normalized $k$-peak solutions for the fractional Schr\"odinger equations with attractive interactions with a class of degenerated trapping potential with non-isolated critical points.…