相关论文: Regularity of many-body Schr\"odinger evolution eq…
In this paper, we prove a multiplicity result of solutions for the following stationary Schr\"odinger-Poisson-Slater equations \begin{equation}\label{eq-abstract} -\Delta u - \lambda u + (\left | x \right |^{-1}\ast \left | u \right |^2) u…
We study the effective time evolution of a large quantum system consisting of a mixture of different species of identical bosons in interaction. If the system is initially prepared so as to exhibit condensation in each component, we prove…
We consider the Schr\"odinger evolution on graph, i.e. solution to the equation $\partial_tu(t,\alpha)=i\sum_{\beta\in\mathcal{A}}L(\alpha,\beta)u(t,\beta)$, here $\mathcal{A}$ is the set of vertices of the graph and the matrix…
Understanding the emergence of collective organizational phenomena is a major goal in many fields of physics from condensed matter to cosmology. Using a recently introduced manybody perturbation formalism for fermions, we propose a…
We consider the cubic nonlinear Schr\"odinger equation with a spatially rough potential, a key equation in the mathematical setup for nonlinear Anderson localization. Our study comprises two main parts: new optimal results on the…
The modulational instability of spatially uniform states in the nonlinear Schr\"odinger equation is examined in the presence of higher-order dissipation. The study is motivated by results on the effects of three-body recombination in…
We prove unique continuation properties for solutions of evolution Schr\"odinger equation with time dependent potentials. In the case of the free solution these correspond to uncertainly principles referred to as being of Morgan type. As an…
In this paper, we investigate that the H\"older regularity of solutions to the time fractional Schr\"odinger equation of order $1<\alpha<2$, which interpolates between the Schr\"odinger and wave equations. This is inspired by Hirata and…
In this paper we give log-convexity properties for solutions to discrete Schr\"odinger equations with different discrete versions of Gaussian decay at two different times. For free evolutions, we use complex analysis arguments to derive…
In this paper we give a discrete version of Hardy's uncertainty principle, by using complex variable arguments, as in the classical proof of Hardy's principle. Moreover, we give an interpretation of this principle in terms of decaying…
We consider the derivative nonlinear Schr\"odinger equation in one space dimension, posed both on the line and on the circle. This model is known to be completely integrable and $L^2$-critical with respect to scaling. The first question we…
In this work we study the phenomenon of increasing stability in the inverse boundary value problem for the Schr\"odinger equation. This problem was previously considered by Isakov in which he discussed the phenomenon in different ranges of…
We consider the spinless Pauli-Fierz Hamiltonian which describes a quantum system of non-relativistic identical particles coupled to the quantized electromagnetic field. We study the time evolution in a mean-field limit where the number $N$…
In this paper, Hardy's uncertainty principle and unique continuation properties of abstract Schr\"odinger equations in vector-valued classes are obtained
For multi-time wave functions, which naturally arise as the relativistic particle-position representation of the quantum state vector, the analog of the Schr\"odinger equation consists of several equations, one for each time variable. This…
This paper mainly discuss the regularity behavior of the hyperbolic magnetic Schroedinger equation with singular coefficients near the origin. We apply the techniques from the microlocal analysis to explore the upper bound of loss of…
The nonlinear Schr{\"o}dinger equation with derivative cubic nonlinearity admits a family of solitons, which are orbitally stable in the energy space. In this work, we prove the orbital stability of multi-solitons configurations in the…
We prove a nonlinear regularity principle in sequence spaces which produces universal estimates for special series defined therein. Some consequences are obtained and, in particular, we establish new inclusion theorems for multiple summing…
In this article, we study the Schr\"odinger equation posed in the Euclidean space. We prove observability inequalities for measurable sets that are thick with respect to decaying densities. The proof relies on quantitative uncertainty…
A method of solving the Schr\"{o}dinger equation based on the use of constant particle-particle interaction potential surfaces (IPS) is proposed. The many-body wave function is presented in a configuration interaction form, with…