相关论文: Regularity of many-body Schr\"odinger evolution eq…
Confined quantum systems involving $N$ identical interacting fermions are found in many areas of physics, including condensed matter, atomic, nuclear and chemical physics. In a previous series of papers, a manybody perturbation method that…
We establish stable quantum ergodicity for spin Hamiltonians, also known as Pauli-Schr\"odinger operators. Our approach combines new analytic techniques of mixed quantization, inspired by local index theory, with stable ergodicity results…
We establish a generic method to analyze the time evolution of open quantum many-body systems. Our approach is based on a variational integration of the quantum master equation describing the dynamics and naturally connects to a variational…
In this article, we study the increasing stability property for the determination of the potential in the Schr\"odinger equation from partial data. We shall assume that the inaccessible part of the boundary is flat and homogeneous boundary…
The goal of this paper is to prove a uniqueness result for a stochastic heat equation with a randomly perturbed potential, which can be considered as a variant of Hardy's uncertainty principle for stochastic heat evolutions.
This paper studies the regularity problem for block uniformly elliptic operators in divergence form with complex bounded measurable coefficients. We consider the case where the boundary data belongs to Lebesgue spaces with weights in the…
The Schr\"odinger equation is universally accepted due to its excellent predictions aligning with observed results within its defined conditions. Nevertheless, it does not seem to possess the simplicity of fundamental laws, such as Newton's…
We establish that the quadratic non-linear Schr\"odinger equation $$ iu_t + u_{xx} = u^2$$ where $u: \R \times \R \to \C$, is locally well-posed in $H^s(\R)$ when $s \geq -1$ and ill-posed when $s < -1$. Previous work of Kenig, Ponce and…
We study in this paper the well-posedness and stability for two linear Schr\"odinger equations in $d$-dimensional open bounded domain under Dirichlet boundary conditions with an infinite memory. First, we establish the well-posedness in the…
In this work we consider stability of recovery of the conductivity and attenuation coefficients of the stationary Maxwell and Schr\"odinger equations from a complete set of (Cauchy) boundary data. By using complex geometrical optics…
We consider the Cauchy problem of a class of higher order Schr\"odinger type equations with constant coefficients. By employing the energy inequality, we show the $L^2$ well-posedness, the parabolic smoothing and a breakdown of the…
A surprising "duality" of the Newton equation with time-dependent forces and the stationary Schroedinger equation is discussed. Wide classes of exact solutions not known before for few-body Newton equations are generated directly from…
A solvable many-body problem in the plane is exhibited. It is characterized by rotation-invariant Newtonian (``acceleration equal force'') equations of motion, featuring one-body (``external'') and pair (``interparticle'') forces. The…
One of the most celebrated problems in Euclidean Harmonic analysis is the Carleson's problem: determining the optimal regularity of the initial condition $f$ of the Schr\"odinger equation given by \begin{equation*}\begin{cases}…
In this paper, the classical Schr\"odinger equation, which allows the study of classical dynamics in terms of wave functions, is analyzed theoretically and numerically. First, departing from classical (Newtonian) mechanics, and assuming an…
A procedure which obviates the constraint imposed by the conflict between consistent quantization and the invariance of the Hamiltonian description under nonlinear canonical transformation is proposed. This new quantization scheme preserves…
In this paper we study the Cauchy problem associated to the Maxwell-Schr\"odinger system with a defocusing pure-power non-linearity. This system has many applications in physics, for instance in the description of a charged non-relativistic…
We consider the many-body quantum evolution of a factorized initial data, in the mean-field regime. We show that fluctuations around the limiting Hartree dynamics satisfy large deviation estimates, that are consistent with central limit…
We find optimal (up to constant) bounds for the following measures for the regularity of the Schramm-Loewner evolution (SLE): variation regularity, modulus of continuity, and law of the iterated logarithm. For the latter two we consider the…
Results concerning the existence and spectral stability and instability of multiple periodic wave solutions for the nonlinear Schr\"odinger system with \textit{dnoidal} and \textit{cnoidal} profile will be determined in this manuscript. The…