相关论文: Exponential localization in 2D pure magnetic wells

We consider a two-dimensional non-commutative inverted oscillator in the presence of a constant magnetic field, coupled to the system in a ``symplectic'' and ``Poisson'' way. We show that it has a discrete energy spectrum for some value of…

Eigenstates of 2D charged electron-hole complexes in magnetic fields are considered. The operator formalism that allows one to partially separate the center-of-mass motion from internal degrees of freedom is presented. The scheme using…

We derive, and validate numerically, an analytical model for electron-only magnetic reconnection applicable to strongly magnetized plasmas. Our model predicts sub-ion-scale reconnection rates significantly higher than those pertaining to…

An optical method is suggested to determine the concentration of two-dimensional electrons in modulation-doped quantum wells at low and moderate electron densities between 10^{9} and 2x10^{11} cm^{-2}. The method is based on an analysis of…

The existence of spontaneous magnetization that fingerprints a ground-state ferromagnetic order was recently observed in two-dimensional (2D) van der Waals materials. Despite progress in the fabrication and manipulation of the atom-thick…

In this paper, we prove local existence and uniqueness for the 2D Prandtl-Hartmann regine in weighted Sobolev spaces. Our proof is based on using uniform estimates of the regularized parabolic equation and maximal principle under the…

In the present paper we focus on building simple nonperturbative analytical relativistic models of magnetars. With this purpose in mind we first develop a method for generating exact interior solutions to the static and axisymmetric…

A microscopic theory of the phonon-induced resistance oscillations in weak perpendicular magnetic fields is presented. The calculations are based on the consideration of interaction of two-dimensional electrons with three-dimensional (bulk)…

We define the random magnetic Laplacien with spatial white noise as magnetic field on the two-dimensional torus using paracontrolled calculus. It yields a random self-adjoint operator with pure point spectrum and domain a random subspace of…

In this paper we study unique continuation theorems for magnetic Schr\"odinger equation via Carleman estimates. We use integration by parts techniques in order to show these estimates. We consider electric and magnetic potentials with…

We prove generalized Strichartz estimates for wave and massless Dirac equations in Aharonov-Bohm magnetic fields. Following a well established strategy to deal with scaling critical perturbations of dispersive PDEs, we make use of Hankel…

Magnetic fields spontaneously grow at unstable interfaces around hot-spot asymmetries during inertial confinement fusion implosions. Although difficult to measure, theoretical considerations and numerical simulations predict field strengths…

Using a finite-size scaling method, we calculate the localization properties of a disordered two-dimensional electron system in the presence of a random magnetic field. Below a critical energy $E_c$ all states are localized and the…

We present simple new examples of pure-jump strict local martingales. The examples are constructed as exponentials of self-exciting affine Markov processes. We characterize the strict local martingale property of these processes by an…

We study localization properties of low-lying eigenfunctions of magnetic Schr\"odinger operators $$\frac{1}{2} \left(- i\nabla - A(x)\right)^2 \phi + V(x) \phi = \lambda \phi,$$ where $V:\Omega \rightarrow \mathbb{R}_{\geq 0}$ is a given…

One of the fundamental results in the theory of localization for discrete Schr\"odinger operators with random potentials is the exponential decay of Green's function and the absence of continuous spectrum. In this paper we provide a new…

We prove a sharp resolvent estimate in scale invariant norms of Amgon--H\"{o}rmander type for a magnetic Schr\"{o}dinger operator on $\mathbb{R}^{n}$, $n\ge3$\begin{equation*} L=-(\partial+iA)^{2}+V \end{equation*}with large potentials…

In this paper, we present a proof of dispersive decay for both linear and nonlinear magnetic Schr\"odinger equations. To achieve this, we introduce the fractional distorted Fourier transforms with magnetic potentials and define the…

This is the first of a series of papers in which we investigate the decay estimates for dispersive equations with Aharonov-Bohm solenoids in a uniform magnetic field. In this first starting paper, we prove the local-in-time dispersive…

We have developed a scanning photoluminescence technique that can directly map out the local two-dimensional electron density with a relative accuracy of $\sim2.2\times10^8$ cm$^{-2}$. The validity of this approach is confirmed by the…