Related papers: Exponential localization in 2D pure magnetic wells
Computational discovery of magnetic materials remains challenging because magnetism arises from the competition between kinetic energy and Coulomb interaction that is often beyond the reach of standard electronic-structure methods. Here we…
Spontaneous magnetization of a two-dimensional electron gas (2DEG) is discussed. It takes place for sufficiently high electron density (i.e. for a quantum fluid state) with $r_s<10$ which is quite beyond the condition of Wigner…
We investigate the behavior of eigenvalues for a magnetic Aharonov-Bohm operator with half-integer circulation and Dirichlet boundary conditions in a planar domain. We provide sharp asymptotics for eigenvalues as the pole is moving in the…
We analyze a general class of self-adjoint difference operators $H_\varepsilon = T_\varepsilon + V_\varepsilon$ on $\ell^2(\varepsilon\mathbb{Z}^d)$, where $V_\varepsilon$ is a one-well potential and $\varepsilon$ is a small parameter. We…
We are mainly interested in extending the known results on ob-servability inequalities and stabilization for the Schr{\"o}dinger equation to the magnetic Schr{\"o}dinger equation. That is in presence of a magnetic potential. We establish…
In this paper, we establish a local smoothing estimate on two-dimensional quantum Euclidean space. This is the noncommutative analogue of the one due to Mockenhaupt$-$Seeger$-$Sogge \cite{MSS}. As an application and simultaneously one…
We show that fixed energy scattering measurements for the magnetic Schroedinger operator uniquely determine the magnetic field and electric potential in dimensions $n \geq 3$. The magnetic potential, its first derivatives, and the electric…
The one dimensional spin-1/2 Heisenberg antiferromagnet in a weak magnetic field h is studied using the bosonization method. We derive a set of renormalization group equations. The fixed point is reached when the field is scaled to the…
We show local smoothing estimates in $L^p$-spaces for solutions to the Hermite wave equation. For this purpose, we obtain a parametrix given by a Fourier Integral Operator, which we linearize. This leads us to analyze local smoothing…
Electron-electron scattering processes involving Landau levels of two subband are considered. A matrix of electron-electron scattering rates containing all tipes of transitions between Landau levels is calculated/ This matrix is analized,…
We present lower bounds on tunneling rates in magnetic double well systems for generic values of the coupling constant. This result was recently announced in \cite{FSW24} and complements our recent counter-example construction which…
We present a practical numerical technique for calculating tunneling ionization rates from arbitrary 1-D potential wells in the presence of a linear external potential by determining the widths of the resonances in the spectral density,…
The aim of this paper is to establish estimates of the lowest eigenvalue of the Neumann realization of $(i\nabla+B\textbf{A})^2$ on an open bounded subset of $\mathbb{R}^2$ $\Omega$ with smooth boundary as $B$ tends to infinity. We…
Effective demagnetizing factors that connect the sample magnetic moment with the applied magnetic field are calculated numerically for perfectly diamagnetic samples of various non-ellipsoidal shapes. The procedure is based on calculating…
In this work, we investigate conditions which ensure the existence of an exponentially localized Wannier basis for a given periodic hamiltonian. We extend previous results in [Pan07] to include periodic zero flux magnetic fields which is…
We report low temperature magnetotransport measurements on a high mobility (\mu=325,000 cm^2/V sec) 2D electron system on a H-terminated Si(111) surface. While low magnetic field data indicate a six-fold valley degenerate system, we observe…
We consider an unusual singular position=dependent-mass particle in an infinite potential well. The corresponding Hamiltonian is mapped through a point-canonical-transformation and an explicit correspondence between the target Hamiltonian…
The electron scattering with longitudinal polar optical phonons in a quantizing magnetic field tilted to the plane of quantum well layers is studied. The scattering rate's behavior at variation of the magnetic field magnitude and…
We investigate analytically the amplification of a weak magnetic field in a homogeneous and isotropic turbulent flow lacking reflectional symmetry (helical turbulence). We propose that the spectral distributions of magnetic energy and…
Density-functional calculations using an exact exchange potential for a two-dimensional electron gas (2DEG) formed in a GaAs single quantum well predict the existence of a spin-polarized phase, when an excited subband becomes slightly…