Displaying similar documents to “Convergence of the Schrödinger-Poisson system to the Euler equations under the influence of a large magnetic field”

Asymptotic Analysis of a Schrödinger-Poisson System with Quantum Wells and Macroscopic Nonlinearities in Dimension 1

Faraj, A. (2010)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 35Q02, 35Q05, 35Q10, 35B40. We consider the stationary one dimensional Schrödinger-Poisson system on a bounded interval with a background potential describing a quantum well. Using a partition function which forces the particles to remain in the quantum well, the limit h®0 in the nonlinear system leads to a uniquely solved nonlinear problem with concentrated particle density. It allows to conclude about the convergence of the solution. ...

Resonances of two-dimensional Schrödinger operators with strong magnetic fields

Tuan Duong, Anh (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 81Q20 (35P25, 81V10). The purpose of this paper is to study the Schrödinger operator P(B,w) = (Dx-By^2+Dy^2+w^2x^2+V(x,y),(x,y) О R^2, with the magnetic field B large enough and the constant w № 0 is fixed and proportional to the strength of the electric field. Under certain assumptions on the potential V, we prove the existence of resonances near Landau levels as B®Ґ. Moreover, we show that the width of resonances is of size O(B^-Ґ). ...

Poisson-Fermi Formulation of Nonlocal Electrostatics in Electrolyte Solutions

Jinn-Liang Liu, Dexuan Xie, Bob Eisenberg (2017)

Molecular Based Mathematical Biology

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We present a nonlocal electrostatic formulation of nonuniform ions and water molecules with interstitial voids that uses a Fermi-like distribution to account for steric and correlation efects in electrolyte solutions. The formulation is based on the volume exclusion of hard spheres leading to a steric potential and Maxwell’s displacement field with Yukawa-type interactions resulting in a nonlocal electric potential. The classical Poisson-Boltzmann model fails to describe steric and correlation...

Maxwell-Schrödinger equations in singular electromagnetic field

Qihong Shi, Yaqian Jia, Jianwei Yang (2024)

Applications of Mathematics

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We investigate the Cauchy problem of the one dimensional Maxwell-Schrödinger (MS) system under the Lorenz gauge condition. Different from the classical case, we consider the electromagnetic and electrostatic potentials which are growing at space infinity. More precisely, the electrostatic potential is allowed to grow linearly, while for the electromagnetic potential the growth is sublinear. Based on the energy estimates and the gauge transformation, we prove the global existence and...

Localization for Schrödinger operators with Poisson random potential

Abel Klein, Peter Hislop, François Germinet (2007)

Journal of the European Mathematical Society

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We prove exponential and dynamical localization for the Schr¨odinger operator with a nonnegative Poisson random potential at the bottom of the spectrum in any dimension. We also conclude that the eigenvalues in that spectral region of localization have finite multiplicity. We prove similar localization results in a prescribed energy interval at the bottom of the spectrum provided the density of the Poisson process is large enough.

Effect of the polarization drift in a strongly magnetized plasma

Daniel Han-Kwan (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider a strongly magnetized plasma described by a Vlasov-Poisson system with a large external magnetic field. The finite Larmor radius scaling allows to describe its behaviour at very fine scales. We give a new interpretation of the asymptotic equations obtained by Frénod and Sonnendrücker [ (2001) 1227–1247] when the intensity of the magnetic field goes to infinity. We introduce the so-called polarization drift and show that its contribution is not negligible in...

Effect of the polarization drift in a strongly magnetized plasma

Daniel Han-Kwan (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

We consider a strongly magnetized plasma described by a Vlasov-Poisson system with a large external magnetic field. The finite Larmor radius scaling allows to describe its behaviour at very fine scales. We give a new interpretation of the asymptotic equations obtained by Frénod and Sonnendrücker [ (2001) 1227–1247] when the intensity of the magnetic field goes to infinity. We introduce the so-called polarization drift and show that its contribution is not negligible in...