• Corpus ID: 117267536

Schroedinger Operator with Strong Magnetic Field near Boundary

@article{Ivrii2010SchroedingerOW,
  title={Schroedinger Operator with Strong Magnetic Field near Boundary},
  author={Victor Ivrii},
  journal={arXiv: Spectral Theory},
  year={2010}
}
  • V. Ivrii
  • Published 3 May 2010
  • Mathematics, Physics
  • arXiv: Spectral Theory
We consider 2-dimensional Schroedinger operator with the non-degenerating magnetic field in the domain with the boundary and under certain non-degeneracy assumptions we derive spectral asymptotics with the remainder estimate better than $O(h^{-1})$, up to $O(\mu^{-1}h^{-1})$ and the principal part $\asymp h^{-2}$ where $h\ll 1$ is Planck constant and $\mu \gg 1$ is the intensity of the magnetic field; $\mu h \le 1$. We also consider generalized Schr\"odinger-Pauli operator in the same framework… 
1 Citations
Research Contributions of Victor Ivrii
[1] V. Ja. Ivrii. Exponential decay of the solution of the wave equation outside an almost star-shaped region. [2] V. Ja. Ivrii. The Cauchy problem for not strictly hyperbolic equations. [3] V. Ja.…

References

SHOWING 1-5 OF 5 REFERENCES
Microlocal Analysis and Precise Spectral Asymptotics
0. Introduction.- I. Semiclassical Microlocal Analysis.- 1. Introduction to Semiclassical Microlocal Analysis.- 2. Propagation of Singularities in the Interior of a Domain.- 3. Propagation of…
AN ESTIMATE NEAR THE BOUNDARY FOR THE SPECTRAL FUNCTION OF THE LAPLACE OPERATOR
The main result of this paper is an estimate as in the title, near a sufficiently smooth part of the boundary of a compact n-dimensional Riemannian manifold Q, for either Dirichlet or Neumann…
An application of semi-classical analysis to the asymptotic study of the supercooling field of a superconducting material
This paper is devoted to a precise description of the properties of the supercooling field of a superconducting film submitted to an external magnetic field. Semi-classical analysis is introduced in…
A sharp asymptotic estimate for the eigenvalues of the Laplacian in a domain of R
  • Advances in Math.,
  • 1978