Semiclassical Analysis with Vanishing Magnetic Fields

نویسندگان

  • Nicolas Dombrowski
  • Nicolas Raymond
  • NICOLAS DOMBROWSKI
چکیده

We analyze the 2D magnetic Laplacian in the semiclassical limit in the case when the magnetic field vanishes along a smooth curve. In particular, we prove local and microlocal estimates for the eigenfunctions and a complete asymptotic expansion of the eigenpairs in powers of h.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Semiclassical quantization of the hydrogen atom in crossed electric and magnetic fields

The S-matrix theory formulation of closed-orbit theory recently proposed by Granger and Greene is extended to atoms in crossed electric and magnetic fields. We present a semiclassical quantization of the hydrogen atom in crossed fields, which succeeds in resolving individual lines in the spectrum, but is restricted to the strongest lines of each n manifold. By means of a detailed semiclassical ...

متن کامل

Semiclassical reduction for magnetic Schrödinger operator with periodic zero-range potentials and applications

The two-dimensional Schrödinger operator with a uniform magnetic field and a periodic zero-range potential is considered. For weak magnetic fields and a weak coupling we reduce the spectral problem to the semiclassical analysis of one-dimensional Harper-like operators. This shows the existence of parts of Cantor structure in the spectrum for special values of the magnetic flux.

متن کامل

Semiclassical Analysis for Spectral Shift Functions in Magnetic Scattering by Two Solenoidal Fields

We study the semiclassical asymptotic behavior of the spectral shift function and of its derivative in magnetic scattering by two solenoidal fields in two dimensions under the assumption that the total magnetic flux vanishes. The system has a trajectory oscillating between the centers of two solenoidal fields. The emphasis is placed on analysing how the trapping effect is reflected in the semic...

متن کامل

The boundary integral method for magnetic billiards

We introduce a boundary integral method for two-dimensional quantum billiards subjected to a constant magnetic field. It allows to calculate spectra and wave functions, in particular at strong fields and semiclassical values of the magnetic length. The method is presented for interior and exterior problems with general boundary conditions. We explain why the magnetic analogues of the field-free...

متن کامل

Electron dynamics in parallel electric and magnetic fields

We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors a rich set of features which find their interpretation in the unusual and interesting properties of the classical motion of the electrons: For instance, the...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2017