Semi-classical Asymptotics for the Counting Functions and Riesz Means of Pauli and Dirac Operators with Large Magnetic Fields
نویسنده
چکیده
We study the asymptotic behavior, as Planck’s constant ~ → 0, of the number of discrete eigenvalues and the Riesz means of Pauli and Dirac operators with a magnetic field μB(x) and an electric field. The magnetic field strength μ is allowed to tend to infinity as ~ → 0. Two main types of results are established: in the first μ~ ≤ constant as ~ → 0, with magnetic fields of arbitrary direction; the second results are uniform with respect to μ ≥ 0 but the magnetic fields have constant direction. The results on the Pauli operator complement recent work of Sobolev.
منابع مشابه
Eigenvalue Estimates in the Semi-classical Limit for Pauli and Dirac Operators with a Magnetic Field
Leading order semi-classical asymptotics are given for the distribution of the eigen-values of Dirac and Pauli operators describing an electron in an electromagnetic eld. Minimal conditions are assumed on the electric and magnetic potentials to ensure the existence of only a nite number of eigenvalues outside the essential spectra. The method used is based on coherent state analysis.
متن کاملNon-Relativistic Limit of Neutron Beta-Decay Cross-Section in the Presence of Strong Magnetic Field
One of the most important reactions of the URCA that lead to the cooling of a neutron star, is neutron beta-decay ( ). In this research, the energy spectra and wave functions of massive fermions taking into account the Anomalous Magnetic Moment (AMM) in the presence of a strong changed magnetic field are calculated. For this purpose, the Dirac-Pauli equation for charged and neutral fermions is ...
متن کاملProgram of a Mini - Course “ Resonances and Threshold Singularities for Magnetic Quantum Hamiltonians ”
1. Basic facts from the spectral theory of magnetic quantum Hamilto-nians (Schrödinger, Pauli, and Dirac operators with magnetic fields): self-adjointness, gauge invariance, diamagnetic inequality, Aharonov-Casher theorem [1, 7]. Constant magnetic fields [1]. 2. Berezin-Toeplitz operators and pseudodifferential operators with con-4. Resonances for the 3D Schrödinger operator with constant magne...
متن کاملLow Energy Asymptotics of the SSF for Pauli Operators with Nonconstant Magnetic Fields
We consider the 3D Pauli operator with nonconstant magnetic field B of constant direction, perturbed by a symmetric matrix-valued electric potential V whose coefficients decay fast enough at infinity. We investigate the low-energy asymptotics of the corresponding spectral shift function. As a corollary, for generic negative V , we obtain a generalized Levinson formula, relating the low-energy a...
متن کاملOn the Dirac and Pauli Operators with Several Aharonov-bohm Solenoids
We study the self-adjoint Pauli operators that can be realized as the square of a self-adjoint Dirac operator and correspond to a magnetic field consisting of a finite number of Aharonov-Bohm solenoids and a regular part, and prove an Aharonov-Casher type formula for the number of zero-modes for these operators. We also see that essentially only one of the Pauli operators are spin-flip invarian...
متن کامل