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Weighted dispersive estimates for two-dimensional Schr\'odinger operators with Aharonov-Bohm magnetic field
- Publication Year :
- 2012
-
Abstract
- We consider two-dimensional Schr\"odinger operators $H$ with Aharonov-Bohm magnetic field and an additional electric potential. We obtain an explicit leading term of the asymptotic expansion of the unitary group $e^{-i t H}$ for $t\to\infty$ in weighted $L^2$ spaces. In particular, we show that the magnetic field improves the decay of $e^{-i t H}$ with respect to the unitary group generated by non-magnetic Schr\"odinger operators, and that the decay rate in time is determined by the magnetic flux.<br />Comment: To appear in J. Differential Equations
- Subjects :
- Mathematics - Spectral Theory
Mathematical Physics
Mathematics - Analysis of PDEs
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1210.7648
- Document Type :
- Working Paper