Schrödinger Operators with Multiple Aharonov–Bohm Fluxes
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Abstract We study the Schrödinger operator describing a two-dimensional quantum particle moving in the presence of $$ N \geqslant 1$$ N ⩾ 1 Aharonov–Bohm magnetic fluxes. We classify all the self-adjont realizations of such an operator, providing an explicit characterization of their domains and actions. Moreover, we examine their spectral and scattering properties, proving in particular the existence and completeness of wave operators in relation with the free dynamics.
Schrödinger operator, Quantum Physics, Original Paper, Scattering theory of linear operators, FOS: Physical sciences, Aharonov-Bohm effect, Quantum scattering theory, Mathematical Physics (math-ph), quadratic form, Forms (bilinear, sesquilinear, multilinear), Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory, Quantum Physics (quant-ph), Mathematical Physics, Selfadjoint operator theory in quantum theory, including spectral analysis
Schrödinger operator, Quantum Physics, Original Paper, Scattering theory of linear operators, FOS: Physical sciences, Aharonov-Bohm effect, Quantum scattering theory, Mathematical Physics (math-ph), quadratic form, Forms (bilinear, sesquilinear, multilinear), Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory, Quantum Physics (quant-ph), Mathematical Physics, Selfadjoint operator theory in quantum theory, including spectral analysis
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