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- Publisher
- Springer Journals
- Copyright
- Copyright © 2018 by The Author(s)
- Subject
- Physics; Theoretical, Mathematical and Computational Physics; Mathematical Physics; Quantum Physics; Complex Systems; Classical and Quantum Gravitation, Relativity Theory
- ISSN
- 0010-3616
- eISSN
- 1432-0916
- DOI
- 10.1007/s00220-018-3106-z
- Publisher site
- See Article on Publisher Site
Abstract
We prove asymptotic formulas of Szegő type for the periodic Schrödinger operator $${H = -\frac{d^2}{dx^2}+V}$$ H = - d 2 d x 2 + V in dimension one. Admitting fairly general functions h with $${h(0)=0}$$ h ( 0 ) = 0 , we study the trace of the operator $${h(\chi_{(-\alpha,\alpha)} \chi_{(-\infty,\mu)}(H)\chi_{(-\alpha,\alpha)})}$$ h ( χ ( - α , α ) χ ( - ∞ , μ ) ( H ) χ ( - α , α ) ) and link its subleading behaviour as $${\alpha \to \infty}$$ α → ∞ to the position of the spectral parameter μ relative to the spectrum of H.
Journal
Communications in Mathematical Physics – Springer Journals
Published: Mar 6, 2018