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Communications in Mathematical Physics

, Volume 332, Issue 2, pp 827–838 | Cite as

A Note on Reflectionless Jacobi Matrices

  • V. Jakšić
  • B. Landon
  • A. Panati
Article

Abstract

The property that a Jacobi matrix is reflectionless is usually characterized either in terms of Weyl m-functions or the vanishing of the real part of the boundary values of the diagonal matrix elements of the resolvent. We introduce a characterization in terms of stationary scattering theory (the vanishing of the reflection coefficients) and prove that this characterization is equivalent to the usual ones. We also show that the new characterization is equivalent to the notion of being dynamically reflectionless, thus providing a short proof of an important result of Breuer et al. (Commun Math Phys 295:531–550, 2010). The motivation for the new characterization comes from recent studies of the non-equilibrium statistical mechanics of the electronic black box model and we elaborate on this connection.

Keywords

Jacobi Matrix Jacobi Matrice Jacobi Operator Diagonal Matrix Element Commun Math Phys 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada
  2. 2.Department of MathematicsHarvard UniversityCambridgeUSA
  3. 3.Aix-Marseille Université, CNRS, CPT, UMR 7332, Case 907MarseilleFrance
  4. 4.Université de Toulon, CNRS, CPT, UMR 7332La GardeFrance
  5. 5.FRUMAMMarseilleFrance

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