Abstract
We study the relation of the adiabatic curvature associated to scattering states and the scattering matrix. We show that the curvature of the scattering states is not determined by the scattering data alone. However, for certain tight binding Hamiltonians, the Chern numbers are determined by theS-matrix and are given explicitly in terms of integrals of certain odd-dimensional forms constructed from the scattering data. Two examples, which are the natural scattering analogs of Berry's spin 1/2 magnetic Hamiltonian and its quadrupole generalization, serve to motivate the questions and to illustrate the results.
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Communicated by B. Simon
Research supported in part by an NSF Mathematical Sciences Postdoctoral Fellowship and Texas ARP Grant 003658-037
Research supported in part by GIF, DFG and the Fund for Promotion of Research at the Technion
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Sadun, L., Avron, J.E. Adiabatic curvature and theS-matrix. Commun.Math. Phys. 181, 685–702 (1996). https://doi.org/10.1007/BF02101293
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DOI: https://doi.org/10.1007/BF02101293