Floquet operators without singular continuous spectrum
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Date
2006
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Abstract
Let U be a unitary operator defined on a infinite-dimensional separable complex Hilbert space R. Assume there exists a self-adjoint operator A on R such that
U*A U - A >= cI + K
for some positive constant c and compact operator K. Then, assuming the commutators U*AU - A and [A, U* A U] admit a bounded extension over H, we prove the spectrum of the operator U has no singular continuous component and only a finite number of eigenvalues of finite multiplicity. We give a localized version of this result and apply it to study the spectrum of the Floquet operator of periodic time-dependent kicked quantum systems. (C) 2006 Elsevier Inc. All rights reserved.
U*A U - A >= cI + K
for some positive constant c and compact operator K. Then, assuming the commutators U*AU - A and [A, U* A U] admit a bounded extension over H, we prove the spectrum of the operator U has no singular continuous component and only a finite number of eigenvalues of finite multiplicity. We give a localized version of this result and apply it to study the spectrum of the Floquet operator of periodic time-dependent kicked quantum systems. (C) 2006 Elsevier Inc. All rights reserved.
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Keywords
unitary operators, spectrum, commutator, kicked quantum system