Physical Review Letters · 1983 · 1.1K citations · 6 references
CartographyPhysicsPotential TheoryRecursion RelationLocalization ProblemTransfer MatricesManifold ModelingInverse ProblemsGeometric Singular Perturbation TheoryLocalization TechniquePeriodic Travelling WaveIntegrable SystemRecursion RelationsLocalization
A one-dimensional Schr\"odinger equation in a discontinuous quasiperiodic potential is reduced to a recursion relation for transfer matrices and then to one for traces of these matrices. When the potential is periodic, the bandwidth goes to zero as an algebraic function of the period with a critical index which depends upon the potential strength. This critical index is also evaluated as the solution to an escape-rate problem for the recursion relations.
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One-Dimensional Schrödinger Equation with an Almost Periodic Potential
Stellan Östlund, Rahul Pandit, D.A.J. Rand et al. · Physical Review Letters · 1983 · 722 citations