Dynamics of Noncommutative Solitons I: Spectral Theory and Dispersive Estimates

We consider the Schrödinger equation with a Hamiltonian given by a second-order difference operator with nonconstant growing coefficients, on the half one-dimensional lattice. This operator appeared first naturally in the construction and dynamics of noncommutative solitons in the context of noncomm...

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Bibliographic Details
Published in:Annales Henri Poincaré 2016-05, Vol.17 (5), p.1181-1208
Main Authors: Krueger, August J., Soffer, Avy
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Decay rate
Dynamical Systems and Ergodic Theory
Elementary Particles
Field theory
Finite differences
Functions (mathematics)
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Operators (mathematics)
Physics
Physics and Astronomy
Polynomials
Quantum Field Theory
Quantum Physics
Relativity Theory
Schrodinger equation
Solitary waves
Spectral theory
Theoretical
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Summary:We consider the Schrödinger equation with a Hamiltonian given by a second-order difference operator with nonconstant growing coefficients, on the half one-dimensional lattice. This operator appeared first naturally in the construction and dynamics of noncommutative solitons in the context of noncommutative field theory. We prove pointwise in time decay estimates with the decay rate t - 1 log - 2 t , which is optimal with the chosen weights and appears to be so generally. We use a novel technique involving generating functions of orthogonal polynomials to achieve this estimate.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-015-0431-z