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arXiv · 1411.5859

Dynamics of Noncommutative Solitons II: Spectral Theory, Dispersive Estimates and Stability

August J. Krueger·Avy Soffer
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Abstract

We consider the Schrödinger equation with a (matrix) 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 completely determine the spectrum of the Hamiltonian linearized around a ground state soliton and prove the optimal decay rate of $t^{-1}\log^{-2}t$ for the associated time decay estimate. We use a novel technique involving generating functions of orthogonal polynomials to achieve this estimate.

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August J. Krueger, Avy Soffer. 2014-11-21. Dynamics of Noncommutative Solitons II: Spectral Theory, Dispersive Estimates and Stability. https://arxiv.org/abs/1411.5859

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