TY - JOUR
TI - Structure and dynamics of noncommutative solitons
DO - https://doi.org/doi:10.7282/T3765CS3
PY - 2014
AB - We consider the Schrödinger equation with a Hamiltonian given by a second order o 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 optimal decay rate t−1 log−2 t generically. We use a novel technique involving generating functions of orthogonal polynomials to achieve these estimates. We construct a ground state soliton for this equation and analyze its properties. In particular we arrive at ∞ and 1 estimates as well as a quasi-exponential spatial decay rate. We completely determine the spectrum of the associated linearized Hamiltonian and prove the optimal decay rate of t−1 log−2 t for the associated time decay estimate. These results are to appear in forthcoming papers
KW - Physics and Astronomy
KW - Noncommutative differential geometry
KW - Spectral theory (Mathematics)
LA - eng
ER -