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Register a new userEstimates on the molecular dynamics for the predissociation process
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We study the survival probability associated with a semi-classical matrix Shrodinger operator that models the predissociation of a general molecule in the Born-Oppenheimer approximation. We show that it is given by its usual time-dependent exponential contribution, up to a reminder term that is exponentially small (in the semiclassical parameter) with arbitrarily large rate of decay. The result applies in any dimension, and in presence of a number of resonances that may tend to infinity as the semiclassical parameter tends to 0.
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We consider Schroedinger operators on regular metric trees and prove Lieb-Thirring and Cwikel-Lieb-Rozenblum inequalities for their negative eigenvalues. The validity of these inequalities depends on the volume growth of the tree. We show that the bounds are valid in the endpoint case and reflect the correct order in the weak or strong coupling limit.
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