منابع مشابه
Positive Commutators
In this short and very elementary note, we will discuss the technique of proving estimates for solutions to certain partial differential equations using positive commutators, which is a widely used and powerful technique in particular in microlocal analysis. In order to keep the necessary prerequisites at the bare minimum, we won’t make any use of pseudodifferential operators and related microl...
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In this paper we consider the Hamiltonian of the standard model of non-relativistic QED. In this model non-relativistic quantum particles interact with quantized electromagnetic eld and their interaction is subjected to an ultraviolet cut-oo. We prove absence of excited states and absolute continuity of the spectrum for suuciently small charges under conditions on the coupling functions which m...
متن کاملPositive Commutators in Non-Equilibrium Quantum Statistical Mechanics
The method of positive commutators, developed for zero temperature problems over the last twenty years, has been powering progress in the spectral analysis of Hamiltonians in quantum mechanics. We extend this method to positive temperatures, i.e. to non-equilibrium quantum statistical mechanics. We use the positive commutator technique to give an alternative proof of a fundamental property of l...
متن کاملPositive Commutators at the Bottom of the Spectrum
Bony and Häfner have recently obtained positive commutator estimates on the Laplacian in the low-energy limit on asymptotically Euclidean spaces; these estimates can be used to prove local energy decay estimates if the metric is non-trapping. We simplify the proof of the estimates of Bony-Häfner and generalize them to the setting of scattering manifolds (i.e. manifolds with large conic ends), b...
متن کاملAlgebras with Positive Bases, Commutators and Covering Numbers
We describe how a general setup called "Algebras with positive bases" can be used for a concurrent study of conjugacy-class covering numbers and character covering numbers in nite groups. This approach yields improvements on the known bounds of the covering numbers.
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1991
ISSN: 0022-1236
DOI: 10.1016/0022-1236(91)90075-g