Quantum nonlinear Schrödinger equation. I. Intertwining operators

Eugène Gutkin

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The classical limit of a class of quantum dynamical semigroups

F. Benatti (1993)

Annales de l'I.H.P. Physique théorique

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Balls defined by nonsmooth vector fields and the Poincaré inequality

Annamaria Montanari, Daniele Morbidelli (2004)

Annales de l’institut Fourier

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We provide a structure theorem for Carnot-Carathéodory balls defined by a family of Lipschitz continuous vector fields. From this result a proof of Poincaré inequality follows.

Schrödinger operators with form-bounded potentials in $L^{p}$ -spaces

M. A. Perelmuter (1990)

Annales de l'I.H.P. Physique théorique

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Hamiltonians for systems of N particles interacting through point interactions

G. F. Dell&amp;#039;Antonio, R. Figari, A. Teta (1994)

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Cramér's formula for Heisenberg manifolds

Mahta Khosravi, John A. Toth (2005)

Annales de l'institut Fourier

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Let $R (λ)$ be the error term in Weyl’s law for a 3-dimensional Riemannian Heisenberg manifold. We prove that $\int_{1}^{T} {| R (t) |}^{2} d t = c T^{\frac{5}{2}} + O_{δ} (T^{\frac{9}{4} + δ})$ , where $c$ is a specific nonzero constant and $δ$ is an arbitrary small positive number. This is consistent with the conjecture of Petridis and Toth stating that $R (t) = O_{δ} (t^{\frac{3}{4} + δ})$ .The idea of the proof is to use the Poisson summation formula to write the error term in a form which can be estimated by the method of the stationary phase. The similar result will be also proven in the $2 n + 1$ -dimensional case. ...

Displaying similar documents to “Quantum nonlinear Schrödinger equation. I. Intertwining operators”

The classical limit of a class of quantum dynamical semigroups

Balls defined by nonsmooth vector fields and the Poincaré inequality

Schrödinger operators with form-bounded potentials in L p -spaces

Hamiltonians for systems of N particles interacting through point interactions

Cramér's formula for Heisenberg manifolds

Schrödinger operators with form-bounded potentials in $L^{p}$ -spaces