The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying 21 – 40 of 67

Showing per page

Lieb–Thirring inequalities with improved constants

Jean Dolbeault, Ari Laptev, Michael Loss (2008)

Journal of the European Mathematical Society

Following Eden and Foias we obtain a matrix version of a generalised Sobolev inequality in one dimension. This allows us to improve on the known estimates of best constants in Lieb–Thirring inequalities for the sum of the negative eigenvalues for multidimensional Schrödinger operators.

Liftings of 1-forms to some non product preserving bundles

Doupovec, Miroslav, Kurek, Jan (1998)

Proceedings of the 17th Winter School "Geometry and Physics"

Summary: The article is devoted to the question how to geometrically construct a 1-form on some non product preserving bundles by means of a 1-form on an original manifold M . First, we will deal with liftings of 1-forms to higher-order cotangent bundles. Then, we will be concerned with liftings of 1-forms to the bundles which arise as a composition of the cotangent bundle with the tangent or cotangent bundle.

Limit distributions of many-particle spectra and q-deformed Gaussian variables

Piotr Śniady (2006)

Banach Center Publications

We find the limit distributions for a spectrum of a system of n particles governed by a k-body interaction. The hamiltonian of this system is modelled by a Gaussian random matrix. We show that the limit distribution is a q-deformed Gaussian distribution with the deformation parameter q depending on the fraction k/√n. The family of q-deformed Gaussian distributions include the Gaussian distribution and the semicircular law; therefore our result is a generalization of the results of Wigner [Wig1,...

Limitations on the control of Schrödinger equations

Reinhard Illner, Horst Lange, Holger Teismann (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We give the definitions of exact and approximate controllability for linear and nonlinear Schrödinger equations, review fundamental criteria for controllability and revisit a classical “No-go” result for evolution equations due to Ball, Marsden and Slemrod. In Section 2 we prove corresponding results on non-controllability for the linear Schrödinger equation and distributed additive control, and we show that the Hartree equation of quantum chemistry with bilinear control ( E ( t ) · x ) u is not controllable...

Currently displaying 21 – 40 of 67