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Quantum scattering near the lowest Landau threshold for a Schrödinger operator with a constant magnetic field

Michael Melgaard (2003)

Open Mathematics

For fixed magnetic quantum number m results on spectral properties and scattering theory are given for the three-dimensional Schrödinger operator with a constant magnetic field and an axisymmetrical electric potential V. In various, mostly singular settings, asymptotic expansions for the resolvent of the Hamiltonian H m+Hom+V are deduced as the spectral parameter tends to the lowest Landau threshold. Furthermore, scattering theory for the pair (H m, H om) is established and asymptotic expansions...

Quasichemical Models of Multicomponent Nonlinear Diffusion

A.N. Gorban, H.P. Sargsyan, H.A. Wahab (2011)

Mathematical Modelling of Natural Phenomena

Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special tools are needed to provide the systematic construction of the nonlinear diffusion equations for multicomponent mixtures with significant interaction between components. We develop an approach to nonlinear multicomponent...

Quasiconvexity at the boundary and concentration effects generated by gradients

Martin Kružík (2013)

ESAIM: Control, Optimisation and Calculus of Variations

We characterize generalized Young measures, the so-called DiPerna–Majda measures which are generated by sequences of gradients. In particular, we precisely describe these measures at the boundary of the domain in the case of the compactification of ℝm × n by the sphere. We show that this characterization is closely related to the notion of quasiconvexity at the boundary introduced by Ball and Marsden [J.M. Ball and J. Marsden, Arch. Ration. Mech. Anal. 86 (1984) 251–277]. As a consequence we get...

Quasiharmonic fields and Beltrami operators

Claudia Capone (2002)

Commentationes Mathematicae Universitatis Carolinae

A quasiharmonic field is a pair ℱ = [ B , E ] of vector fields satisfying div B = 0 , curl E = 0 , and coupled by a distorsion inequality. For a given ℱ , we construct a matrix field 𝒜 = 𝒜 [ B , E ] such that 𝒜 E = B . This remark in particular shows that the theory of quasiharmonic fields is equivalent (at least locally) to that of elliptic PDEs. Here we stress some properties of our operator 𝒜 [ B , E ] and find their applications to the study of regularity of solutions to elliptic PDEs, and to some questions of G-convergence.

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