Spectre negatif d'un operateur elliptique avec des conditions au bords de Robin

In this article we discuss some estimates of the number of the negative eigenvalues and their moments of energy for an elliptic operator L = L0 - V(x) defined in Hm(Rn+) with the Robin boundary conditions containing a potential W(x), in terms of some integrals of V and W

Boundary values as Hamiltonian variables. I. New Poisson brackets

The ordinary Poisson brackets in field theory do not fulfil the Jacobi identity if boundary values are not reasonably fixed by special boundary conditions. We show that these brackets can be modified by adding some surface terms to lift this restriction. The new brackets generalize a canonical bracket considered by Lewis, Marsden, Montgomery and Ratiu for the free boundary problem in hydrodynamics. Our definition of Poisson brackets permits to treat boundary values of a field on equal footing with its internal values and directly estimate the brackets between both surface and volume integrals. This construction is applied to any local form of Poisson brackets. A prescription for delta-function on closed domains and a definition of the {\it full} variational derivative are proposed.Comment: 26 pages, LaTex, IHEP 93-4

Spin-dependent electron dynamics and recombination in GaAs(1-x)N(x) alloys at room temperature

We report on both experimental and theoretical study of conduction-electron spin polarization dynamics achieved by pulsed optical pumping at room temperature in GaAs(1-x)N(x) alloys with a small nitrogen content (x = 2.1, 2.7, 3.4%). It is found that the photoluminescence circular polarization determined by the mean spin of free electrons reaches 40-45% and this giant value persists within 2 ns. Simultaneously, the total free-electron spin decays rapidly with the characteristic time ~150 ps. The results are explained by spin-dependent capture of free conduction electrons on deep paramagnetic centers resulting in dynamical polarization of bound electrons. We have developed a nonlinear theory of spin dynamics in the coupled system of spin-polarized free and localized carriers which describes the experimental dependencies, in particular, electron spin quantum beats observed in a transverse magnetic field.Comment: 5 pages, 4 figures, Submitted to JETP Letter