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Comment: Submitted as a chapter in the book "Fifty Years of Anderson Localization"
Comment: Lectures given at the Les Houches Summer School "Applications of Random Matrices in Physics", June 2004, 45p
Comment: 4 pages, revtex, no figures
Comment: 37 pages, Latex, the manuscript has been submitted to Phys.Rev.B on April 10
We consider properties of a two-dimensional electron system in a random magnetic field. It is assumed that the magnetic field not only influences orbital electron motion but also acts on the electron spin. For calculations, we suggest a new trick replacing the initial Hamiltonian by a Dirac Hamiltonian. This allows us to do easily a perturbation theory and derive a supermatrix sigma model, which takes a form of the conventional sigma model with the unitary symmetry. Using this sigma model we calculate several correlation functions including a spin-spin correlation function. As compared to the model without spin, we get different expressions for the single-particle lifetime and the transport time. The diffusion constant turns out to be 2 times smaller than the one for spinless particles.
Comment: 18 pages, 8 figures, published version with minor changes
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