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Avant propos , 1) website pour le cour:

Avant propos , 1) website pour le cour: http://www.trt.thalesgroup.com/ump-cnrs-thales/umr-0137/oral/oral.html 2) Ref érences pour les calculs de resistivity avec la principe variationelle; A.Fert et I.A. Campbell, J. Phys.F 6 , 849 (1976) Fert, J.Phys.C 2 , 1784 (1969).

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Avant propos , 1) website pour le cour:

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  1. Avant propos, 1) website pour le cour: http://www.trt.thalesgroup.com/ump-cnrs-thales/umr-0137/oral/oral.html 2) Reférences pour les calculs de resistivity avec la principe variationelle; A.Fert et I.A. Campbell, J. Phys.F6, 849 (1976) Fert, J.Phys.C2, 1784 (1969). 3)Entre ballistique et diffusive transport. Voir Y.-N. Qi et S. Zhang, PRB65, 214407(2002).

  2. Transport in magnetically layered structures Let us start off with the Kubo, or two point conductivity, formalism.

  3. Note the scattering at a distance; how is accounted for in the Boltzmann formalsim?

  4. The approach we outlined with no mixing of spin channels yields figures on left; however as we presently show when mixing is important these curves begin to flex as shown on the right.

  5. Example

  6. Layer by layer approach to transport in metallic structures: In the layer-by-layer approach one solves for the transport in each layer as if it is homogenous. The specular scattering at the interfaces between layers provide the boundary conditions that provide for the solution the transport across the entire multilayer. • Due to screening in metals transport in each layer can be modeled by equilibrium band structure. • Solve for distribution function ( statistical density matrix) in each layer by using the Boltzmann equation. • The distribution functions describing the out of equilibrium transport across layers are connected by the scattering matrices at the interfaces. This interface scattering manifests itself differently in periodic superlattices from simple multilayered structures. In the former it does not alter the transmission; rather it changes the conductance by introducing superzone gaps.

  7. More generally in multilayered structures the interface scattering is represented by the reflection and transmission amplitudes and probabilities

  8. See Asya Shpiro cond-mat/0401613.

  9. Let us return for a moment to the concept of local equilibrium and electrochemical potential. See Asya Shpiro cond-mat/0401613.

  10. See Asya Shpiro cond-mat/0401613.

  11. Expansion of the angular dependence of out of equilibrium distribution function in terms of Legendre polynomials. Valet & Fert PRB 48, 7099 (1993).

  12. A propos: Transition from ballistic to diffusive transport; see Qi and Zhang PRB65, 214407 (2002).

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