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Article Contents

# A kinetic equation for spin polarized Fermi systems

• This paper considers a kinetic Boltzmann equation, having a general type of collision kernel and modelling spin-dependent Fermi gases at low temperatures. The distribution functions have values in the space of positive hermitean $2\times2$ complex matrices. Global existence of weak solutions is proved in $L^1\cap L^{\infty}$ for the initial value problem of this Boltzmann equation in a periodic box.
Mathematics Subject Classification: 82C10, 82C22, 82C40.

 Citation:

•  [1] J. Dolbeault, Kinetic models and quantum effects, Arch. Rat. Mech. Anal., 127 (1994), 101-131.doi: 10.1007/BF00377657. [2] R. El Hajj, Étude Mathématique et Numérique de Modèles de Transport: Application à la Spintronique, Ph.D Thèse, IMT Université de Toulouse, 2008. [3] R. El Hajj, Diffusion Models for Spin Transport Derived from the Spinor Boltzmann Equation, to appear in Comm. in Math. Sci. [4] J. Jeon and W. Mullin, Kinetic equation for dilute, spin-polarized quantum systems, J. Phys. France, 49 (1988), 1691-1706.doi: 10.1051/jphys:0198800490100169100. [5] D. S. Jin and C. A. Regal, Fermi Gas Experiments, Proc. Int. School of Physics Enrico Fermi, course CLXIV, IOS Press, Amsterdam 2008. [6] P. L. Lions, Compactness in Boltzmann's equation via Fourier integral operators and applications III, J. Math. Kyoto Univ., 34 (1994), 539-584. [7] J. Lukkarinen, P. Mei and H. Spohn, Global well-posedness of the spatially homogeneous Hubbard-Boltzmann equation, arXiv:1212.2575. [8] P. C. Nasher, G. Taslevin, M. Leduc, S. B. Crampton and F. Laloë, Spin rotation effects and spin waves in gaseous $^3He\uparrow$, J. Phys. Lett., 45 (1984), 441-448. [9] V. P. Silin, Introduction to the Kinetic Theory of Gases, (in Russian), Nauka, Moscow, 1971.