March  2014, 7(1): 1-8. doi: 10.3934/krm.2014.7.1

A kinetic equation for spin polarized Fermi systems

1. 

Mathematical Sciences, S-41296 Gothenburg, Sweden

Received  December 2012 Revised  May 2013 Published  December 2013

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.
Citation: Leif Arkeryd. A kinetic equation for spin polarized Fermi systems. Kinetic & Related Models, 2014, 7 (1) : 1-8. doi: 10.3934/krm.2014.7.1
References:
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J. Dolbeault, Kinetic models and quantum effects,, Arch. Rat. Mech. Anal., 127 (1994), 101.  doi: 10.1007/BF00377657.  Google Scholar

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R. El Hajj, Diffusion Models for Spin Transport Derived from the Spinor Boltzmann Equation,, to appear in Comm. in Math. Sci., ().   Google Scholar

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J. Lukkarinen, P. Mei and H. Spohn, Global well-posedness of the spatially homogeneous Hubbard-Boltzmann equation,, , ().   Google Scholar

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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.   Google Scholar

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V. P. Silin, Introduction to the Kinetic Theory of Gases,, (in Russian), (1971).   Google Scholar

show all references

References:
[1]

J. Dolbeault, Kinetic models and quantum effects,, Arch. Rat. Mech. Anal., 127 (1994), 101.  doi: 10.1007/BF00377657.  Google Scholar

[2]

R. El Hajj, Étude Mathématique et Numérique de Modèles de Transport: Application à la Spintronique,, Ph.D Thèse, (2008).   Google Scholar

[3]

R. El Hajj, Diffusion Models for Spin Transport Derived from the Spinor Boltzmann Equation,, to appear in Comm. in Math. Sci., ().   Google Scholar

[4]

J. Jeon and W. Mullin, Kinetic equation for dilute, spin-polarized quantum systems,, J. Phys. France, 49 (1988), 1691.  doi: 10.1051/jphys:0198800490100169100.  Google Scholar

[5]

D. S. Jin and C. A. Regal, Fermi Gas Experiments,, Proc. Int. School of Physics Enrico Fermi, (2008).   Google Scholar

[6]

P. L. Lions, Compactness in Boltzmann's equation via Fourier integral operators and applications III,, J. Math. Kyoto Univ., 34 (1994), 539.   Google Scholar

[7]

J. Lukkarinen, P. Mei and H. Spohn, Global well-posedness of the spatially homogeneous Hubbard-Boltzmann equation,, , ().   Google Scholar

[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.   Google Scholar

[9]

V. P. Silin, Introduction to the Kinetic Theory of Gases,, (in Russian), (1971).   Google Scholar

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