Velocity and Entropy of Motion in Periodic Potentials
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1996-1997), Talk no. 17, 11 p.

This is a report on recent joint work with J. Asch, and with T. Hudetz and F. Benatti.

We consider classical, quantum and semiclassical motion in periodic potentials and prove various results on the distribution of asymptotic velocities.

The Kolmogorov-Sinai entropy and its quantum generalization, the Connes-Narnhofer-Thirring entropy, of the single particle and of a gas of noninteracting particles are related.

Knauf, Andreas 1

1 Max-Planck-Institut für Math. in den Naturw., Inselstr. 22–26, D-04103 Leipzig, Germany
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     title = {Velocity and {Entropy} of {Motion} in {Periodic} {Potentials}},
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Knauf, Andreas. Velocity and Entropy of Motion in Periodic Potentials. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1996-1997), Talk no. 17, 11 p. http://www.numdam.org/item/SEDP_1996-1997____A17_0/

[1] Asch, J., Knauf, A.: Motion in Periodic Potentials. Preprint (1997) | MR | Zbl

[2] Benatti, F., Hudetz, T., Knauf, A.: Quantum Chaos and Dynamical Entropy. Preprint (1997) | MR | Zbl

[3] Connes, A., Narnhofer, H., Thirring, W.: Dynamical Entropy for C* algebras and von Neumann Algebras. Commun. Math. Phys. 112, 691 (1987). | MR | Zbl

[4] Gérard, Ch., Nier, F.: Scattering Theory for the Perturbations of Periodic Schrödinger Operators. Preprint Ecole Polytechnique (1997) | MR | Zbl

[5] Klein, M., Knauf, A.: Classical Planar Scattering by Coulombic Potentials. Lecture Notes in Physics m 13. Berlin, Heidelberg, New York: Springer; 1993 | Zbl

[6] Knauf, A.: Ergodic and Topological Properties of Coulombic Periodic Potentials. Commun. Math. Phys. 110, 89–112 (1987) | MR | Zbl

[7] Knauf, A.: Coulombic Periodic Potentials: The Quantum Case. Annals of Physics 191, 205–240 (1989) | MR

[8] Knauf, A.: Closed orbits and converse KAM theory. Nonlinearity 3, 961–973 (1990) | MR | Zbl

[9] Reed, M., Simon, B.: Methods in Mathematical Physics, Vol. IV: Analysis of Operators. New York: Academic Press 1978 | MR | Zbl

[10] Thomas, L.E.: Time Dependent Approach to Scattering from Impurities in a Crystal. Commun. Math. Phys 33, 335–343 (1973) | MR