Abstract
Scattering experiments are a primary source of our knowledge about elementary particles, atoms and molecules. Similarly celestial bodies are scattered by the sun or the whole solar system.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Berry, M.V.: Quantizing a Classically Ergodic System: Sinai’s Billiard and the KKR Method. Annals of Physics 131, 163–216 (1981)
Eckhardt, B.: Irregular Scattering. Physica D 33, 89–98 (1988)
Cvitanović, P., Eckhardt, B., Russberg, G., Rosenqvist, P., Scherer, P.: Pinball Scattering. In: Quantum Chaos, G. Casati, B., Chirikov Eds. Cambridge University Press 1993
Duistermaat, J.: Oscillatory Integrals, Lagrange Immersions and Unfolding of Singularities. Commun. Pure Appl. Math. 27, 207–281 (1974)
Gaspard, P., Rice, S.: Semiclassical quantization of the scattering from a classically chaotic repellor. Exact quantization of the scattering from a classically chaotic repellor. J. Chem. Phys. 90, 2242–2254, 2255-2262 (1989) Erratum: J. Chem. Phys. 91, 3280 (1989)
Hadamard, J.: Les surfaces à courbures opposées et leur lignes géodesiques. Journ. Math. 5e série, t. 4, 27–73 (1898); Œvres, Tome II
Hunziker, W.: Scattering in Classical Mechanics. In: Scattering Theory in Mathematical Physics. J.A. La Vita and J.-P. Marchand, Eds., Dordrecht: Reidel 1974
Hunziker, W., Sigal, L: The General Theory of N-Body Quantum Systems. CRM Proceedings and Lecture Notes 8, 35–72, American Mathematical Society 1995
Klein, M., Knauf, A.: Classical Planar Scattering by Coulombic Potentials. Lecture Notes in Physics m 13. Berlin, Heidelberg, New York: Springer; 1993
Knauf, A.: Irregular Scattering, Number Theory, and Statistical Mechanics. In: Stochasticity and Quantum Chaos. Z. Haba et al, Eds. Dordrecht: Kluwer 1995
Lopes, A., Markarian, R.: Open Billiards: Invariant and Conditionally Invariant Probabilities on Cantor Sets. SIAM J. Appl. Math. 56, 651–680 (1996)
Mather, J., McGehee, R.: Solutions of the Collinear four Body Problem which Become Unbounded in Finite Time. In: Dynamical Systems, Theory and Applications. J. Moser, Ed. Lecture Notes in Physics 38. Berlin, Heidelberg, New York: Springer; 1975
Morita, T.: The symbolic representation of billiards without boundary condition. Trans. Am. Math. Soc. 325, 819–828 (1991)
Narnhofer, H.: Another Definition for Time Delay. Phys. Rev. D 22, 2387–2390 (1980)
Reed, M., Simon, B.: Methods of Modern Mathematical Physics. Vol. III: Scattering Theory. New York: Academic Press 1979
Simon, B.: Wave Operators for Classical Particle Scattering. Commun. Math. Phys. 23, 37–49 (1971)
Sinai, Ya.: Dynamical Systems with Elastic Reflections. Russ. Math. Surv. 25, 137–189 (1970)
Sjüstrand, J.: Geometric Bounds on the Density of Resonances for Semiclassical Problems. Duke Math. J. 60, 1–57 (1990)
Smilansky, U.: The Classical and Quantum Theory of Chaotic Scattering. In: Chaos and Quantum Physics. M.-J. Giannoni et al, Eds. Les Houches LII. Amsterdam: North-Holland 1989
Tél, T.: Transient Chaos. In: Directions in Chaos, Vol. 4 Ed. Hao Bai-lin. Singapore: World Scientific 1990
Troll, G.: How to Escape a Sawtooth-Transition to Chaos in a Simple Scattering Model. Nonlinearity 5, 1151–1192 (1992)
Walters, P.: An Introduction to Ergodic Theory, New York, Heidelberg, Berlin: Springer 1982
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Basel AG
About this chapter
Cite this chapter
Knauf, A., Sinai, Y.G., Baladi, V. (1997). Irregular Scattering. In: Classical Nonintegrability, Quantum Chaos. DMV Seminar, vol 27. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8932-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8932-2_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-5708-5
Online ISBN: 978-3-0348-8932-2
eBook Packages: Springer Book Archive