Semiclassical theory of long time propagation in quantum chaos. First part
Abstract
We develop a semiclassical theory of wave propagation based on invariant Lagrangian manifolds existing in conservative Hamiltonian systems with chaotic dynamics. They are stable and unstable manifolds of unstable periodic orbits, and their intersections consist of homoclinic and heteroclinic orbits. For arbitrary long times, we find matrix elements of the evolution operator between wave functions constructed in the neighbourhood of short unstable periodic orbits, in terms of canonical invariants of homoclinic and heteroclinic orbits. We verify the accuracy of these expressions by computing millions of homoclinic orbits and thousands of heteroclinic ones in the hyperbola billiard. Here we describe diagonal matrix elements while in another article named second part we will describe off-diagonal matrix elements.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- October 2020
- DOI:
- 10.1088/1751-8121/aba72f
- Bibcode:
- 2020JPhA...53M5703V
- Keywords:
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- semiclassical wave propagation;
- quantum chaos;
- classical invariants;
- canonical invariants