On the quantisation of Arnold's cat
- 7 June 1990
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 23 (11) , 2013-2025
- https://doi.org/10.1088/0305-4470/23/11/025
Abstract
Characterises the quantisation UA of the classical map A in SL(2, Z) using the Heisenberg group, constructs the eigenstates for N=perfect square (where =2 pi /N) and shows that the Fourier components of the Wigner functions of a complete set of eigenstates go to zero for N=p2, p prime, p to infinity , A hyperbolic.Keywords
This publication has 17 references indexed in Scilit:
- Quantum scars of classical closed orbits in phase spaceProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1989
- Quantum mechanics of a classically chaotic system: Observations on scars, periodic orbits, and vibrational adiabaticityPhysical Review A, 1989
- The quantized Baker's transformationAnnals of Physics, 1989
- Smoothed wave functions of chaotic quantum systemsPhysica D: Nonlinear Phenomena, 1988
- The Quantized Baker's TransformationEurophysics Letters, 1987
- Exact eigenfunctions for a quantised mapJournal of Physics A: General Physics, 1986
- Born-Oppenheimer adiabatic mechanism for regularity of states in the quantum stadium billiardPhysical Review A, 1985
- Quantization of linear maps on a torus-fresnel diffraction by a periodic gratingPhysica D: Nonlinear Phenomena, 1980
- Regular and irregular semiclassical wavefunctionsJournal of Physics A: General Physics, 1977
- Periodic Orbits and Classical Quantization ConditionsJournal of Mathematical Physics, 1971