NONLINEAR DYNAMICS: QUANTUM CHAOS ----------------------------------------------------------- Georgia Tech PHYS 7224 Spring semester 2002 Predrag Cvitanovic' Lecture 26 Tue, Apr 16 2002 12:05-13:25 in Howey S106 Collinear helium, periodic orbits -------------------------- This might help: Cristel Chandre has contributed his implementation of the periodic orbits routines for a Hamiltonian flow. Carl Dettmann has contributed his notes on cycle search on a Poincare section. Igor Romanovski has contributed his 3-disk fortran code that finds all cycles up to a given length. Links to C, fortran code, notes: -------- Classical and Quantum Chaos --- www.nbi.dk/ChaosBook/extras/Welcome.html#chapterCycles chapter 12 - Fixed points, and how to get them / extras / -- Cristel Chandre's implementation of sect. 12.3.1 "Newton method for flows", for a 2-degree of freedom Hamiltonian flow, periodic orbits of a forced pendulum. Should be easily adoptable to other 2-degree of freedom Hamiltonian systems, such as the collinear helium: the overview, the C code. Problem set ----------- was due Tue 16 2002: Exer 24.5 Collinear helium cycles. Guess some short cycles by requiring that topologically they correspond to sequences of bounces either returning to the same r_i axis or reflecting off the diagonal. Compute them by some method or other. (if you are quantizing 3-disks rather than helium, find all cycles up in fundamental domain to length 5.) Exer 24.6 Collinear helium cycle stabilities Compute the stability eigenvalues for you collinear helium cycles. Compare with Table 24.1 If you have developed some half-way decent programs, comment them richly and contribute to the ChaosBook extras homepage. -------------------------------------------------------------- The solution of problems starting with these three and ending with the helium spectrum form the final exam in the course. If you prefer, you can compute the 3-disk resonances instead, the determination of perioidc orbits is easier in billards than it is in the flows. -------------------------------------------------------------------