Threshold law for escaping from the Hénon-Heiles system.
We report a theoretical study of the escape rates of the Hénon-Heiles system above threshold. An analytic formula for the escape rate as a function of energy is presented. We also simulated the escaping process by following the motions of a large number of particles. Two algorithms are employed to solve the equations of motion. One is the Runge-Kutta-Fehlberg method, and another is a recently proposed fourth order symplectic method. Our simulations show the escape of Hénon-Heiles system follows exponential laws. We extracted the escape rates from the time dependence of particle numbers in the Hénon-Heiles potential. The extracted escape rates agree with the analytic result. Close to threshold we find the rate alpha(DeltaE) can be written as a series expansion, the first term of this expansion is 4/3DeltaE.
Zhao
H J
HJ
Institute of Theoretical Physics, Chinese Academy of Sciences, P.O.Box 2735, Beijing 100080, China.
Du
M L
ML