TY - JOUR
T1 - Algebraic decay and fluctuations of the decay exponent in Hamiltonian systems
AU - Lai, Ying Cheng
AU - Ding, Mingzhou
AU - Grebogi, Celso
AU - Blümel, Reinhold
N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 1992
Y1 - 1992
N2 - Particle-decay processes in a nonhyperbolic Hamiltonian system are typically characterized by algebraic laws. That is, for a fixed set of parameter values, if one initializes a particle in a chaotic region near some Kol'mogorov-Arnol'd-Moser (KAM) tori, the probability for this particle to remain in the region at time t decays with time algebraically: P(t)∼t-z, where z is the decay exponent. As a system parameter varies, the numerically calculated exponent z exhibits rather large fluctuations. In this paper we examine the dynamical origin of such fluctuations using a model system which exhibits unbounded chaotic dynamics (i.e., chaotic scattering). Our results indicate that the fluctuating behavior of z, as a function of the parameter, can be attributed to the breakup of KAM surfaces in phase space. A particularly interesting finding is that, when the outermost KAM surfaces enclosing some central island transform from absolute barriers to partial barriers (Cantori), as the parameter varies, the survival probability P(t) displays two different regions of scaling behavior with different decay exponents. The time scale where this crossover takes place is found to coincide with the typical time for a particle to penetrate the newly created Cantori.
AB - Particle-decay processes in a nonhyperbolic Hamiltonian system are typically characterized by algebraic laws. That is, for a fixed set of parameter values, if one initializes a particle in a chaotic region near some Kol'mogorov-Arnol'd-Moser (KAM) tori, the probability for this particle to remain in the region at time t decays with time algebraically: P(t)∼t-z, where z is the decay exponent. As a system parameter varies, the numerically calculated exponent z exhibits rather large fluctuations. In this paper we examine the dynamical origin of such fluctuations using a model system which exhibits unbounded chaotic dynamics (i.e., chaotic scattering). Our results indicate that the fluctuating behavior of z, as a function of the parameter, can be attributed to the breakup of KAM surfaces in phase space. A particularly interesting finding is that, when the outermost KAM surfaces enclosing some central island transform from absolute barriers to partial barriers (Cantori), as the parameter varies, the survival probability P(t) displays two different regions of scaling behavior with different decay exponents. The time scale where this crossover takes place is found to coincide with the typical time for a particle to penetrate the newly created Cantori.
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U2 - 10.1103/PhysRevA.46.4661
DO - 10.1103/PhysRevA.46.4661
M3 - Article
AN - SCOPUS:0001656616
SN - 1050-2947
VL - 46
SP - 4661
EP - 4669
JO - Physical Review A
JF - Physical Review A
IS - 8
ER -