ترغب بنشر مسار تعليمي؟ اضغط هنا

An asymptotic relationship between homoclinic points and periodic orbit stability exponents

75   0   0.0 ( 0 )
 نشر من قبل Jizhou Li
 تاريخ النشر 2019
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

The magnitudes of the terms in periodic orbit semiclassical trace formulas are determined by the orbits stability exponents. In this paper, we demonstrate a simple asymptotic relationship between those stability exponents and the phase-space positions of particular homoclinic points.

قيم البحث

اقرأ أيضاً

Homoclinic and unstable periodic orbits in chaotic systems play central roles in various semiclassical sum rules. The interferences between terms are governed by the action functions and Maslov indices. In this article, we identify geometric relation s between homoclinic and unstable periodic orbits, and derive exact formulae expressing the periodic orbit classical actions in terms of corresponding homoclinic orbit actions plus certain phase space areas. The exact relations provide a basis for approximations of the periodic orbit actions as action differences between homoclinic orbits with well-estimated errors. This make possible the explicit study of relations between periodic orbits, which results in an analytic expression for the action differences between long periodic orbits and their shadowing decomposed orbits in the cycle expansion.
107 - Jizhou Li , Steven Tomsovic 2018
Homoclinic and heteroclinic orbits provide a skeleton of the full dynamics of a chaotic dynamical system and are the foundation of semiclassical sums for quantum wave packet, coherent state, and transport quantities. Here, the homoclinic orbits are o rganized according to the complexity of their phase-space excursions, and exact relations are derived expressing the relative classical actions of complicated orbits as linear combinations of those with simpler excursions plus phase-space cell areas bounded by stable and unstable manifolds. The total number of homoclinic orbits increases exponentially with excursion complexity, and the corresponding cell areas decrease exponentially in size as well. With the specification of a desired precision, the exponentially proliferating set of homoclinic orbit actions is expressible by a slower-than-exponentially increasing set of cell areas, which may present a means for developing greatly simplified semiclassical formulas.
We introduce the concepts of perpetual points and periodic perpetual loci in discrete--time systems (maps). The occurrence and analysis of these points/loci are shown and basic examples are considered. We discuss the potential usage and properties of introduced concepts. The comparison of perpetual points and loci in discrete--time and continuous--time systems is presented. Discussed methods can be widely applied in other dynamical systems.
148 - S. Huang , C. Chandre , T. Uzer 2007
We investigate the multiphoton ionization of hydrogen driven by a strong bichromatic microwave field. In a regime where classical and quantum simulations agree, periodic orbit analysis captures the mechanism: Through the linear stability of periodic orbits we match qualitatively the variation of experimental ionization rates with control parameters such as the amplitudes of the two modes of the field or their relative phases. Moreover, we discuss an empirical formula which reproduces quantum simulations to a high degree of accuracy. This quantitative agreement shows the mechanism by which short periodic orbits organize the dynamics in multiphoton ionization. We also analyze the effect of longer pulse durations. Finally we compare our results with those based on the peak amplitude rule. Both qualitative and quantitative analyses are implemented for different mode locked fields. In parameter space, the localization of the period doubling and halving allows one to predict the set of parameters (amplitudes and phase lag) where ionization occurs.
110 - S. Huang , C. Chandre , T. Uzer 2006
The multiphoton ionization of hydrogen by a strong bichromatic microwave field is a complex process prototypical for atomic control research. Periodic orbit analysis captures this complexity: Through the stability of periodic orbits we can match qual itatively the variation of experimental ionization rates with a control parameter, the relative phase between the two modes of the field. Moreover, an empirical formula reproduces quantum simulations to a high degree of accuracy. This quantitative agreement shows how short periodic orbits organize the dynamics in multiphoton ionization.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا