Asymptotic boundary layer method for unstable trajectories: Semiclassics for individual scar wavefunctions
نویسنده
چکیده
A. Vagov, 2 H. Schomerus, and V. V. Zalipaev 4 Institut für Theoretische Physik III, Bayreuth Universität, Bayreuth 95440, Germany Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom Steklov Mathematical Institute, Fontanka 27, St.-Petersburg 191023, Russia 4 Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom (Dated: July 9, 2009)
منابع مشابه
Scar functions in the Bunimovich Stadium billiard
In the context of the semiclassical theory of short periodic orbits, scar functions play a crucial role. These wavefunctions live in the neighbourhood of the trajectories, resembling the hyperbolic structure of the phase space in their immediate vicinity. This property makes them extremely suitable for investigating chaotic eigenfunctions. On the other hand, for all practical purposes reduction...
متن کاملA hybrid method for singularly perturbed delay boundary value problems exhibiting a right boundary layer
The aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. The method is a combination of the asymptotic expansion technique and the reproducing kernel method (RKM). First an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. Then the reduced regular delayed diffe...
متن کاملNumerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type
In this paper, we have proposed a numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided in...
متن کاملWavefunction Statistics using Scar States
We describe the statistics of chaotic wavefunctions near periodic orbits using a basis of states which optimise the effect of scarring. These states reflect the underlying structure of stable and unstable manifolds in phase space and provide a natural means of characterising scarring effects in individual wavefunctions as well as their collective statistical properties. In particular, these sta...
متن کاملSemiclassical wavefunctions in chaotic scattering systems
We have computed quantum wavefunctions in the high-energy (semiclassical) regime in a system—the stadium billiard with leads allowing particles to enter and escape—exemplifying chaotic scattering. The results exhibit a structure associated with classical paths that is dramatically more pronounced than the scars due to periodic orbits seen in bound systems. Moreover, this structure is seen at al...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008