Renormalization Group Reduction of Non Integrable Hamiltonian Systems

نویسنده

  • Stephan I. Tzenov
چکیده

Based on the Renormalization Group method, a reduction of non integrable multi-dimensional hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density, and for the amplitudes of the angular modes have been derived. It has been shown that these equations are precisely the Renormalization Group equations. As an application of the approach developed, the modulational diffusion in one-and-ahalf degree of freedom dynamical system has been studied in detail. Submitted to the New Journal of Physics

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Canonical structure of renormalization group equations and separability of Hamiltonian systems

2 Abstract. We investigate perturbed Hamiltonian systems with two degrees of freedom by renormalization group method, which derives a reduced equation called renormalization group equation (RGE) by handling secular terms. We found that RGE is not always a Hamiltonian system. The necessary and sufficient condition that RGE becomes a Hamiltonian system up to the second leading order of a small pa...

متن کامل

Time-Dependent Real-Space Renormalization Group Method

In this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent Hamiltonians. We drive the time-dependent recursion relations for the renormalized tight-binding Hamiltonian by decimating selective sites of lattice iteratively. The formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...

متن کامل

On the Renormalization of Hamiltonian Flows , and Critical Invariant Tori

We analyze a renormalization group transformation R for partially analytic Hamiltonians, with emphasis on what seems to be needed for the construction of non-integrable xed points. Under certain assumptions, which are supported by numerical data in the golden mean case, we prove that such a xed point has a critical invariant torus. The proof is constructive and can be used for numerical computa...

متن کامل

Renormalization group method and canonical perturbation theory

Abstract. Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action variables. We show that the renormalization group method gives the same approximate solutions as canonical perturbation theory up to the second order of...

متن کامل

Renormalization group equations and integrability in Hamiltonian systems

We investigate Hamiltonian systems with two degrees of freedom by using renormalization group method. We show that the original Hamiltonian systems and the renormalization group equations are integrable if the renormalization group equations are Hamiltonian systems up to the second leading order of small parameter. To understand temporal evolutions of Hamiltonian systems, one useful method is t...

متن کامل

ذخیره 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 2001