Related papers: Renormalization group, secular term resummation an…
The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory…
For singular perturbation problems in dynamical systems, various appropriate singular perturbation methods have been proposed to eliminate secular terms appearing in the naive expansion. For example, the method of multiple time scales, the…
A perturbative renormalization group method is used to obtain steady-state density profiles of a particle non-conserving asymmetric simple exclusion process. This method allows us to obtain a globally valid solution for the density profile…
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…
For scalar fields in AdS with masses slightly above the Breitenlohner-Freedman bound, appropriate non-local boundary conditions can define a unitary theory. Such boundary conditions correspond to non-local deformations of the dual CFT, and…
The general behaviour of perturbation series in non-equilibrium scalar field theory is analysed in some detail, with a particular emphasis on the ``pathological terms'', generated by multiple products of $\delta$-functions. Using an…
The perturbative renormalization group(RG) equation is applied to resum divergent series of perturbative wave functions of quantum anharmonic oscillator. It is found that the resummed series gives the cumulant of the naive perturbation…
Renormalization procedure is generalized to be applicable for non renormalizable theories. It is shown that introduction of an extra expansion parameter allows to get rid of divergences and express physical quantities as series of finite…
We use perturbation theory to construct a family of time-dependent microstrata: a set of non-extremal solutions of IIB supergravity asymptotic to $AdS_3 \times S^3 \times T^4$. Our construction shows that the "special locus" constraints of…
We develop a method for treating a series of secularly growing terms obtained from quantum perturbative calculations: autonomous first-order differential equations are constructed such that they reproduce this series to the given order. The…
In the AdS/CFT correspondence motion in the radial direction of the AdS space is identified with renormalization group flow in the field theory. For the N=4 Yang-Mills theory this motion is trivial. More interesting examples of…
We study the long-time asymptotics of a certain class of nonlinear diffusion equations with time-dependent diffusion coefficients which arise, for instance, in the study of transport by randomly fluctuating velocity fields. Our primary goal…
Considerable effort has been dedicated to study the nonlinear instability of Anti-de Sitter (AdS) within spherical symmetry, but little is known about this nonlinear instability in the purely gravitational sector, where spherical symmetry…
Based on the Taylor expansion, we propose a renormalization method for asymptotic analysis. The standard renormalization group (RG) method for asymptotic analysis can be derived out from this new method, and hence the mathematical essence…
A semi-analytic approach to the computation of the non-linear power-spectrum of dark matter density fluctuations is proposed. The method is based on the Renormalization Group technique and can be applied to any underlying cosmological…
The renormalization group flow of the worldvolume theory depends very much from the number of unbroken supersymmetries. In the dual $AdS$ picture we break supersymmetry by adding different types of BPS black holes. We argue, that this BPS…
The renormalization group method is applied for obtaining the asymptotic form of the wave function of the quantum anharmonic oscillator by resumming the perturbation series. It is shown that the resumed series is the cumulant of the naive…
Field theoretical renormalization group methods are applied to a simple model of a passive scalar quantity advected by the Gaussian non-solenoidal (``compressible'') velocity field with the covariance $\propto\delta(t-t')|…
This paper presents a secular term removal methodology based on the homotopy perturbation method for analytical solutions of nonlinear problems with periodic boundary condition. The analytical solution for groundwater response to tidal…
Anti-de Sitter (AdS) is conjectured to be nonlinear unstable to a weakly turbulent mechanism that develops a cascade towards high frequencies, leading to black hole formation [1,2]. We give evidence that the gravitational sector of…