Related papers: Renormalization group and diffusion equation
The exact renormalization group is applied to a nonlinear diffusion equation with a discontinuous diffusion coefficient. The generating functional of the solution for the initial-value problem of nonlinear diffusion equations is first…
The "exact" or "functional" renormalization group equation describes the renormalization group flow of the effective average action $\Gamma_k$. The ordinary effective action $\Gamma_0$ can be obtained by integrating the flow equation from…
The existence of fluctuations together with interactions leads to scale-dependence in the couplings of quantum field theories for the case of quantum fluctuations, and in the couplings of stochastic systems when the fluctuations are of…
The paper is an attempt to relate two vast areas of the applicability of the renormalization group (RG): field theoretic models and partial differential equations. It is shown that the Green function of a nonlinear diffusion equation can be…
We consider the exact renormalization group for a non-canonical scalar field theory in which the field is coupled to the external source in a special non linear way. The Wilsonian action and the average effective action are then simply…
Phase equations describing the evolution of large scale modulation of spatially periodic patterns in two dimensional systems are derived by employing the renormalization group method. A general formula for phase diffusion coefficients is…
We establish a concrete correspondence between a gradient flow and the renormalization group flow for a generic scalar field theory. We use the exact renormalization group formalism with a particular choice of the cutoff function.
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…
The flow equations of the Functional Renormalization Group are applied to the O(N)-symmetric scalar theory, for N=1 and N=4, in four Euclidean dimensions, d=4, to determine the effective potential and the renormalization function of the…
An exact renormalization group equation describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. It interpolates between the microphysical laws and the complex macroscopic phenomena. We…
In the Yukawa model with two different mass scales the renormalization group equation is used to obtain relations between scattering amplitudes at low energies. Considering fermion-fermion scattering as an example, a basic one-loop…
We investigate the renormalization group approach to nonequilibrium field theory. We show that it is possible to derive nontrivial renormalization group flow from iterative coarse graining of a closed-time-path action. This renormalization…
We analyse approximate solutions to an exact renormalisation group equation with particular emphasis on their dependence on the regularisation scheme, which is kept arbitrary. Physical quantities related to the coarse-grained potential of…
In effective field theories, the concept of renormalization of perturbative divergences is replaced by renormalization group concepts such as relevance and universality. Universality is related to cutoff scheme independence in…
Quantum field theories require a cutoff to regulate divergences that result from local interactions, and yet physical results can not depend on the value of this cutoff. The renormalization group employs a transformation that changes the…
The normalization of the quantum corrected action is resolving the equation divergent dependence of the cutoff towards the system apparent result in quantum gravity. Here we consider the normalization to Einstein R twice scalar action with…
A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the…
The one-loop renormalization of the action for a set Dirac fermions and a set of scalars spanning an arbitrary manifold coupled via Yukawa-like and gauge interactions is presented. The computation is performed with functional methods and in…
We continue the study of the renormalization group and decoupling of massive fields in curved space, started in the previous article and analyse the higher derivative sector of the vacuum metric-dependent action of the Standard Model. The…
An exact functional renormalization group flow equation is derived for the divergence functional which is a generalization of the Kullback-Leibler divergence to quantum field theories in the Euclidean domain. It compares distributions with…