Related papers: How to measure the effective action for disordered…
In this article, we propose a new method to compute the effective properties of non-linear disordered media. We use the fact that the effective constants can be defined through the minimum of an energy functional. We express this minimum in…
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…
The free energy of the Coulomb Gap problem is expanded as a set of Feynman diagrams, using the standard diagrammatic methods of perturbation theory. The gap in the one-particle density of states due to long-ranged interactions corresponds…
Simultaneous measurement of several noncommuting observables is modeled by using semigroups of completely positive maps on an algebra with a non-trivial center. The resulting piecewise-deterministic dynamics leads to chaos and to nonlinear…
Current diagnostic practice in psychiatry is not relying on objective biophysical evidence. Recent pandemic emphasized the need to address the rising number of mood disorders (in particular, depression) cases in a more efficient way. We are…
We present a detailed discussion of a novel dynamical renormalization group scheme: the Dynamically Driven Renormalization Group (DDRG). This is a general renormalization method developed for dynamical systems with non-equilibrium critical…
In these lectures I discuss peculiarities of the critical behaviour of ``non-ideal'' systems as it is explained by the renormalization group approach. Examples considered here include account of the single-ion anisotropy, structural…
There are a number of measures of direct and indirect effects in the literature. They are suitable in some cases and unsuitable in others. We describe a case where the existing measures are unsuitable and propose new suitable ones. We also…
Some recent results showed that renormalization group can be considered as a promising framework to address open issues in data analysis. In this work, we focus on one of these aspects, closely related to principal component analysis for…
In physics we attempt to infer the rules governing a system given only the results of imprecise measurements. This is an ill-posed problem because certain features of the system's state cannot be resolved by the measurements. However, by…
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…
Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on…
The functional renormalization group method is used to take into account the vacuum polarization around localized bound states generated by external potential. The application to Atomic Physics leads to improved Hartree-Fock and Kohn-Sham…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
The critical behaviour of the randomly spin-diluted Ising model in two space dimensions is investigated by a new method which combines a grand ensemble approach to disordered systems proposed by Morita with the phenomenological…
We provide and study complete sets of one-loop renormalization group equations of several Finkel'stein non-linear $\sigma$-models, the effective field theories describing the diffusive quantum fluctuations in correlated disordered systems.…
We demonstrate the feasibility of a nonperturbative analysis of quantum field theory in the worldline formalism with the help of an efficient numerical algorithm. In particular, we compute the effective action for a super-renormalizable…
This paper is the fifth in a series devoted to the development of a rigorous renormalisation group method applicable to lattice field theories containing boson and/or fermion fields, and comprises the core of the method. In the…
In this paper we present an efficient numerical approach based on the Renormalization Group method for the computation of self-similar dynamics. The latter arise, for instance, as the long-time asymptotic behavior of solutions to nonlinear…
We review the formalism of the effective average action in quantum field theory which corresponds to a coarse grained free energy in statistical mechanics. The associated exact renormalization group equation and possible nonperturbative…