Related papers: The regulator dependence in the functional renorma…
The determination of the critical exponents by means of the Exact Renormalizion Group approach is still a topic of debate. The general flow equation is by construction scheme independent, but the use of the truncated derivative expansion…
A renormalization group theory for a system consisting of coupled superconducting layers as a model for typical high-temperature superconducters is developed. In a first step the electromagnetic interaction over infinitely many layers is…
This paper proposes a framework for adaptively learning a feedback linearization-based tracking controller for an unknown system using discrete-time model-free policy-gradient parameter update rules. The primary advantage of the scheme over…
We study exact renormalisation group flows for background field dependent regularisations. It is shown that proper-time flows are approximations to exact background field flows for a specific class of regulators. We clarify the role of the…
We study a model of asymptotically free theories with bound states using the similarity renormalization group for hamiltonians. We find that the renormalized effective hamiltonians can be approximated in a large range of widths by…
I introduce an approximation scheme that allows to deduce differential equations for the renormalization group $\beta$-function from a Schwinger--Dyson equation for the propagator. This approximation is proven to give the dominant…
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…
We study elastic systems such as interfaces or lattices, pinned by quenched disorder. To escape triviality as a result of ``dimensional reduction'', we use the functional renormalization group. Difficulties arise in the calculation of the…
Nonrelativistic two-body scattering by a short-ranged potential is studied using the renormalisation group. Two fixed points are identified: a trivial one and one describing systems with a bound state at zero energy. The eigenvalues of the…
We apply the renormalization group theory to the dynamical systems with the simplest example of basic biological motifs. This includes the interpretation of complex networks as the perturbation to simple network. This is the first step to…
The relationship between mappings of sets and renormalization group transformations is established, and renormalization group invariants of such mappings are found. These results are valid both for continuous and discrete mappings and for…
This paper proposes a unique optimization approach for estimating the minimax rational approximation and its application for evaluating matrix functions. Our method enables the extension to generalized rational approximations and has the…
A Wilsonian renormalisation group is used to study nonrelativistic two-body scattering by a short-ranged potential. We identify two fixed points: a trivial one and one describing systems with a bound state at zero energy. The eigenvalues of…
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…
The Polchinski version of the exact renormalisation group equations is applied to multicritical fixed points, which are present for dimensions between two and four, for scalar theories using both the local potential approximation and its…
We present an approximation scheme of the nonperturbative renormalization group that preserves the momentum dependence of correlation functions. This approximation scheme can be seen as a simple improvement of the local potential…
Using an infinitesimal approach, this work addresses the renormalization problem to deal with the ultraviolet divergences arising in quantum field theory. Under the assumption that the action has already been renormalized to yield an…
We revisit the approach to the lower critical dimension $d_{\rm lc}$ in the Ising-like $\varphi^4$ theory within the functional renormalization group by studying the lowest approximation levels in the derivative expansion of the effective…
We study online control of an unknown nonlinear dynamical system that is approximated by a time-invariant linear system with model misspecification. Our study focuses on robustness, a measure of how much deviation from the assumed linear…
We consider control constrained optimal control problems governed by parameterized stationary Maxwell's system with the Gauss's law. The parameters enter through dielectric, magnetic permeability, and charge density. Moreover, the parameter…