Related papers: Exact Renormalization Groups as a form of Entropic…
We study a generic problem of dissipative quantum mechanics, a small local quantum system with discrete states coupled in an arbitrary way (i.e. not necessarily linear) to several infinitely large particle or heat reservoirs. For both…
In renormalization group (RG) flow, the low energy states form a code subspace that is approximately protected against the local short-distance errors. We motivate this connection with an example of spin-blocking RG in classical spin…
The Wilsonian renormalization group (RG) method is applied to finite temperature systems for the study of non-perturbative methods in the field theory. We choose the O(N) linear sigma model as the first step. Under the local potential…
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…
Large-$N$ renormalization group equations for one- and two-matrix models are derived. The exact renormalization group equation involving infinitely many induced interactions can be rewritten in a form that has a finite number of coupling…
We investigate how additive weak noise (correlated as well as uncorrelated) modifies the parameters of the Gray-Scott (GS) reaction diffusion system by performing numerical simulations and applying a Renormalization Group (RG) analysis in…
Evolution of the concept known in the theoretical physics as the Renormalization Group (RG) is presented. The corresponding symmetry, that has been first introduced in QFT in mid-fifties, is a continuous symmetry of a solution with respect…
Flow-based generative models have become an important class of unsupervised learning approaches. In this work, we incorporate the key ideas of renormalization group (RG) and sparse prior distribution to design a hierarchical flow-based…
In the beginning of the 1970's, Wilson developed the concept of a fully non-perturbative renormalization group transformation. Applied to the Kondo problem, this numerical renormalization group method (NRG) gave for the first time the full…
For cosmologies including scale dependence of both the cosmological and the gravitational constant, an additional consistency condition dictated by the Bianchi identities emerges, even if the energy-momentum tensor of ordinary matter stays…
Tensor renormalization group (TRG) constitutes an important methodology for accurate simulations of strongly correlated lattice models. Facilitated by the automatic differentiation technique widely used in deep learning, we propose a…
Turbulence is a complex nonlinear and multi-scale phenomenon. Although the fundamental underlying Navier-Stokes equations have been known for two centuries, it remains extremely challenging to extract from them the statistical properties of…
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…
Dense relativistic matter has attracted a lot of attention over many decades now, with a focus on an understanding of the phase structure and thermodynamics of dense strong-interaction matter. The analysis of dense strong-interaction matter…
Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a…
The gradient flow is the evolution of fields and physical quantities along a dimensionful parameter~$t$, the flow time. We give a simple argument that relates this gradient flow and the Wilsonian renormalization group (RG) flow. We then…
In this paper we employ the Renormalization Group (RG) method to study higher order corrections to the long-time asymptotics of a class of nonlinear integral equations with a generalized heat kernel and with time-dependent coefficients.…
We derive generic relativistic hydrodynamical equations with dissipative effects from the underlying Boltzmann equation in a mechanical and systematic way on the basis of so called the renormalization-group (RG) method. A macroscopic frame…
Scheme independence of exact renormalization group equations, including independence of the choice of cutoff function, is shown to follow from general field redefinitions, which remains an inherent redundancy in quantum field theories.…
The renormalization group (RG) properties of quantum gravity are explored, using the vielbein and the spin connection as the fundamental field variables. The scale dependent effective action is required to be invariant both under space time…