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Renormalization-Group (RG) improvement has been frequently applied to capture the effect of quantum corrections on cosmological and black-hole spacetimes. This work utilizes an algebraically complete set of curvature invariants to establish…
The operator-theoretic renormalization group (RG) methods are powerful analytic tools to explore spectral properties of field-theoretical models such as quantum electrodynamics (QED) with non-relativistic matter. In this paper these methods…
We improve on the description of the relationship that exists between critical clusters in thermal systems and intermittency near the onset of chaos in low-dimensional systems. We make use of the statistical-mechanical language of…
We develop a perturbative renormalization-group method in real time to describe nonequilibrium properties of discrete quantum systems coupled linearly to an environment. We include energy broadening and dissipation and develop a…
A non-perturbative and continuous definition of RG transformations as stochastic processes is proposed, inspired by the observation that the functional RG equations for effective Boltzmann factors may be interpreted as Fokker-Planck…
We study the scaling behaviors of the active model B+ using the functional renormalization group (FRG) approach, based on the nonequilibrium effective action formulated via the Martin-Siggia-Rose path-integral formalism. We derive the…
We review recent results based on an application of the real-space renormalization group (RG) approach to a network model for the integer quantum Hall (QH) transition. We demonstrate that this RG approach reproduces the critical…
We propose a numerical renormalization group (NRG) approach to steady-state currents through nano-devices. A discretization of the scattering-states continuum ensures the correct boundary condition for an open quantum system. We introduce…
Non-Hermiticity plays a fundamental role in open quantum systems and describes a wide variety of effects of interactions with environments, including quantum measurement. However, understanding its consequences in strongly interacting…
We show how to extract the scaling behavior of quantum walks using the renormalization group (RG). We introduce the method by efficiently reproducing well-known results on the one-dimensional lattice. As a nontrivial model, we apply this…
Far from equilibrium, neural systems self-organize across multiple scales. Exploiting multiscale self-organization in neuroscience and artificial intelligence requires a computational framework for modeling the effective non-equilibrium…
We investigate the RG-time integration of the effective potential in the functional renormalization group in the presence of spontaneous symmetry breaking and its subsequent convexity restoration on the example of a scalar theory in $d=3$.…
According to the available publications, the field theoretical renormalization group (RG) approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This fact was attempted to explain by the…
The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling…
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…
The goal of this work is to analyze the long-term behavior of reaction-diffusion systems arising in two-species chemical models and to identify the minimal set of modes that determine their dynamics. The models considered include, as…
Recent advances in quantum simulator experiments enable unprecedented access to quantum many-body states through snapshot measurements of individual many-body configurations. Here, we introduce an exact renormalization group (RG)…
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…
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…
Image denoising is a fundamental and challenging task in the field of computer vision. Most supervised denoising methods learn to reconstruct clean images from noisy inputs, which have intrinsic spectral bias and tend to produce…