Related papers: Wilsonian vs. 1PI renormalization group flow irrev…
In this paper we prove two backward uniqueness theorems for extrinsic geometric flow of possibly non-compact hypersurfaces in general ambient complete Riemannian manifolds. These are applicable to a wide range of extrinsic geometric flow,…
We examine the precise connection between the exact renormalisation group with local couplings and the renormalisation of correlation functions of composite operators in scale-invariant theories. A geometric description of theory space…
Michor and Mumford showed that the mean curvature flow is a gradient flow on a Riemannian structure with a degenerate geodesic distance. It is also known to destroy the uniform density of gridpoints on the evolving surfaces. We introduce a…
This paper is the last of the series investigating renormalization group aspects of stochastic random matrices, including a Wigner-like disorder. We consider the equilibrium dynamics formalism that can be merged with the Ward identities…
We analyze the exact behavior of the renormalization group flow in one-dimensional clock-models which undergo first order phase transitions by the presence of complex interactions. The flow, defined by decimation, is shown to be…
Nonperturbative approximation schemes based on two-particle irreducible (2PI) effective actions provide an important means for our current understanding of (non-)equilibrium quantum field theory. A remarkable property is their…
We analyze the Navier Stokes equation, and show that all non-viscous, irrotational flows are barotropic. As far as we know, this has never been stated in the literature before, and indirectly suggests that vorticity is required to make…
In the study of integrable non-linear $\sigma$-models which are assemblies and/or deformations of principal chiral models and/or WZW models, a rational function called the twist function plays a central role. For a large class of such…
We develop a continuous Wilsonian renormalized-flow theory of weak wave turbulence directly in spectral frequency space, for finite cascades in experimentally driven Newtonian fluids. The central quantity is a scale-dependent effective…
We study a normalized version of the second order renormalization group flow on closed Riemannian surfaces. We discuss some general properties of this flow and establish several basic formulas. In particular, we focus on surfaces with zero…
Based on the study of non-invertible symmetries, we propose there exist infinitely many new renormalization group flows between Virasoro minimal models $\mathcal{M}(kq + I, q) \to\mathcal{M}(kq-I, q)$ induced by $\phi_{(1,2k+1)}$. They…
We review current progress in the functional renormalization group treatment of disordered systems. After an elementary introduction into the phenomenology, we show why in the context of disordered systems a functional renormalization group…
We consider the singularities of the zero temperature renormalization group flow for random elastic manifolds. When starting from small scales, this flow goes through two particular points $l^{*}$ and $l_{c}$, where the average value of the…
We present one-loop perturbative results of the renormalization functions for a complete set of nonlocal quark bilinear operators containing an asymmetric staple-shaped Wilson line, using a family of improved lattice actions. This study is…
Given a compact three-manifold together with a Riemannian metric, we prove the short-time existence of a solution to the renormalization group flow, truncated at the second order term, under a suitable hypothesis on the sectional curvature…
Within the exact renormalisation group, the scaling solutions for O(N) symmetric scalar field theories are studied to leading order in the derivative expansion. The Gaussian fixed point is examined for d>2 dimensions and arbitrary infrared…
This paper presents an algebraic formulation of the renormalization group flow in quantum mechanics on flat target spaces. For any interacting quantum mechanical theory, the fixed point of this flow is a theory of classical probability, not…
Lie symmetry group method is applied to study Newtonian incompressible fluid's equations flow in turbulent boundary layers. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are…
Time irreversibility is a distinctive feature of non-equilibrium phenomena such as turbulent flows, where irreversibility is mainly associated with an energy cascade process. An Eulerian, multiscale analysis of time irreversibility in…
This paper introduces a new method to build linear flows, by taking the exponential of a linear transformation. This linear transformation does not need to be invertible itself, and the exponential has the following desirable properties: it…