Related papers: Similarity Renormalization, Hamiltonian Flow Equat…
In this work, the exact reproduction of a moving-water steady flow via the numerical solution of the one-dimensional shallow water equations is studied. A new scheme based on a modified version of the HLLEM approximate Riemann solver…
Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose,…
We provide a general algorithm to construct a Hamiltonian, such that its dynamical flow covariantly defines any given spherically symmetric and static metric. This Hamiltonian is defined as a linear combination of the standard (general…
We compare different methods used for non-perturbative calculations in strongly interacting fermionic systems. Mean field theory often shows a basic ambiguity related to the possibility to perform Fierz transformations. The results may then…
We present a non-perturbative formulation of renormalization by viewing the regularized Schwinger-Dyson hierarchy as a meromorphic connection, that is, as a D-module on the product of spacetime with the regulator disc. The irregular…
In the companion paper we motivated a renormalisation flow on Osterwalder-Schrader data (OS-data) consisting of 1. a Hilbert space, 2. a cyclic vacuum and 3. a Hamiltonian annihilating that vacuum. As the name suggests, the motivation was…
In 1995, Hamilton introduced a Harnack inequality for convex solutions of the mean curvature flow. In this paper we prove an alternative Harnack inequality for curve shortening flow, i.e. one-dimensional mean curvature flow, that does not…
We carry out a field-theoretical renormalization group procedure based on the Callan-Symanzik equation to calculate the detailed flow for the (multi) two-channel Kondo model and its compactified versions. In doing so, we go beyond the…
Many experimental techniques aim at determining the Hamiltonian of a given system. The Hamiltonian describes the system's evolution in the absence of dissipation, and is often central to control or interpret an experiment. Here, we…
In this paper, we propose a second-order energy-conserving approximation procedure for Hamiltonian systems with holonomic constraints. The derivation of the procedure relies on the use of the so-called line integral framework. We provide…
We prove first-order convergence of semi-discrete monotone finite difference schemes for Hamilton--Jacobi equations on the Wasserstein space over a finite graph. A central challenge is the boundary degeneracy of the Wasserstein simplex,…
We investigated the back reaction of cosmological perturbations on the evolution of the universe using the second order perturbation of the Einstein's equation. To incorporate the back reaction effect due to the inhomogeneity into the…
We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not…
Following Manin's approach to renormalization in the theory of computation, we investigate Dyson-Schwinger equations on Hopf algebras, operads and properads of flow charts, as a way of encoding self-similarity structures in the theory of…
A new two-step renormalization procedure is proposed. In the first step, the effects of high-energy states are considered in the conventional (Feynman) perturbation theory. In the second step, the coupling to many-body states is eliminated…
We develop a renormalization group for weak Harris-marginal disorder in otherwise strongly interacting quantum critical theories, focusing on systems which have emergent conformal invariance. Using conformal perturbation theory, we argue…
Normalizing flows are a powerful tool for generative modelling, density estimation and posterior reconstruction in Bayesian inverse problems. In this paper, we introduce proximal residual flows, a new architecture of normalizing flows.…
Within the Functional Renormalisation Group (FRG) approach, we present a fluid-dynamical approach to solving flow equations for models living in a multi-dimensional field space. To this end, the underlying exact flow equation of the…
Using Dirac's approach to constrained dynamics, the Hamiltonian formulation of regular higher order Lagrangians is developed. The conventional description of such systems due to Ostrogradsky is recovered. However, unlike the latter, the…
The Hamiltonian formulation of Mimetic Gravity is formulated. Although there are two more equations than those of general relativity, these are proved to be the constraint equation and the conservation of energy-momentum tensor. The Poisson…