Related papers: Vertex functions and their flow equations from the…
We derive the vorticity equation for an incompressible fluid on a 2-dimensional surface with arbitrary topology embedded in 3-dimensional Euclidean space by using a tailored Clebsch parametrization of the flow. In the inviscid limit, we…
Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies…
An exact functional renormalization group flow equation is derived for the divergence functional which is a generalization of the Kullback-Leibler divergence to quantum field theories in the Euclidean domain. It compares distributions with…
We use the vorticity transportation equation as the start point--with the help of stream function for two-dimensional planar incompressible flows--to obtain exact solutions that characterize evolution and dynamics of the flows. These…
We propose to apply the two-particle irreducible (2PI) formalism to the problem of thermalization in heavy-ion collisions in the Color Glass Condensate (CGC) picture. We consider the 2PI effective action to three loops and derive a set of…
The Active Flux scheme is a Finite Volume scheme with additional point values distributed along the cell boundary. It is third order accurate and does not require a Riemann solver: the continuous reconstruction serves as initial data for…
For the O(N) field theory with lambda Phi^4 self-coupling, we construct the two-particle-irreducible (2PI), closed-time-path (CTP) effective action in a general curved spacetime. From this we derive a set of coupled equations for the mean…
This paper provides some first steps in developing empirical process theory for functions taking values in a vector space. Our main results provide bounds on the entropy of classes of smooth functions taking values in a Hilbert space, by…
We evaluate analytically some ground state properties of two-dimensional harmonically confined Fermi vapors with isotropy and for an arbitrary number of closed shells. We first derive a differential form of the virial theorem and an…
The use of the complex velocity potential and the complex velocity is widely disseminated in the study of two-dimensional incompressible potential flows. The advantages of working with complex analytical functions made this representation…
Non-perturbative renormalisation of a general class of scalar field theories is performed at the Hartree level truncation of the 2PI effective action in the broken symmetry regime. Renormalised equations are explicitly constructed for the…
At present in the fluid mechanics, mostly one like to use the vortex as a basic physical quantity, such that some exact solutions is based on the vorticity evolution equation. For the vortex flow problem with axisymmetry, it is well known…
We study geodesics flows on curved quantum Riemannian geometries using a recent formulation in terms of bimodule connections and completely positive maps. We complete this formalism with a canonical $*$ operation on noncommutative vector…
Multipoint vertex functions, and the four-point vertex in particular, are crucial ingredients in many-body theory. Recent years have seen significant algorithmic progress toward numerically computing their dependence on multiple frequency…
We give a coalgebra structure on 1-vertex irreducible graphs which is that of a cocommutative coassociative graded connected coalgebra. We generalize the coproduct to the algebraic representation of graphs so as to express a bare 1-particle…
We consider two-dimensional quantum gravity coupled to matter fields which are renormalizable, but not conformal invariant. Questions concerning the $\b$ function and the effective action are addressed, and the effective action and the…
It is well-known that the dynamics of vortices in an ideal incompressible two-dimensional fluid contained in a bounded not necessarily simply connected smooth domain is described by the Kirchhoff--Routh point vortex system. In this paper,…
We perform an analysis of a number of approximations and methods used in numerical simulations of real-time Kadanoff-Baym equations based on truncations of the 2PI effective action. We compare the loop expansion to the 1/N expansion and…
We present a method for reconstructing two-dimensional velocity fields at specified length scales using observational data from tracer particles in a flow, without the need for interpolation or smoothing. The algorithm, adapted from…
The flow equations of the renormalisation group permit to analyse the perturbative $n$-point functions of renormalisable quantum field theories. Rigorous bounds implying renormalisablility allow to control large momentum behaviour, infrared…