18,316 research outputs found
Generalized Gradient Flow Equation and Its Application to Super Yang-Mills Theory
We generalize the gradient flow equation for field theories with nonlinearly
realized symmetry. Applying the formalism to super Yang-Mills theory, we
construct a supersymmetric extension of the gradient flow equation. It can be
shown that the super gauge symmetry is preserved in the gradient flow.
Furthermore, choosing an appropriate modification term to damp the gauge
degrees of freedom, we obtain a gradient flow equation which is closed within
the Wess-Zumino gauge.Comment: 35 pages, v2: typos corrected and references added, v3: published
versio
Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1D
We prove the equivalence between the notion of Wasserstein gradient flow for
a one-dimensional nonlocal transport PDE with attractive/repulsive Newtonian
potential on one side, and the notion of entropy solution of a Burgers-type
scalar conservation law on the other. The solution of the former is obtained by
spatially differentiating the solution of the latter. The proof uses an
intermediate step, namely the gradient flow of the pseudo-inverse
distribution function of the gradient flow solution. We use this equivalence to
provide a rigorous particle-system approximation to the Wasserstein gradient
flow, avoiding the regularization effect due to the singularity in the
repulsive kernel. The abstract particle method relies on the so-called
wave-front-tracking algorithm for scalar conservation laws. Finally, we provide
a characterization of the sub-differential of the functional involved in the
Wasserstein gradient flow
Topological Susceptibility under Gradient Flow
We study the impact of the Gradient Flow on the topology in various models of
lattice field theory. The topological susceptibility is measured
directly, and by the slab method, which is based on the topological content of
sub-volumes ("slabs") and estimates even when the system remains
trapped in a fixed topological sector. The results obtained by both methods are
essentially consistent, but the impact of the Gradient Flow on the
characteristic quantity of the slab method seems to be different in 2-flavour
QCD and in the 2d O(3) model. In the latter model, we further address the
question whether or not the Gradient Flow leads to a finite continuum limit of
the topological susceptibility (rescaled by the correlation length squared,
). This ongoing study is based on direct measurements of in lattices, at .Comment: 8 pages, LaTex, 5 figures, talk presented at the 35th International
Symposium on Lattice Field Theory, June 18-24, 2017, Granada, Spai
A compactness result for non-local unregularized gradient flow lines
We prove an abstract compactness result for gradient flow lines of a
non-local unregularized gradient flow equation on a scale Hilbert space. This
is the first step towards Floer theory on scale Hilbert spaces.Comment: 27 page
Gradient flows as a selection procedure for equilibria of nonconvex energies
For atomistic material models, global minimization gives the wrong qualitative behavior; a theory of equilibrium solutions needs to be defined in different terms. In this paper, a concept based on gradient flow evolutions, to describe local minimization for simple atomistic models based on the Lennard–Jones potential, is presented. As an application of this technique, it is shown that an atomistic gradient flow evolution converges to a gradient flow of a continuum energy as the spacing between the atoms tends to zero. In addition, the convergence of the resulting equilibria is investigated in the case of elastic deformation and a simple damaged state
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