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Related papers: Spectral Flow and Index Theorem for Staggered Ferm…

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We follow up on a suggestion by Adams and construct explicit domain wall fermion operators with staggered kernels. We compare different domain wall formulations, namely the standard construction as well as Borici's modified and Chiu's…

High Energy Physics - Lattice · Physics 2016-07-06 Christian Hoelbling , Christian Zielinski

We introduce the notion of spectral flow along a periodic semi-Riemannian geodesic, as a suitable substitute of the Morse index in the Riemannian case. We study the growth of the spectral flow along a closed geodesic under iteration,…

Differential Geometry · Mathematics 2007-11-06 Miguel Angel Javaloyes , Paolo Piccione

Measurements of the lowest-lying eigenvalues of the staggered fermion Dirac operator are made on ensembles of equilibrium gauge field configurations in quenched SU(3) lattice gauge theory. The results are compared with exact analytical…

High Energy Physics - Lattice · Physics 2009-10-31 P. H. Damgaard , U. M. Heller , A. Krasnitz

We prove a spectral flow formula for one-parameter families of Hamiltonian systems under homoclinic boundary conditions, which relates the spectral flow to the relative Maslov index of a pair of curves of Lagrangians induced by the stable…

Dynamical Systems · Mathematics 2017-05-17 Nils Waterstraat

We discuss possible definitions of discrete Dirac operators, and discuss their continuum limits. It is well-known in the lattice field theory that the straightforward discretization of the Dirac operator introduces unwanted spectral…

Mathematical Physics · Physics 2023-08-17 Shu Nakamura

We consider a Wilson-Dirac operator with improved chiral properties. We show that, for arbitrarily rough gauge fields, it satisfies the index theorem if we identify the zero modes with the small real eigenvalues of the fermion operator and…

High Energy Physics - Lattice · Physics 2009-10-31 P. Hernandez

The spectra of parallel flows (that is, flows governed by first-order differential operators parallel to one direction) are investigated, on both $L^2$ spaces and weighted-$L^2$ spaces. As a consequence, an example of a flow admitting a…

Spectral Theory · Mathematics 2013-10-29 Jonathan Ben-Artzi

We discuss the well known ``Fredholm index=spectral flow'' theorem and show that it can be interpreted as a limit case of an identity involving two spectral shift functions.

Spectral Theory · Mathematics 2007-11-02 Alexander Pushnitski

The spectral density of euclidean Dirac operator is investigated in partially quenched QCD with arbitrary quark masses. A representation of scalar and pseudoscalar correlators in terms of the spectral density is discussed. The spectral…

High Energy Physics - Phenomenology · Physics 2009-10-31 K. Zyablyuk

Due to their capability to reduce turbulent transport in magnetized plasmas, understanding the dynamics of zonal flows is an important problem in the fusion programme. Since the pioneering work by Rosenbluth and Hinton in axisymmetric…

Random matrix theory and chiral Lagrangians offer a convenient tool for the exact calculation of microscopic spectral correlators of the Dirac operator in a well-defined finite-volume scaling regime.

High Energy Physics - Lattice · Physics 2009-10-31 P. H. Damgaard

We compute, in topological terms, the spectral flow of an arbitrary family of self-adjoint Dirac type operators with classical (local) boundary conditions on a compact Riemannian manifold with boundary under the assumption that the initial…

Analysis of PDEs · Mathematics 2012-10-08 M. I. Katsnelson , V. E. Nazaikinskii

In this work we study the Dirac equation on the cosmic string background, which models a one--dimensional topological defect in the spacetime. We first define the Dirac operator in this setting, classifying all of its selfadjoint…

Analysis of PDEs · Mathematics 2025-01-22 Piero D'Ancona , Zhiqing Yin , Junyong Zhang

In this paper we propose Discretely Indexed flows (DIF) as a new tool for solving variational estimation problems. Roughly speaking, DIF are built as an extension of Normalizing Flows (NF), in which the deterministic transport becomes…

Machine Learning · Statistics 2022-04-05 Elouan Argouarc'h , François Desbouvries , Eric Barat , Eiji Kawasaki , Thomas Dautremer

We develop an index theory for variational problems on noncompact quantum graphs. The main results are a spectral flow formula, relating the net change of eigenvalues to the Maslov index of boundary data, and a Morse index theorem, equating…

Functional Analysis · Mathematics 2026-03-26 Daniele Garrisi , Alessandro Portaluri , Li Wu

Recently, properties of the fixed point action for fermion theories have been pointed out indicating realization of chiral symmetry on the lattice. We check these properties by numerical analysis of the spectrum of a parametrized fixed…

High Energy Physics - Lattice · Physics 2009-10-31 F. Farchioni , I. Hip , C. B. Lang , M. Wohlgenannt

We consider a gauge invariant one parameter family of families of fiberwise twisted Dirac type operators on a fiberation with the typical fiber an even dimensional compact manifold with boundary, i.e., a family $\{D_u\}, u\in [0,1]$ with…

Differential Geometry · Mathematics 2014-10-23 Jianqing Yu

We study topological aspects of a Dirac fermion coupled with a Higgs field associated with the lattice model introduced by Benalcazar et al. which shows the topological quadrupole phase. Using the index theorem, we show that the index of…

Mesoscale and Nanoscale Physics · Physics 2019-04-24 T. Fukui

Large ensembles of complete spectra of the Euclidean Dirac operator for staggered fermions are calculated for SU(2) lattice gauge theory. The accumulation of eigenvalues near zero is analyzed as a signal of chiral symmetry breaking and…

High Energy Physics - Lattice · Physics 2009-10-30 M. E. Berbenni-Bitsch , S. Meyer , A. Schäfer , J. J. M. Verbaarschot , T. Wettig

We consider incompressible flows between two transversely vibrating solid walls and construct an asymptotic expansion of solutions of the Navier-Stokes equations in the limit when both the amplitude of vibrations and the thickness of the…

Fluid Dynamics · Physics 2011-08-16 Konstantin Ilin , Andrey Morgulis