Related papers: Spectral Flow and Index Theorem for Staggered Ferm…
We present results of the eigenvalue spectrum for the staggered Dir\"ac operator obtained using a modified Lanczos algorithm. We identify zero modes and non-zero modes. We derive the chiral Ward identity derived from the conserved $U(1)_A$…
The spectral flow is a classical notion of functional analysis and differential geometry which was given different interpretations as Fredholm index, Witten index, and Maslov index. The classical theory treats spectral flow outside the…
One may trace the idea that spectral flow should be given as the integral of a one form back to the 1974 Vancouver ICM address of I.M. Singer. Our main theorem gives analytic formulae for the spectral flow along a norm differentiable path…
Over three decades ago the advection-diffusion equation for a steady fluid velocity field was homogenized, leading to a Stieltjes integral representation for the effective diffusivity, which is given in terms of a spectral measure of a…
Using mean field theory and a mesoscale elastoplastic model, we analyze the steady state shear rheology of thermally activated amorphous solids. At sufficiently high temperature and driving rates, flow is continuous and described by…
We give a definition of the spectral flow for continuous paths in the space of bounded and essentially hyperbolic operators. We provide a homotopical characterization of the spectral flow in terms of a group homomorphism of the fundamental…
Staggered fermion shift symmetries correspond to translations of the fermion field within the unit cell of a hypercubic lattice. They satisfy an algebra and in four Euclidean dimensions can be related to a discrete subgroup of an $SU(4)$…
We give a comprehensive account of an analytic approach to spectral flow along paths of self-adjoint Breuer-Fredholm operators in a type $I_{\infty}$ or $II_\infty$ von Neumann algebra ${\mathcal N}$. The framework is that of {\it odd…
We study the chirality of staggered quarks on the Dirac eigenvalue spectrum using deep learning (DL) techniques. The Kluberg-Stern method to construct staggered bilinear operators conserves continuum property such as recursion relations,…
Discretizing the Dirac equation on a uniform grid with the central difference formula often generates spurious states. We propose a staggered-grid scheme in the framework of the finite-difference method that suppresses these spurious states…
Smearing the gauge links of dynamical configurations removes small scale unphysical vacuum fluctuations and thus improves the chiral properties of lattice fermions. Recently we proposed the hypercubic smearing (HYP) that improves the flavor…
As shown in earlier work, skew-adjoint linear differential operators, mapping efforts into flows, give rise to Dirac structures on a bounded spatial domain by a proper definition of boundary variables. In the present paper this is extended…
The classical problem of steady streaming induced by an oscillating object has been studied extensively, but prior work has focused almost exclusively on single-frequency oscillations, which result in symmetric, quadrupole-like flows. Here…
The discrete Lax operators with the spectral parameter on an algebraic curve are defined. A hierarchy of commuting flows on the space of such operators is constructed. It is shown that these flows are linearized by the spectral transform…
We report on numerical experiments using deflation to compute quark propagators for the highly improved staggered quark (HISQ) action. The method is tested on HISQ gauge configurations, generated by the MILC collaboration, with lattice…
In this paper, we present an improvement of a method for computing scattering amplitudes that include external (polarized) fermions with the following features: the formulas are quite general and work for different kinematic configurations…
We generalize the theory of flow equations to open quantum systems focusing on Lindblad master equations. We introduce and discuss three different generators of the flow that transform a linear non-Hermitian operator into a diagonal one. We…
The application of Random Matrix Theory to the Dirac operator of QCD yields predictions for the probability distributions of the lowest eigenvalues. We measured Dirac operator spectra using massless overlap fermions in quenched QCD at…
Inferring physical parameters of turbulent flows by assimilation of data measurements is an open challenge with key applications in meteorology, climate modeling and astrophysics. Up to now, spectral nudging was applied for empirical…
We study the instability of the spectrum for a class of non-selfadjoint anharmonic oscillators, estimating the behavior of the instability indices (i. e. the norm of spectral projections) associated with the large eigenvalues of these…