General bounds on the Wilson-Dirac operator

Abstract

Lower bounds on the magnitude of the spectrum of the Hermitian Wilson-Dirac operator H(m) have previously been derived for 0<m<2 when the lattice gauge field satisfies a certain smoothness condition. In this paper lower bounds are derived for 2p-2<m<2p for general p=1,2,...,d where d is the spacetime dimension. The bounds can alternatively be viewed as localisation bounds on the real spectrum of the usual Wilson-Dirac operator. They are needed for the rigorous evaluation of the classical continuum limit of the axial anomaly and index of the overlap Dirac operator at general values of m, and provide information on the topological phase structure of overlap fermions. They are also useful for understanding the instanton size-dependence of the real spectrum of the Wilson-Dirac operator in an instanton background.Comment: 26 pages, 2 figures. v3: Completely rewritten with new material and new title; to appear in Phys.Rev.

Effects of serum, enzyme, thiol, and forced degradation on the stabilities of αO‐Conotoxin GeXIVA[1,2] and GeXIVA [1,4]

“…According to the relevant guidelines issued by International Conference on Harmonization (ICH) Q1A (R2), [14] forced degradations (stress testing) on GeXIVA [1,2] and GeXIVA [1,4] were carried out under acidic, alkaline, oxidative, photolytic, thermal, pH, and freeze-thaw conditions ( Table 1). At least three repetitions were prepared for each stress conditions.…”

Filtered overlap: speedup, locality, kernel non-normality andZAsimeq 1

“…Though quantitatively unsuccessful, this connection still gives a qualitative hint that the overlap operator with a filtered Wilson kernel might enjoy better localization properties due to the reduced condition number of H W . There are more detailed bounds in the literature [30,31,32,33,34], but it seems fair to say that a quantitative understanding of the localization of D ov in terms of the spectral properties of H W is a challenge. The localization ν as a function of the projection parameter ρ is presented in Fig.…”

Rooting issue for a lattice fermion formulation similar to staggered fermions but without taste mixing

“…where the last equality follows from λ λ(0) |λ(0)| = 1, a consequence of the known fact that T r H(0) |H(0)| = 0; see, e.g., [34]. On the other hand, the eigenvalues λ low (m) do cross zero in the small positive m region.…”

“…An upper bound can be analytically derived when the plaquette variables satisfy a bound ||1 − U µν − 1|| < ǫ [32,33]. More generally, a bound constraining the real eigenvalues to lie in neighborhoods of 0, 2/a, 4/a, 6/a, 8/a can be derived in this case [34].…”

“…In sufficiently smooth gauge backgrounds where the Index Theorem relation between chirality of would-be zero-modes and topological charge holds, it is known that for each would-be chiral zero-mode of the Wilson-Dirac operator there are 15 "doubler" modes [27,34]. …”