Related papers: The Consequences of Non-Normality
The QCD partition function for the Wilson Dirac operator, $D_W$, at nonzero lattice spacing $a$ can be expressed in terms of a chiral Lagrangian as a systematic expansion in the quark mass, the momentum and $a^2$. Starting from this chiral…
We derive the distributions of individual eigenvalues for the Hermitian Wilson Dirac Operator D5 as well as for real eigenvalues of the Wilson Dirac Operator DW. The framework we provide is valid in the epsilon regime of chiral perturbation…
Random Matrix Theory has been successfully applied to lattice Quantum Chromodynamics. In particular, a great deal of progress has been made on the understanding, numerically as well as analytically, of the spectral properties of the Wilson…
The truncated Hilbert transform with overlap $H_T$ is an operator that arises in tomographic reconstruction from limited data, more precisely in the method of Differentiated Back-Projection (DBP). Recent work [1] has shown that the singular…
In this survey we gather recent results on Dirac operators coupled with $\delta$-shell interactions. We start by discussing recent advances regarding the question of self-adjointness for these operators. Afterward we switch to an…
We use a continued fraction expansion of the sign-function in order to obtain a five dimensional formulation of the overlap lattice Dirac operator. Within this formulation the inverse of the overlap operator can be calculated by a single…
We study the influence of a strong imaginary vector potential on the quantum mechanics of particles confined to a two-dimensional plane and propagating in a random impurity potential. We show that the wavefunctions of the non-Hermitian…
Our aim is to compute the lower moments of the unpolarized and polarized deep-inelastic structure functions of the nucleon on the lattice. The theoretical basis of the calculation is the operator product expansion. To construct operators…
The Ginsparg-Wilson (GW) relation elegantly captures how the anomalous chiral symmetry of a Dirac fermion manifests on the lattice. In this talk, we discuss how the GW relation and its closed-form solution, the overlap operator, can be…
We present the first numerical implementation of a non-perturbative renormalization method for lattice operators, based on the study of correlation functions in coordinate space at short Euclidean distance. The method is applied to compute…
Recently, Kalkreuter obtained complete Dirac spectra for $SU(2)$ lattice gauge theory both for staggered fermions and for Wilson fermions. The lattice size was as large as $12^4$. We performed a statistical analysis of these data and found…
We note that Fujikawa's proposal of generalization of the Ginsparg-Wilson relation is equivalent to setting $R = (a \gamma_5 D)^{2k}$ in the original Ginsparg-Wilson relation $D \gamma_5 + \gamma_5 D = 2 a D R \gamma_5 D$. An explicit…
We generalize the vertex expansion approach of the functional renormalization group to non-Hermitian systems. As certain anomalous expectation values might not vanish, additional terms as compared to the Hermitian case can appear in the…
We derive the vector-like four dimensional overlap Dirac operator starting from a five dimensional Dirac action in the presence of a delta-function space-time defect. The effective operator is obtained by first integrating out all the…
The spectral analysis of a non-Hermitian unbounded operator appearing in quantum physics is our main concern. The properties of such an operator are essentially different from those of Hermitian Hamiltonians, namely due to spectral…
We provide a complete description of the Harnack part for normalized truncated shift of size five with numerical radius one. We prove that any operator in this Harnack component must assume one of two distinct forms: either it belongs to…
We consider a semi-classical Dirac operator in arbitrary spatial dimensions with a smooth potential whose partial derivatives of any order are bounded by suitable constants. We prove that the distribution kernel of the inverse operator…
Eigenvalues of the Hermitian Wilson-Dirac operator are of special interest in several lattice QCD simulations, e.g., for noise reduction when evaluating all-to-all propagators. In this paper we present a Davidson-type eigensolver that…
We study and simulate N=2 supersymmetric Wess-Zumino models in one and two dimensions. For any choice of the lattice derivative, the theories can be made manifestly supersymmetric by adding appropriate improvement terms corresponding to…
The microscopic spectral density of the Hermitian Wilson-Dirac operator is computed numerically in quenched lattice QCD. We demonstrate that the results given for fixed index of the Wilson-Dirac operator can be matched by the predictions…