The integrated density of states for the Wilson Dirac operator

DOI10.1515/ROSE-2012-0001zbMATH Open1276.81118arXiv1009.1949OpenAlexW2963666261MaRDI QIDQ4923230

Volker Bach, Carolin Kurig

Publication date: 6 June 2013

Published in: Random Operators and Stochastic Equations (Search for Journal in Brave)

Abstract: It is shown that gauge field-dependent fermion Dirac operators from lattice QCD form an ergodic operator family in the probabilistic sense, provided the gauge field is an ergodic random field. As a consequence, the integrated density of states of such Dirac operators in the thermodynamic limit exists and is almost surely independent of the chosen gauge field configuration.

Full work available at URL: https://arxiv.org/abs/1009.1949

zbMATH Keywords

random Schrödinger operatorsintegrated density of stateslattice QCD

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Random operators and equations (aspects of stochastic analysis) (60H25) Strong interaction, including quantum chromodynamics (81V05) Quantum field theory on lattices (81T25) PDEs with randomness, stochastic partial differential equations (35R60) Random linear operators (47B80)

Related Items (3)

A remark on the Dirichlet-Neumann decoupling and the integrated density of states ⋮ ON THE HIGH-ENERGY ASYMPTOTICS OF THE INTEGRATED DENSITY OF STATES ⋮ Integration of coupling Dirac structures

Recommendations

• Individual eigenvalue distributions for the Wilson Dirac operator 👍 👎
• The integrated density of states for an interacting multiparticle homogeneous model and applications to the Anderson model 👍 👎
• The integrated density of states for magnetic Schrödinger operators 👍 👎
• Fine properties of the integrated density of states and a quantitative separation property of the Dirichlet eigenvalues 👍 👎
• Integrated density of states for the periodic Schrödinger operator in dimension two 👍 👎
• Spectral properties of the Wilson Dirac operator in the \(\epsilon\)-regime 👍 👎
• Integrated density of states: From the finite range to the periodic Airy–Schrödinger operator 👍 👎
• ON THE HIGH-ENERGY ASYMPTOTICS OF THE INTEGRATED DENSITY OF STATES 👍 👎
• A remark on the Dirichlet-Neumann decoupling and the integrated density of states 👍 👎
• Dirac operator spectral density and low energy sum rules 👍 👎

This page was built for publication: The integrated density of states for the Wilson Dirac operator

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q4923230)