2005/09/08 by Falk Bruckmann, Ernst-Michael Ilgenfritz · 2 citations
Mathematics · Physics and Astronomy · #Boundary value problem #Cold Atom Physics and Bose-Einstein Condensates #Eigenvalues and eigenvectors #Gauge theory #Laplace operator #Laplace transform #Lattice (music) #Mathematical analysis #Mathematics #Operator (biology) #Physics #Physics of Superconductivity and Magnetism #Quantum electrodynamics #Quantum mechanics #Quantum, superfluid, helium dynamics #Statistical physics #hep-lat #hep-th
paper · pdf · doi:10.1103/physrevd.72.114502
published as Phys.Rev. D72 (2005) 114502 · 43 pages, 26 figures
arxiv created 2005/09/08 · openalex publication_date 2005/12/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that low-lying eigenmodes of the Laplace operator are suitable to represent properties of the underlying SU(2) lattice configurations. We study this for the case of finite temperature background fields, yet in the confinement phase. For calorons as classical solutions put on the lattice, the lowest mode localizes one of the constituent monopoles by a maximum and the other one by a minimum, respectively. We introduce adjustable phase boundary conditions in the time direction, under which the role of the monopoles in the mode localization is interchanged. Similar hopping phenomena are observed for thermalized configurations. We also investigate periodic and antiperiodic modes of the adjoint Laplacian for comparison. In the second part we introduce a new Fourier-like low-pass filter method. It provides link variables by truncating a sum involving the Laplacian eigenmodes. The filter not only reproduces classical structures, but also preserves the confining potential for thermalized ensembles. We give a first characterization of the structures emerging from this procedure.