Critical bending point in the Lyapunov localization spectra of many-particle systems

The localization spectra of Lyapunov vectors in many-particle systems at low density exhibit a characteristic bending behavior. It is shown that this behavior is due to a restriction on the maximum number of the most localized Lyapunov vectors determined by the system configuration and mutual orthogonality. For a quasi-one-dimensional system this leads to a predicted bending point at n_c \approx 0.432 N for an N particle system. Numerical evidence is presented that confirms this predicted bending point as a function of the number of particles N.Comment: 4 pages, 4 figure

Schroedinger functional formalism with domain-wall fermion

Finite volume renormalization scheme is one of the most fascinating scheme for non-perturbative renormalization on lattice. By using the step scaling function one can follow running of renormalized quantities with reasonable cost. It has been established the Schroedinger functional is very convenient to define a field theory in a finite volume for the renormalization scheme. The Schroedinger functional, which is characterized by a Dirichlet boundary condition in temporal direction, is well defined and works well for the Yang-Mills theory and QCD with the Wilson fermion. However one easily runs into difficulties if one sets the same sort of the Dirichlet boundary condition for the overlap Dirac operator or the domain-wall fermion. In this paper we propose an orbifolding projection procedure to impose the Schroedinger functional Dirichlet boundary condition on the domain-wall fermion.Comment: 32 page