Related papers: Poisson to Random Matrix Transition in the QCD Dir…
We study the statistics of the local resolvent and non-ergodic properties of eigenvectors for a generalised Rosenzweig-Porter $N\times N$ random matrix model, undergoing two transitions separated by a delocalised non-ergodic phase.…
We examine the eigenvalues and eigenvectors of the staggered Dirac operator on thermal ensembles created in QCD with two flavours of staggered quarks. We see that across the phase transition a gap opens in the spectrum. For finite volume…
In this paper I will describe some results that have been recently obtained in the study of random Euclidean matrices, i.e. matrices that are functions of random points in Euclidean space. In the case of {\sl translation invariant} matrices…
We study the local eigenvalue statistics (LES) associated with one-dimensional lattice models of random polymers. We consider models constructed from two polymers. Each polymer is a finite interval of lattice points with a finite potential.…
The single-parameter scaling hypothesis predicts the absence of delocalized states for noninteracting quasiparticles in low-dimensional disordered systems. We show analytically and numerically that extended states may occur in the one- and…
We study QCD at finite density and low temperature by using the complex Langevin method. We employ the gauge cooling to control the unitarity norm and introduce a deformation parameter in the Dirac operator to avoid the singular-drift…
We discuss the construction and properties of an approximate solution of the Ginsparg-Wilson equation, the so-called chirally improved lattice Dirac operator. In particular we study the behavior of its eigenmodes in smooth instanton…
System of Dirac fermions with random-varying mass is studied in detail. We reformulate the system by transfer-matrix formalism. Eigenvalues and wave functions are obtained numerically for various configurations of random telegraphic mass…
Common belief, confirmed by existing experiments, is that arbitrarily weak disorder should lead to spatial localization of eigenmodes of scalar wave equations when wave propagation is two-dimensional (2D). We predict that contrary to this…
We study the hopping transport of a quantum particle through randomly diluted percolation clusters in two dimensions realized both on the square and triangular lattices. We investigate the nature of localization of the particle by…
One dimensional system of Dirac fermions with a random-varying mass is studied by the transfer-matrix methods which we developed recently. We investigate the effects of nonlocal correlation of the spatial-varying Dirac mass on the…
Across the finite temperature transition to the quark-gluon plasma, the QCD topological susceptibility decreases sharply. Thus in the high temperature phase the remaining topological objects (possibly calorons) form a weakly interacting…
The lattice QCD results for the temperature-dependent magnetic susceptibility of the medium below the cross-over temperature are not possible to reconcile with the widely used Hadron Resonance Gas model, also amended with the physical…
We study a random Schroedinger operator, the Laplacian with random Dirac delta potentials on a torus T^d_L = R^d/LZ^d, in the thermodynamic limit L\to\infty, for dimension d=2. The potentials are located on a randomly distorted lattice…
We study the phase transition of random radii Poisson Boolean percolation: Around each point of a planar Poisson point process, we draw a disc of random radius, independently for each point. The behavior of this process is well understood…
We investigate and clarify the role of topology and the issues surrounding the epsilon regime for staggered quarks. We study unimproved and improved staggered quark Dirac operators on quenched lattice QCD gluon backgrounds generated using a…
I propose a simple model of the distribution of the small eigenvalues of the QCD Dirac operator well above the finite temperature phase transition where chiral symmetry is restored and the spectral density at zero vanishes. Assuming the…
The random-dimer model is probably the most popular model for a one-dimensional disordered system where correlations are responsible for delocalization of the wave functions. This is the primary model used to justify the insulator-metal…
We study the global symmetries of naive lattices Dirac operators in QCD-like theories in any dimension larger than two. In particular we investigate how the chosen number of lattice sites in each direction affects the global symmetries of…
The finite temperature phase diagram of QCD with two massless quark flavors is not yet understood because of the subtle effects of anomalous $U_A(1)$ symmetry. In this work we address this issue by studying the fate of the anomalous…