In this lecture we argue that the fluctuations of Dirac eigenvalues on the finest scale, i.e. on the scale of the average level spacing do not depend on the underlying dynamics and can be obtained from a chiral random matrix theory with the same low energy effective theory. We present three pieces of evidence supporting that such microscopic correlations of lattice QCD Dirac spectra are given b...

The instantaneous amplitude (IA) based on the higher order differential energy operator is proposed. And its general form for arbitrary order is also proposed. The various definitions of the IA and the instantaneous frequency (IF) estimators are considered. The IA and IF estimators based on the energy operators need less computational cost than the conventional IF and IA estimators exploiting t...

We study the effect of a finite topology on the temperature correlations of the cosmic microwave background in a flat universe. Analytic expressions for the angular power spectrum are given for all possible finite flat models. We examine the angular correlation function itself, pointing out visible and discrete features that arise from topology. While observations of the power spectrum on large...

In the formulation of Banks, Peskin and Susskind, we show that one can construct evolution equations for the quantum mechanical density matrix ρ with operators which do not commute with hamiltonian which evolve pure states into mixed states, preserve the normalization and positivity of ρ and conserve energy. Furthermore, it seems to be different from a quantum mechanical system with random sour...

We show that the non-equilibrium steady state (NESS) of the free lattice Fermion model far from equilibrium is macroscopically unstable. The problem is translated to that of the spectral analysis of Liouville Operator. We use the method of positive commutators to investigate it. We construct a positive commutator on the lattice Fermion system, whose dispersion relation is ω(k) = cos k − γ.

Loop spaces LM of compact complex manifolds M promise to have rich analytic cohomology theories, and it is expected that sheaf and Dolbeault cohomology groups of LM will shed new light on the complex geometry and analysis of M itself. This idea first occurs in [W], in the context of the infinite dimensional Dirac operator, and then in [HBJ] that touches upon Dolbeault groups of loop spaces; but...

It has been proven experimentally, that a combination of textual and visual representations can improve the retrieval performance ([20], [23]). It is due to the fact, that the textual and visual feature spaces often represent complementary yet correlated aspects of the same image, thus forming a composite system. In this paper, we present a model for the combination of visual and textual sub-sy...

We prove the complete asymptotic expansion of the integrated density of states of a two-dimensional Schrödinger operator with a smooth periodic potential.

We present a generalized projection-based order-N method which is applicable within nonorthogonal basis sets of spatially localized orbitals. The projection to the occupied subspace of a Hamiltonian, performed by means of a Chebyshev-polynomial representation of the density operator, allows the nonvariational computation of band-structure energies, density matrices, and forces for systems with ...