More evidence of localization in the low-lying Dirac spectrum

We have extended our computation of the inverse participation ratio of low-lying (asqtad) Dirac eigenvectors in quenched SU(3). The scaling dimension of the confining manifold is clearer and very near 3. We have also computed the 2-point correlator which further characterizes the localization.Comment: presented at Lattice2005(Topology and Confinement), Dublin, July 25-30, 2005, 6 pages, 3 figures, to appear in Proceedings of Scienc

The scaling dimension of low lying Dirac eigenmodes and of the topological charge density

As a quantitative measure of localization, the inverse participation ratio of low lying Dirac eigenmodes and topological charge density is calculated on quenched lattices over a wide range of lattice spacings and volumes. Since different topological objects (instantons, vortices, monopoles, and artifacts) have different co-dimension, scaling analysis provides information on the amount of each present and their correlation with the localization of low lying eigenmodes.Comment: Lattice2004(topology), Fermilab, June 21 - 26, 2004; 3 pages, 3 figure

Moments of nucleon spin-dependent generalized parton distributions

We present a lattice measurement of the first two moments of the spin-dependent GPD H-tilde(x,xi,t). From these we obtain the axial coupling constant and the second moment of the spin-dependent forward parton distribution. The measurements are done in full QCD using Wilson fermions. In addition, we also present results from a first exploratory study of full QCD using Asqtad sea and domain-wall valence fermions.Comment: Lattice2003(Theory), 3 pages, 3 figures, to appear in the Proceedings of Lattice 200

On the glueball spectrum in O(a)-improved lattice QCD

We calculate the light `glueball' mass spectrum in N_f=2 lattice QCD using a fermion action that is non-perturbatively O(a) improved. We work at lattice spacings a ~0.1 fm and with quark masses that range down to about half the strange quark mass. We find the statistical errors to be moderate and under control on relatively small ensembles. We compare our mass spectrum to that of quenched QCD at the same value of a. Whilst the tensor mass is the same (within errors), the scalar mass is significantly smaller in the dynamical lattice theory, by a factor of ~(0.84 +/- 0.03). We discuss what the observed m_q dependence of this suppression tells us about the dynamics of glueballs in QCD. We also calculate the masses of flux tubes that wind around the spatial torus, and extract the string tension from these. As we decrease the quark mass we see a small but growing vacuum expectation value for the corresponding flux tube operators. This provides clear evidence for `string breaking' and for the (expected) breaking of the associated gauge centre symmetry by sea quarks.Comment: 33pp LaTeX. Version to appear in Phys. Rev.

Heavy Quark Potentials in Quenched QCD at High Temperature

Heavy quark potentials are investigated at high temperatures. The temperature range covered by the analysis extends from $T$ values just below the deconfinement temperature up to about $4 T_c$ in the deconfined phase. We simulated the pure gauge sector of QCD on lattices with temporal extents of 4, 6 and 8 with spatial volumes of $32^3$. On the smallest lattice a tree level improved action was employed while in the other two cases the standard Wilson action was used. Below $T_c$ we find a temperature dependent logarithmic term contributing to the confinement potential and observe a string tension which decreases with rising temperature but retains a finite value at the deconfinement transition. Above $T_c$ the potential is Debye-screened, however simple perturbative predictions do not apply.Comment: 20 pages, 9 figure

Decoherence as Decay of the Loschmidt Echo in a Lorentz Gas

Classical chaotic dynamics is characterized by the exponential sensitivity to initial conditions. Quantum mechanics, however, does not show this feature. We consider instead the sensitivity of quantum evolution to perturbations in the Hamiltonian. This is observed as an atenuation of the Loschmidt Echo, $M(t)$, i.e. the amount of the original state (wave packet of width $\sigma$) which is recovered after a time reversed evolution, in presence of a classically weak perturbation. By considering a Lorentz gas of size $L$, which for large $L$ is a model for an {\it unbounded} classically chaotic system, we find numerical evidence that, if the perturbation is within a certain range, $M(t)$ decays exponentially with a rate $1/\tau_{\phi}$ determined by the Lyapunov exponent $\lambda$ of the corresponding classical dynamics. This exponential decay extends much beyond the Eherenfest time $t_{E}$ and saturates at a time $t_{s}\simeq \lambda^{-1}\ln (\widetilde{N})$, where $\widetilde{N}\simeq (L/\sigma)^2$ is the effective dimensionality of the Hilbert space. Since $\tau _{\phi}$ quantifies the increasing uncontrollability of the quantum phase (decoherence) its characterization and control has fundamental interest.Comment: 3 ps figures, uses Revtex and epsfig. Major revision to the text, now including discussion and references on averaging and Ehrenfest time. Figures 2 and 3 content and order change

Universality of the Lyapunov regime for the Loschmidt echo

The Loschmidt echo (LE) is a magnitude that measures the sensitivity of quantum dynamics to perturbations in the Hamiltonian. For a certain regime of the parameters, the LE decays exponentially with a rate given by the Lyapunov exponent of the underlying classically chaotic system. We develop a semiclassical theory, supported by numerical results in a Lorentz gas model, which allows us to establish and characterize the universality of this Lyapunov regime. In particular, the universality is evidenced by the semiclassical limit of the Fermi wavelength going to zero, the behavior for times longer than Ehrenfest time, the insensitivity with respect to the form of the perturbation and the behavior of individual (non-averaged) initial conditions. Finally, by elaborating a semiclassical approximation to the Wigner function, we are able to distinguish between classical and quantum origin for the different terms of the LE. This approach renders an understanding for the persistence of the Lyapunov regime after the Ehrenfest time, as well as a reinterpretation of our results in terms of the quantum--classical transition.Comment: 33 pages, 17 figures, uses Revtex

Wave Function Structure in Two-Body Random Matrix Ensembles

We study the structure of eigenstates in two-body interaction random matrix ensembles and find significant deviations from random matrix theory expectations. The deviations are most prominent in the tails of the spectral density and indicate localization of the eigenstates in Fock space. Using ideas related to scar theory we derive an analytical formula that relates fluctuations in wave function intensities to fluctuations of the two-body interaction matrix elements. Numerical results for many-body fermion systems agree well with the theoretical predictions.Comment: 4 pages, 2 figure