3,585 research outputs found
Two-flavor lattice QCD in the epsilon-regime and chiral Random Matrix Theory
The low-lying eigenvalue spectrum of the QCD Dirac operator in the
epsilon-regime is expected to match with that of chiral Random Matrix Theory
(ChRMT). We study this correspondence for the case including sea quarks by
performing two-flavor QCD simulations on the lattice. Using the overlap fermion
formulation, which preserves exact chiral symmetry at finite lattice spacings,
we push the sea quark mass down to \sim 3 MeV on a 16^3\times 32 lattice at a
lattice spacing a \simeq 0.11 fm. We compare the low-lying eigenvalue
distributions and find a good agreement with the analytical predictions of
ChRMT. By matching the lowest-lying eigenvalue we extract the chiral
condensate, \Sigma(2 GeV)[MSbar] = [251(7)(11) MeV]^3, where errors represent
statistical and higher order effects in the epsilon expansion. We also
calculate the eigenvalue distributions on the lattices with heavier sea quarks
at two lattice spacings. Although the epsilon expansion is not applied for
those sea quarks, we find a reasonable agreement of the Dirac operator spectrum
with ChRMT. The value of Sigma, after extrapolating to the chiral limit, is
consistent with the estimate in the epsilon-regime.Comment: 28pages, 12figures, accepted versio
Quantum Graphs: A simple model for Chaotic Scattering
We connect quantum graphs with infinite leads, and turn them to scattering
systems. We show that they display all the features which characterize quantum
scattering systems with an underlying classical chaotic dynamics: typical
poles, delay time and conductance distributions, Ericson fluctuations, and when
considered statistically, the ensemble of scattering matrices reproduce quite
well the predictions of appropriately defined Random Matrix ensembles. The
underlying classical dynamics can be defined, and it provides important
parameters which are needed for the quantum theory. In particular, we derive
exact expressions for the scattering matrix, and an exact trace formula for the
density of resonances, in terms of classical orbits, analogous to the
semiclassical theory of chaotic scattering. We use this in order to investigate
the origin of the connection between Random Matrix Theory and the underlying
classical chaotic dynamics. Being an exact theory, and due to its relative
simplicity, it offers new insights into this problem which is at the fore-front
of the research in chaotic scattering and related fields.Comment: 28 pages, 13 figures, submitted to J. Phys. A Special Issue -- Random
Matrix Theor
The fractality of the relaxation modes in deterministic reaction-diffusion systems
In chaotic reaction-diffusion systems with two degrees of freedom, the modes
governing the exponential relaxation to the thermodynamic equilibrium present a
fractal structure which can be characterized by a Hausdorff dimension. For long
wavelength modes, this dimension is related to the Lyapunov exponent and to a
reactive diffusion coefficient. This relationship is tested numerically on a
reactive multibaker model and on a two-dimensional periodic reactive Lorentz
gas. The agreement with the theory is excellent
Semiclassical Accuracy in Phase Space for Regular and Chaotic Dynamics
A phase-space semiclassical approximation valid to at short times
is used to compare semiclassical accuracy for long-time and stationary
observables in chaotic, stable, and mixed systems. Given the same level of
semiclassical accuracy for the short time behavior, the squared semiclassical
error in the chaotic system grows linearly in time, in contrast with quadratic
growth in the classically stable system. In the chaotic system, the relative
squared error at the Heisenberg time scales linearly with ,
allowing for unambiguous semiclassical determination of the eigenvalues and
wave functions in the high-energy limit, while in the stable case the
eigenvalue error always remains of the order of a mean level spacing. For a
mixed classical phase space, eigenvalues associated with the chaotic sea can be
semiclassically computed with greater accuracy than the ones associated with
stable islands.Comment: 9 pages, 6 figures; to appear in Physical Review
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