27,161 research outputs found
Quantum Spectra of Triangular Billiards on the Sphere
We study the quantal energy spectrum of triangular billiards on a spherical
surface. Group theory yields analytical results for tiling billiards while the
generic case is treated numerically. We find that the statistical properties of
the spectra do not follow the standard random matrix results and their peculiar
behaviour can be related to the corresponding classical phase space structure.Comment: 18 pages, 5 eps figure
Spectral fluctuations and 1/f noise in the order-chaos transition regime
Level fluctuations in quantum system have been used to characterize quantum
chaos using random matrix models. Recently time series methods were used to
relate level fluctuations to the classical dynamics in the regular and chaotic
limit. In this we show that the spectrum of the system undergoing order to
chaos transition displays a characteristic noise and is
correlated with the classical chaos in the system. We demonstrate this using a
smooth potential and a time-dependent system modeled by Gaussian and circular
ensembles respectively of random matrix theory. We show the effect of short
periodic orbits on these fluctuation measures.Comment: 4 pages, 5 figures. Modified version. To appear in Phys. Rev. Let
An analysis of the transient behavior of infiltrated tungsten composites including the effect of the melt layer Final report
Transient one dimensional heat transfer analysis of infiltrated tungsten composite
Nodal domain distributions for quantum maps
The statistics of the nodal lines and nodal domains of the eigenfunctions of
quantum billiards have recently been observed to be fingerprints of the
chaoticity of the underlying classical motion by Blum et al. (Phys. Rev. Lett.,
Vol. 88 (2002), 114101) and by Bogomolny and Schmit (Phys. Rev. Lett., Vol. 88
(2002), 114102). These statistics were shown to be computable from the random
wave model of the eigenfunctions. We here study the analogous problem for
chaotic maps whose phase space is the two-torus. We show that the distributions
of the numbers of nodal points and nodal domains of the eigenvectors of the
corresponding quantum maps can be computed straightforwardly and exactly using
random matrix theory. We compare the predictions with the results of numerical
computations involving quantum perturbed cat maps.Comment: 7 pages, 2 figures. Second version: minor correction
Nonclassical Degrees of Freedom in the Riemann Hamiltonian
The Hilbert-Polya conjecture states that the imaginary parts of the zeros of
the Riemann zeta function are eigenvalues of a quantum hamiltonian. If so,
conjectures by Katz and Sarnak put this hamiltonian in Altland and Zirnbauer's
universality class C. This implies that the system must have a nonclassical
two-valued degree of freedom. In such a system, the dominant primitive periodic
orbits contribute to the density of states with a phase factor of -1. This
resolves a previously mysterious sign problem with the oscillatory
contributions to the density of the Riemann zeros.Comment: 4 pages, no figures; v3-6 have minor corrections to v2, v2 has a more
complete solution of the sign problem than v
The Edge of Quantum Chaos
We identify a border between regular and chaotic quantum dynamics. The border
is characterized by a power law decrease in the overlap between a state evolved
under chaotic dynamics and the same state evolved under a slightly perturbed
dynamics. For example, the overlap decay for the quantum kicked top is well
fitted with (with the nonextensive entropic
index and depending on perturbation strength) in the region
preceding the emergence of quantum interference effects. This region
corresponds to the edge of chaos for the classical map from which the quantum
chaotic dynamics is derived.Comment: 4 pages, 4 figures, revised version in press PR
Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
The intrinsic anomalous Hall effect in metallic ferromagnets is shown to be
controlled by Berry phases accumulated by adiabatic motion of quasiparticles on
the Fermi surface, and is purely a Fermi-liquid property, not a ``bulk'' Fermi
sea property like Landau diamagnetism, as has been previously supposed. Berry
phases are a new topological ingredient that must be added to Landau
Fermi-liquid theory in the presence of broken inversion or time-reversal
symmetry.Comment: 4 pages, 0 figures; to appear in Physical Review Letters; cleaner
form of main formula+note added confirming continued validity of result in
interacting Fermi liquids: + improved summary paragraph stating result; final
published version (minor changes
Fluctuations of wave functions about their classical average
Quantum-classical correspondence for the average shape of eigenfunctions and
the local spectral density of states are well-known facts. In this paper, the
fluctuations that quantum mechanical wave functions present around the
classical value are discussed. A simple random matrix model leads to a Gaussian
distribution of the amplitudes. We compare this prediction with numerical
calculations in chaotic models of coupled quartic oscillators. The expectation
is broadly confirmed, but deviations due to scars are observed.Comment: 9 pages, 6 figures. Sent to J. Phys.
Separating the regular and irregular energy levels and their statistics in Hamiltonian system with mixed classical dynamics
We look at the high-lying eigenstates (from the 10,001st to the 13,000th) in
the Robnik billiard (defined as a quadratic conformal map of the unit disk)
with the shape parameter . All the 3,000 eigenstates have been
numerically calculated and examined in the configuration space and in the phase
space which - in comparison with the classical phase space - enabled a clear
cut classification of energy levels into regular and irregular. This is the
first successful separation of energy levels based on purely dynamical rather
than special geometrical symmetry properties. We calculate the fractional
measure of regular levels as which is in remarkable
agreement with the classical estimate . This finding
confirms the Percival's (1973) classification scheme, the assumption in
Berry-Robnik (1984) theory and the rigorous result by Lazutkin (1981,1991). The
regular levels obey the Poissonian statistics quite well whereas the irregular
sequence exhibits the fractional power law level repulsion and globally
Brody-like statistics with . This is due to the strong
localization of irregular eigenstates in the classically chaotic regions.
Therefore in the entire spectrum we see that the Berry-Robnik regime is not yet
fully established so that the level spacing distribution is correctly captured
by the Berry-Robnik-Brody distribution (Prosen and Robnik 1994).Comment: 20 pages, file in plain LaTeX, 7 figures upon request submitted to J.
Phys. A. Math. Gen. in December 199
Persistent Currents in Quantum Chaotic Systems
The persistent current of ballistic chaotic billiards is considered with the
help of the Gutzwiller trace formula. We derive the semiclassical formula of a
typical persistent current for a single billiard and an average
persistent current for an ensemble of billiards at finite temperature.
These formulas are used to show that the persistent current for chaotic
billiards is much smaller than that for integrable ones. The persistent
currents in the ballistic regime therefore become an experimental tool to
search for the quantum signature of classical chaotic and regular dynamics.Comment: 4 pages (RevTex), to appear in Phys. Rev. B, No.59, 12256-12259
(1999
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