815 research outputs found
Eigenstate Structure in Graphs and Disordered Lattices
We study wave function structure for quantum graphs in the chaotic and
disordered regime, using measures such as the wave function intensity
distribution and the inverse participation ratio. The result is much less
ergodicity than expected from random matrix theory, even though the spectral
statistics are in agreement with random matrix predictions. Instead, analytical
calculations based on short-time semiclassical behavior correctly describe the
eigenstate structure.Comment: 4 pages, including 2 figure
Uncertainties on parton distribution functions from the ZEUS NLO QCD fit to data on deep inelastic scattering
An NLO QCD analysis of the ZEUS data on deep inelastic scattering
together with fixed-target data has been performed from which the gluon and
quark densities of the proton and the value of the strong coupling parameter,
, have been extracted. The study includes a full treatment of
the experimental systematic uncertainties, including point-to-point
correlations. Different ways of incorporating correlated systematic
uncertainties into the fit are discussed and compared.Comment: 8 pages, 1 figure. Invited talk at the Conference on Advanced
Statistical Techniques in Particle Physics, March 18-22 2002, Durham, U
Scattering theory on graphs (2): the Friedel sum rule
We consider the Friedel sum rule in the context of the scattering theory for
the Schr\"odinger operator -\Dc_x^2+V(x) on graphs made of one-dimensional
wires connected to external leads. We generalize the Smith formula for graphs.
We give several examples of graphs where the state counting method given by the
Friedel sum rule is not working. The reason for the failure of the Friedel sum
rule to count the states is the existence of states localized in the graph and
not coupled to the leads, which occurs if the spectrum is degenerate and the
number of leads too small.Comment: 20 pages, LaTeX, 6 eps figure
Determination of the longitudinal structure function at HERA
Recent results from the HERA experiment H1 on the longitudinal stucture
function of the proton are presented. They include proton structure
function analyses with particular emphasis on those kinematic regions which are
sensitive to . All results can be consistently described within the
framework of perturbative QCD.Comment: 16 pages, 11 figures (requires iopart, iopams and epsfig); Talk
presented in the Intern. Workshop on New Trends in HERA Physics 2001, 17-22
June 2001, Ringberg Castle, Tegernsee, Germany; To appear in the Proceeding
Suppression of level hybridization due to Coulomb interactions
We investigate an ensemble of systems formed by a ring enclosing a magnetic
flux. The ring is coupled to a side stub via a tunneling junction and via
Coulomb interaction. We generalize the notion of level hybridization due to the
hopping, which is naturally defined only for one-particle problems, to the
many-particle case, and we discuss the competition between the level
hybridization and the Coulomb interaction. It is shown that strong enough
Coulomb interactions can isolate the ring from the stub, thereby increasing the
persistent current. Our model describes a strictly canonical system (the number
of carriers is the same for all ensemble members). Nevertheless for small
Coulomb interactions and a long side stub the model exhibits a persistent
current typically associated with a grand canonical ensemble of rings and only
if the Coulomb interactions are sufficiently strong does the model exhibit a
persistent current which one expects from a canonical ensemble.Comment: 19 pages, 6 figures, uses iop style files, version as publishe
Explicitly solvable cases of one-dimensional quantum chaos
We identify a set of quantum graphs with unique and precisely defined
spectral properties called {\it regular quantum graphs}. Although chaotic in
their classical limit with positive topological entropy, regular quantum graphs
are explicitly solvable. The proof is constructive: we present exact periodic
orbit expansions for individual energy levels, thus obtaining an analytical
solution for the spectrum of regular quantum graphs that is complete, explicit
and exact
Spectra of regular quantum graphs
We consider a class of simple quasi one-dimensional classically
non-integrable systems which capture the essence of the periodic orbit
structure of general hyperbolic nonintegrable dynamical systems. Their behavior
is simple enough to allow a detailed investigation of both classical and
quantum regimes. Despite their classical chaoticity, these systems exhibit a
``nonintegrable analog'' of the Einstein-Brillouin-Keller quantization formula
which provides their spectra explicitly, state by state, by means of convergent
periodic orbit expansions.Comment: 32 pages, 10 figure
Pauli principle and chaos in a magnetized disk
We present results of a detailed quantum mechanical study of a gas of
noninteracting electrons confined to a circular boundary and subject to
homogeneous dc plus ac magnetic fields , with
). We earlier found a one-particle {\it classical}
phase diagram of the (scaled) Larmor frequency
{\rm vs} that
separates regular from chaotic regimes. We also showed that the quantum
spectrum statistics changed from Poisson to Gaussian orthogonal ensembles in
the transition from classically integrable to chaotic dynamics. Here we find
that, as a function of and , there are clear
quantum signatures in the magnetic response, when going from the
single-particle classically regular to chaotic regimes. In the quasi-integrable
regime the magnetization non-monotonically oscillates between diamagnetic and
paramagnetic as a function of . We quantitatively understand this behavior
from a perturbation theory analysis. In the chaotic regime, however, we find
that the magnetization oscillates as a function of but it is {\it always}
diamagnetic. Equivalent results are also presented for the orbital currents. We
also find that the time-averaged energy grows like in the
quasi-integrable regime but changes to a linear dependence in the chaotic
regime. In contrast, the results with Bose statistics are akin to the
single-particle case and thus different from the fermionic case. We also give
an estimate of possible experimental parameters were our results may be seen in
semiconductor quantum dot billiards.Comment: 22 pages, 7 GIF figures, Phys. Rev. E. (1999
From quantum graphs to quantum random walks
We give a short overview over recent developments on quantum graphs and
outline the connection between general quantum graphs and so-called quantum
random walks.Comment: 14 pages, 6 figure
- …