72 research outputs found
Quantum Graphs: A model for Quantum Chaos
We study the statistical properties of the scattering matrix associated with
generic quantum graphs. The scattering matrix is the quantum analogue of the
classical evolution operator on the graph. For the energy-averaged spectral
form factor of the scattering matrix we have recently derived an exact
combinatorial expression. It is based on a sum over families of periodic orbits
which so far could only be performed in special graphs. Here we present a
simple algorithm implementing this summation for any graph. Our results are in
excellent agreement with direct numerical simulations for various graphs.
Moreover we extend our previous notion of an ensemble of graphs by considering
ensemble averages over random boundary conditions imposed at the vertices. We
show numerically that the corresponding form factor follows the predictions of
random-matrix theory when the number of vertices is large---even when all bond
lengths are degenerate. The corresponding combinatorial sum has a structure
similar to the one obtained previously by performing an energy average under
the assumption of incommensurate bond lengths.Comment: 8 pages, 3 figures. Contribution to the conference on Dynamics of
Complex Systems, Dresden (1999
Nonadiabatic couplings and incipience of quantum chaos
The quantization of the electronic two site system interacting with a
vibration is considered by using as the integrable reference system the
decoupled oscillators resulting from the adiabatic approximation. A specific
Bloch projection method is applied which demonstrates how besides some regular
regions in the fine structure of the spectrum and the associated eigenvectors
irregularities appear when passing from the low to the high coupling case. At
the same time even for strong coupling some of the regular structure of the
spectrum rooted in the adiabatic potentials is kept intact justifying the
classification of this situation as incipience of quantum chaos.Comment: 16 pages including figure
Directed chaos in a billiard chain with transversal magnetic field
In generic Hamiltonian systems with a mixed phase space chaotic transport may
be directed and ballistic rather than diffusive. We investigate one particular
model showing this behaviour, namely a spatially periodic billiard chain in
which electrons move under the influence of a perpendicular magnetic field. We
analyze the phase-space structure and derive an explicit expression for the
chaotic transport velocity. Unlike previous studies of directed chaos our model
has a parameter regime in which the dispersion of an ensemble of chaotic
trajectories around its moving center of mass is essentially diffusive. We
explain how in this limit the deterministic chaos reduces to a biased random
walk in a billiard with a rough surface. The diffusion constant for this
simplified model is calculated analytically
Statistical properties of resonance widths for open Quantum Graphs
We connect quantum compact graphs with infinite leads, and turn them into
scattering systems. We derive an exact expression for the scattering matrix,
and explain how it is related to the spectrum of the corresponding closed
graph. The resulting expressions allow us to get a clear understanding of the
phenomenon of resonance trapping due to over-critical coupling with the leads.
Finally, we analyze the statistical properties of the resonance widths and
compare our results with the predictions of Random Matrix Theory. Deviations
appearing due to the dynamical nature of the system are pointed out and
explained.Comment: 17 pages, 7 figures. submitted to Waves in Random Media, special
issue for graph
Signature of directed chaos in the conductance of a nanowire
We study the conductance of chaotic or disordered wires in a situation where
equilibrium transport decomposes into biased diffusion and a counter-moving
regular current. A possible realization is a semiconductor nanostructure with
transversal magnetic field and suitably patterned surfaces. We find a
non-trivial dependence of the conductance on the wire length which differs
qualitatively from Ohm's law by the existence of a characteristic length scale
and a finite saturation value
The influence of tax regimes on distribution police of corporations: Evidence from German tax reforms
For more than 50 years, researchers around the world have been searching for a solution to Blacks famous 'dividend-puzzle'. However, despite tremendous efforts in different fields of economics, the influence of taxation on the distribution policy of firms has remained elusive and is still subject to extensive debate amongst scholars, professionals and politicians alike. In this paper, we try to shed some light on the discussion by presenting new empirical evidence from German tax reforms. Using a sample containing all firms listed at the Frankfurt stock exchange in the years from 1993 to 2009, we find robust evidence, that the switch from a split-rate tax system with full imputation to a shareholder relief system in 2002 and the change to a flat tax system in 2009 led to significant changes in the payout behavior of German firms. In line with the 'traditional view' of dividend taxation, German decision-makers cut back their dividend payments in response to the reduced advantageousness of dividends in comparison to capital gains after the reform. --Dividends,Taxation,Payout Policy
Topological Resonances in Scattering on Networks (Graphs)
We report on a hitherto unnoticed type of resonances occurring in scattering
from networks (quantum graphs) which are due to the complex connectivity of the
graph - its topology. We consider generic open graphs and show that any cycle
leads to narrow resonances which do not fit in any of the prominent paradigms
for narrow resonances (classical barriers, localization due to disorder,
chaotic scattering). We call these resonances `topological' to emphasize their
origin in the non-trivial connectivity. Topological resonances have a clear and
unique signature which is apparent in the statistics of the resonance
parameters (such as e.g., the width, the delay time or the wave-function
intensity in the graph). We discuss this phenomenon by providing analytical
arguments supported by numerical simulation, and identify the features of the
above distributions which depend on genuine topological quantities such as the
length of the shortest cycle (girth). These signatures cannot be explained
using any of the other paradigms for narrow resonances. Finally, we propose an
experimental setting where the topological resonances could be demonstrated,
and study the stability of the relevant distribution functions to moderate
dissipation
Combinatorial Identities from the Spectral Theory of Quantum Graphs
We present a few combinatorial identities which were encountered in our work
on the spectral theory of quantum graphs. They establish a new connection
between the theory of random matrix ensembles and combinatorics.Comment: 16 pages, RevTeX, 1 figur
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