773 research outputs found
Phase-space correlations of chaotic eigenstates
It is shown that the Husimi representations of chaotic eigenstates are
strongly correlated along classical trajectories. These correlations extend
across the whole system size and, unlike the corresponding eigenfunction
correlations in configuration space, they persist in the semiclassical limit. A
quantitative theory is developed on the basis of Gaussian wavepacket dynamics
and random-matrix arguments. The role of symmetries is discussed for the
example of time-reversal invariance.Comment: Published version with minor corrections to version
Synergetic Analysis of the Haeussler-von der Malsburg Equations for Manifolds of Arbitrary Geometry
We generalize a model of Haeussler and von der Malsburg which describes the
self-organized generation of retinotopic projections between two
one-dimensional discrete cell arrays on the basis of cooperative and
competitive interactions of the individual synaptic contacts. Our generalized
model is independent of the special geometry of the cell arrays and describes
the temporal evolution of the connection weights between cells on different
manifolds. By linearizing the equations of evolution around the stationary
uniform state we determine the critical global growth rate for synapses onto
the tectum where an instability arises. Within a nonlinear analysis we use then
the methods of synergetics to adiabatically eliminate the stable modes near the
instability. The resulting order parameter equations describe the emergence of
retinotopic projections from initially undifferentiated mappings independent of
dimension and geometry.Comment: Dedicated to Hermann Haken on the occasion of his 80th birthda
Periodic-Orbit Theory of Anderson Localization on Graphs
We present the first quantum system where Anderson localization is completely
described within periodic-orbit theory. The model is a quantum graph analogous
to an a-periodic Kronig-Penney model in one dimension. The exact expression for
the probability to return of an initially localized state is computed in terms
of classical trajectories. It saturates to a finite value due to localization,
while the diagonal approximation decays diffusively. Our theory is based on the
identification of families of isometric orbits. The coherent periodic-orbit
sums within these families, and the summation over all families are performed
analytically using advanced combinatorial methods.Comment: 4 pages, 3 figures, RevTe
Rate of energy absorption by a closed ballistic ring
We make a distinction between the spectroscopic and the mesoscopic
conductance of closed systems. We show that the latter is not simply related to
the Landauer conductance of the corresponding open system. A new ingredient in
the theory is related to the non-universal structure of the perturbation matrix
which is generic for quantum chaotic systems. These structures may created
bottlenecks that suppress the diffusion in energy space, and hence the rate of
energy absorption. The resulting effect is not merely quantitative: For a
ring-dot system we find that a smaller Landauer conductance implies a smaller
spectroscopic conductance, while the mesoscopic conductance increases. Our
considerations open the way towards a realistic theory of dissipation in closed
mesoscopic ballistic devices.Comment: 18 pages, 5 figures, published version with updated ref
Excitonic - vibronic coupled dimers: A dynamic approach
The dynamical properties of exciton transfer coupled to polarization
vibrations in a two site system are investigated in detail. A fixed point
analysis of the full system of Bloch - oscillator equations representing the
coupled excitonic - vibronic flow is performed. For overcritical polarization a
bifurcation converting the stable bonding ground state to a hyperbolic unstable
state which is basic to the dynamical properties of the model is obtained. The
phase space of the system is generally of a mixed type: Above bifurcation chaos
develops starting from the region of the hyperbolic state and spreading with
increasing energy over the Bloch sphere leaving only islands of regular
dynamics. The behaviour of the polarization oscillator accordingly changes from
regular to chaotic.Comment: uuencoded compressed Postscript file containing text and figures. In
case of questions, please, write to [email protected]
Shot noise from action correlations
We consider universal shot noise in ballistic chaotic cavities from a
semiclassical point of view and show that it is due to action correlations
within certain groups of classical trajectories. Using quantum graphs as a
model system we sum these trajectories analytically and find agreement with
random-matrix theory. Unlike all action correlations which have been considered
before, the correlations relevant for shot noise involve four trajectories and
do not depend on the presence of any symmetry.Comment: 4 pages, 2 figures (a mistake in version 1 has been corrected
Classical dynamics on graphs
We consider the classical evolution of a particle on a graph by using a
time-continuous Frobenius-Perron operator which generalizes previous
propositions. In this way, the relaxation rates as well as the chaotic
properties can be defined for the time-continuous classical dynamics on graphs.
These properties are given as the zeros of some periodic-orbit zeta functions.
We consider in detail the case of infinite periodic graphs where the particle
undergoes a diffusion process. The infinite spatial extension is taken into
account by Fourier transforms which decompose the observables and probability
densities into sectors corresponding to different values of the wave number.
The hydrodynamic modes of diffusion are studied by an eigenvalue problem of a
Frobenius-Perron operator corresponding to a given sector. The diffusion
coefficient is obtained from the hydrodynamic modes of diffusion and has the
Green-Kubo form. Moreover, we study finite but large open graphs which converge
to the infinite periodic graph when their size goes to infinity. The lifetime
of the particle on the open graph is shown to correspond to the lifetime of a
system which undergoes a diffusion process before it escapes.Comment: 42 pages and 8 figure
Photogalvanic current in artificial asymmetric nanostructures
We develop a theoretic description of the photogalvanic current induced by a
high frequency radiation in asymmetric nanostructures and show that it
describes well the results of numerical simulations. Our studies allow to
understand the origin of the electronic ratchet transport in such systems and
show that they can be used for creation of new types of detectors operating at
room temperature in a terahertz radiation range.Comment: 11 pages, 9 figs, EPJ latex styl
Spectral Statistics in Chaotic Systems with Two Identical Connected Cells
Chaotic systems that decompose into two cells connected only by a narrow
channel exhibit characteristic deviations of their quantum spectral statistics
from the canonical random-matrix ensembles. The equilibration between the cells
introduces an additional classical time scale that is manifest also in the
spectral form factor. If the two cells are related by a spatial symmetry, the
spectrum shows doublets, reflected in the form factor as a positive peak around
the Heisenberg time. We combine a semiclassical analysis with an independent
random-matrix approach to the doublet splittings to obtain the form factor on
all time (energy) scales. Its only free parameter is the characteristic time of
exchange between the cells in units of the Heisenberg time.Comment: 37 pages, 15 figures, changed content, additional autho
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