1,079 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
Combinatorial identities for binary necklaces from exact ray-splitting trace formulae
Based on an exact trace formula for a one-dimensional ray-splitting system,
we derive novel combinatorial identities for cyclic binary sequences (P\'olya
necklaces).Comment: 15 page
Trace identities and their semiclassical implications
The compatibility of the semiclassical quantization of area-preserving maps
with some exact identities which follow from the unitarity of the quantum
evolution operator is discussed. The quantum identities involve relations
between traces of powers of the evolution operator. For classically {\it
integrable} maps, the semiclassical approximation is shown to be compatible
with the trace identities. This is done by the identification of stationary
phase manifolds which give the main contributions to the result. The same
technique is not applicable for {\it chaotic} maps, and the compatibility of
the semiclassical theory in this case remains unsettled. The compatibility of
the semiclassical quantization with the trace identities demonstrates the
crucial importance of non-diagonal contributions.Comment: LaTeX - IOP styl
Spin-Boson Hamiltonian and Optical Absorption of Molecular Dimers
An analysis of the eigenstates of a symmetry-broken spin-boson Hamiltonian is
performed by computing Bloch and Husimi projections. The eigenstate analysis is
combined with the calculation of absorption bands of asymmetric dimer
configurations constituted by monomers with nonidentical excitation energies
and optical transition matrix elements. Absorption bands with regular and
irregular fine structures are obtained and related to the transition from the
coexistence to a mixing of adiabatic branches in the spectrum. It is shown that
correlations between spin states allow for an interpolation between absorption
bands for different optical asymmetries.Comment: 15 pages, revTeX, 8 figures, accepted for publication in Phys. Rev.
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
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
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
Controls on earthflow formation in the Teanaway River basin, central Washington State, USA
Earthflows create landscape heterogeneity, increase local erosion rates, and heighten sediment loads in streams. These slow moving and fine-grained mass movements make up much of the Holocene erosion in the Teanaway River basin, central Cascade Range, Washington State, yet controls on earthflow activity and the resulting topographic impacts are unquantified. We mapped earthflows based on morphologic characteristics and relatively dated earthflow activity using a flow directional surface roughness metric called MADstd. The relative MADstd activity is supported by six radiocarbon ages, three lake sedimentation ages, and 16 cross-cutting relationships, indicating that MADstd is a useful tool to identify and relatively date earthflow activity, especially in heavily vegetated regions. Nearly all of the mapped earthflows are in the Teanaway and lower Roslyn formations, which comprise just 32.7 % of the study area. Earthflow aspect follows bedding planes in these units, demonstrating a strong lithologic control on earthflow location. Based on absolute ages and MADstd distributions, a quarter of the earthflows in the Teanaway Basin were active in the last few hundred years; the timing coincides with deforestation and increased land use in the Teanaway. Major tributaries initiate in earthflows and valley width is altered by earthflows that create wide valleys upstream and narrow constrictions within the earthflow zone. Although direct sediment delivery from earthflows brings fine sediment to the channel, stream power is sufficient to readily transport fines downstream. Based on our findings, over the Holocene – and particularly in the last few hundred years – lithologic-controlled earthflow erosion in the Teanaway basin has altered valley bottom connectivity and increased delivery of fine sediments to tributary channels.</p
Convolution quadrature for the wave equation with impedance boundary conditions
We consider the numerical solution of the wave equation with impedance boundary conditions and start from a boundary integral formulation for its discretization. We develop the generalized convolution quadrature (gCQ) to solve the arising acoustic retarded potential integral equation for this impedance problem.
For the special case of scattering from a spherical object, we derive representations of analytic solutions which allow to investigate the effect of the impedance coefficient on the acoustic pressure analytically. We have performed systematic numerical experiments to study the convergence rates as well as the sensitivity of the acoustic pressure from the impedance coefficients.
Finally, we apply this method to simulate the acoustic pressure in a building with a fairly complicated geometry and to study the influence of the impedance coefficient also in this situation
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