368 research outputs found
Universal spectral properties of spatially periodic quantum systems with chaotic classical dynamics
We consider a quasi one-dimensional chain of N chaotic scattering elements
with periodic boundary conditions. The classical dynamics of this system is
dominated by diffusion. The quantum theory, on the other hand, depends
crucially on whether the chain is disordered or invariant under lattice
translations. In the disordered case, the spectrum is dominated by Anderson
localization whereas in the periodic case, the spectrum is arranged in bands.
We investigate the special features in the spectral statistics for a periodic
chain. For finite N, we define spectral form factors involving correlations
both for identical and non-identical Bloch numbers. The short-time regime is
treated within the semiclassical approximation, where the spectral form factor
can be expressed in terms of a coarse-grained classical propagator which obeys
a diffusion equation with periodic boundary conditions. In the long-time
regime, the form factor decays algebraically towards an asymptotic constant. In
the limit , we derive a universal scaling function for the form
factor. The theory is supported by numerical results for quasi one-dimensional
periodic chains of coupled Sinai billiards.Comment: 33 pages, REVTeX, 13 figures (eps
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.
The measurement of primary productivity in a high-rate oxidation pond (HROP)
A high-rate oxidation pond is studied as a model system for comparing 14C and oxygen evolution methods as tools for measuring primary productivity in hypertrophic aquatic systems. Our results indicate that at very dense algal populations (up to 5 mg chl. a l−1) and high photosynthetic rates, 14C based results may severely underestimate primary productivity, unless a way is found to keep incubation times very short. Results obtained with our oxygen electrode were almost an order of magnitude higher than those obtained by all 14C procedures. These higher values correspond fairly well with a field-tested computer-simulation model, as well as with direct harvest data obtained at the same pond when operated under similar conditions. The examination of the size-fractionation of the photosynthetic activity underscored the important contribution of nannoplanktonic algae to the total production of the syste
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
Degeneracies in the length spectra of metric graphs
The spectral theory of quantum graphs is related via an exact trace formula
with the spectrum of the lengths of periodic orbits (cycles) on the graphs. The
latter is a degenerate spectrum, and understanding its structure (i.e.,finding
out how many different lengths exist for periodic orbits with a given period
and the average number of periodic orbits with the same length) is necessary
for the systematic study of spectral fluctuations using the trace formula. This
is a combinatorial problem which we solve exactly for complete (fully
connected) graphs with arbitrary number of vertices.Comment: 13 pages, 7 figure
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