932 research outputs found
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
Directed Chaotic Transport in Hamiltonian Ratchets
We present a comprehensive account of directed transport in one-dimensional
Hamiltonian systems with spatial and temporal periodicity. They can be
considered as Hamiltonian ratchets in the sense that ensembles of particles can
show directed ballistic transport in the absence of an average force. We
discuss general conditions for such directed transport, like a mixed classical
phase space, and elucidate a sum rule that relates the contributions of
different phase-space components to transport with each other. We show that
regular ratchet transport can be directed against an external potential
gradient while chaotic ballistic transport is restricted to unbiased systems.
For quantized Hamiltonian ratchets we study transport in terms of the evolution
of wave packets and derive a semiclassical expression for the distribution of
level velocities which encode the quantum transport in the Floquet band
spectra. We discuss the role of dynamical tunneling between transporting
islands and the chaotic sea and the breakdown of transport in quantum ratchets
with broken spatial periodicity.Comment: 22 page
Can One Hear the Shape of a Graph?
We show that the spectrum of the Schrodinger operator on a finite, metric
graph determines uniquely the connectivity matrix and the bond lengths,
provided that the lengths are non-commensurate and the connectivity is simple
(no parallel bonds between vertices and no loops connecting a vertex to
itself). That is, one can hear the shape of the graph! We also consider a
related inversion problem: A compact graph can be converted into a scattering
system by attaching to its vertices leads to infinity. We show that the
scattering phase determines uniquely the compact part of the graph, under
similar conditions as above.Comment: 9 pages, 1 figur
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.
Three-point correlations for quantum star graphs
We compute the three point correlation function for the eigenvalues of the
Laplacian on quantum star graphs in the limit where the number of edges tends
to infinity. This extends a work by Berkolaiko and Keating, where they get the
2-point correlation function and show that it follows neither Poisson, nor
random matrix statistics. It makes use of the trace formula and combinatorial
analysis.Comment: 10 pages, 2 figure
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