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

High-Order Variational Calculation for the Frequency of Time-Periodic Solutions

We develop a convergent variational perturbation theory for the frequency of time-periodic solutions of nonlinear dynamical systems. The power of the theory is illustrated by applying it to the Duffing oscillator.Comment: Author Information under http://www.physik.fu-berlin.de/~pelster/, http://www.physik.fu-berlin.de/~kleinert/ and http://www.informatik.uni-stuttgart.de/ipvr/bv/personen/schanz.htm

De Koninklijke Nederlandse Bosbouw Vereniging en het imago bij haar leden

Het bestuur van de Koninklijke Nederlandse Bosbouw Vereniging besloot in 2000 om door middel van een intern onderzoek onder de leden bouwstenen te vinden voor een nieuw verenigingsbeleid. Dit is gebeurd door middel van een enquête onder alle leden. De analyse van de antwoorden had betrekking op 44% van de leden, zijnde de respons. De functie van de KNBV wordt thans nog vooral gezien als een kennis- en informatieplatform, maar in de toekomst zou de KNBV meer als belangenorganisatie mogen fungeren. Leeftijd speelt een rol bij de mate van betrokkenheid bij en tevredenheid over de KNBV. Deze zijn groter naarmate men ouder is. Desondanks is meer aandacht voor de wensen en ideeën van de jongere leden noodzakelijk voor de ‘verjonging’ en het voortbestaan van de vereniging, zeker als 80% van de respondenten aangeeft het jammer te vinden als de KNBV zou worden opgeheven

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

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 $N\to\infty$, 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

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

Monosomal karyotype in MDS : explaining the poor prognosis?

Schanz, J., Tüchler, H., Solé, F., Mallo, M., Luño, E., Cervera, J., Grau, J., Hildebrandt, B., Slovak, M.L., Ohyashiki, K., Steidl, C., Fonatsch, C., Pfeilstöcker, M., Nösslinger, T., Valent, P., Giagounidis, A., Aul, C., Lübbert, M., Stauder, R., Krieger, O., Le Beau, M.M., Bennett, J.M., Greenberg, P., Germing, U., Haase, D

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.

Transport and dynamics on open quantum graphs

We study the classical limit of quantum mechanics on graphs by introducing a Wigner function for graphs. The classical dynamics is compared to the quantum dynamics obtained from the propagator. In particular we consider extended open graphs whose classical dynamics generate a diffusion process. The transport properties of the classical system are revealed in the scattering resonances and in the time evolution of the quantum system.Comment: 42 pages, 13 figures, submitted to PR