Quantum pumping: The charge transported due to a translation of a scatterer

The amount of charge which is pushed by a moving scatterer is $dQ = -G dX$, where $dX$ is the displacement of the scatterer. The question is what is $G$. Does it depend on the transmission $g_0$ of the scatterer? Does the answer depend on whether the system is open (with leads attached to reservoirs) or closed? In the latter case: what are the implications of having ``quantum chaos" and/or coupling to to the environment? The answers to these questions illuminate some fundamental aspects of the theory of quantum pumping. For the analysis we take a network (graph) as a model system, and use the Kubo formula approach.Comment: 4 pages, 2 figures, minor changes, to be published in PRE (Rapid

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.

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

Application of Two-Phase Regression to Geotechnical Data

2000 Mathematics Subject Classification: 62F10, 62J05, 62P30A method for estimating a transition parameter in two-phase regression is described. The two phases are fitted and simultaneously the transition point is estimated. Practical application of the method is demonstrated on the data for determining soil hydraulic properties.Partly supported by projects FOR 444, Deutsche Forschungsgemeinschaft, Germany, MM1301/2003, National Science Fund, Bulgaria, and PRO-ENBIS: GTC1-2001-43031

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

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

Scars on quantum networks ignore the Lyapunov exponent

We show that enhanced wavefunction localization due to the presence of short unstable orbits and strong scarring can rely on completely different mechanisms. Specifically we find that in quantum networks the shortest and most stable orbits do not support visible scars, although they are responsible for enhanced localization in the majority of the eigenstates. Scarring orbits are selected by a criterion which does not involve the classical Lyapunov exponent. We obtain predictions for the energies of visible scars and the distributions of scarring strengths and inverse participation ratios.Comment: 5 pages, 2 figure

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

7. Untersuchungen über die platonischen handschrlften

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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