A Colored Version of Tverberg\u27s Theorem

The main result of this paper is that given n red, n white, and n green points in the plane, it is possible to form n vertex-disjoint triangles Δ 1 ,…,Δ n in such a way that the Δ i has one one red, one white, and one green vertex for every i = 1,…, n and the intersection of these triangles is nonempty

Shape Analysis of the Level Spacing Distribution around the Metal Insulator Transition in the Three Dimensional Anderson Model

We present a new method for the numerical treatment of second order phase transitions using the level spacing distribution function $P(s)$. We show that the quantities introduced originally for the shape analysis of eigenvectors can be properly applied for the description of the eigenvalues as well. The position of the metal--insulator transition (MIT) of the three dimensional Anderson model and the critical exponent are evaluated. The shape analysis of $P(s)$ obtained numerically shows that near the MIT $P(s)$ is clearly different from both the Brody distribution and from Izrailev's formula, and the best description is of the form $P(s)=c_1\,s\exp(-c_2\,s^{1+\beta})$, with $\beta\approx 0.2$. This is in good agreement with recent analytical results.Comment: 14 pages in plain TeX, 6 figures upon reques

Joint searches between gravitational-wave interferometers and high-energy neutrino telescopes: science reach and analysis strategies

Many of the astrophysical sources and violent phenomena observed in our Universe are potential emitters of gravitational waves (GWs) and high-energy neutrinos (HENs). A network of GW detectors such as LIGO and Virgo can determine the direction/time of GW bursts while the IceCube and ANTARES neutrino telescopes can also provide accurate directional information for HEN events. Requiring the consistency between both, totally independent, detection channels shall enable new searches for cosmic events arriving from potential common sources, of which many extra-galactic objects.Comment: 4 pages. To appear in the Proceedings of the 2d Heidelberg Workshop: "High-Energy Gamma-rays and Neutrinos from Extra-Galactic Sources", Heidelberg (Germany), January 13-16, 200

The generalized localization lengths in one dimensional systems with correlated disorder

The scale invariant properties of wave functions in finite samples of one dimensional random systems with correlated disorder are analyzed. The random dimer model and its generalizations are considered and the wave functions are compared. Generalized entropic localization lengths are introduced in order to characterize the states and compared with their behavior for exponential localization. An acceptable agreement is obtained, however, the exponential form seems to be an oversimplification in the presence of correlated disorder. According to our analysis in the case of the random dimer model and the two new models the presence of power-law localization cannot be ruled out.Comment: 7 pages, LaTeX (IOP style), 2 figure

Comment on ``Critical Behavior in Disordered Quantum Systems Modified by Broken Time--Reversal Symmetry''

In a recent Letter [Phys. Rev. Lett. 80, 1003 (1998)] Hussein and Pato employed the maximum entropy principle (MEP) in order to derive interpolating ensembles between any pair of universality classes in random matrix theory. They apply their formalism also to the transition from random matrix to Poisson statistics of spectra that is observed for the case of the Anderson-type metal-insulator transition. We point out the problems with the latter procedure.Comment: 1 page in PS, to appear in PRL Sept. 2

Statistical mechanics of topological phase transitions in networks

We provide a phenomenological theory for topological transitions in restructuring networks. In this statistical mechanical approach energy is assigned to the different network topologies and temperature is used as a quantity referring to the level of noise during the rewiring of the edges. The associated microscopic dynamics satisfies the detailed balance condition and is equivalent to a lattice gas model on the edge-dual graph of a fully connected network. In our studies -- based on an exact enumeration method, Monte-Carlo simulations, and theoretical considerations -- we find a rich variety of topological phase transitions when the temperature is varied. These transitions signal singular changes in the essential features of the global structure of the network. Depending on the energy function chosen, the observed transitions can be best monitored using the order parameters Phi_s=s_{max}/M, i.e., the size of the largest connected component divided by the number of edges, or Phi_k=k_{max}/M, the largest degree in the network divided by the number of edges. If, for example the energy is chosen to be E=-s_{max}, the observed transition is analogous to the percolation phase transition of random graphs. For this choice of the energy, the phase-diagram in the [,T] plane is constructed. Single vertex energies of the form E=sum_i f(k_i), where k_i is the degree of vertex i, are also studied. Depending on the form of f(k_i), first order and continuous phase transitions can be observed. In case of f(k_i)=-(k_i+c)ln(k_i), the transition is continuous, and at the critical temperature scale-free graphs can be recovered.Comment: 12 pages, 12 figures, minor changes, added a new refernce, to appear in PR

Husimi Transform of an Operator Product

It is shown that the series derived by Mizrahi, giving the Husimi transform (or covariant symbol) of an operator product, is absolutely convergent for a large class of operators. In particular, the generalized Liouville equation, describing the time evolution of the Husimi function, is absolutely convergent for a large class of Hamiltonians. By contrast, the series derived by Groenewold, giving the Weyl transform of an operator product, is often only asymptotic, or even undefined. The result is used to derive an alternative way of expressing expectation values in terms of the Husimi function. The advantage of this formula is that it applies in many of the cases where the anti-Husimi transform (or contravariant symbol) is so highly singular that it fails to exist as a tempered distribution.Comment: AMS-Latex, 13 page

Novel multiple-band superconductor SrPt2As2

We present LDA calculated electronic structure of recently discovered superconductor SrPt2As2 with Tc=5.2K. Despite its chemical composition and crystal structure are somehow similar to FeAs-based high-temperature superconductors, the electronic structure of SrPt2As2 is very much different. Crystal structure is orthorhombic (or tetragonal if idealized) and has layered nature with alternating PtAs4 and AsPt4 tetrahedra slabs sandwiched with Sr ions. The Fermi level is crossed by Pt-5d states with rather strong admixture of As-4p states. Fermi surface of SrPt2As2 is essentially three dimensional, with complicated sheets corresponding to multiple bands. We compare SrPt2As2 with 1111 and 122 representatives of FeAs-class of superconductors, as well as with isovalent (Ba,Sr)Ni2As2 superconductors. Brief discussion of superconductivity in SrPt2As2 is also presented.Comment: 5 pages, 4 figure

Elucidating the Ultrafast Dynamics of Photoinduced Charge Separation in Metalloporphyrin-Fullerene Dyads Across the Electromagnetic Spectrum

Metalloporphyrins are prominent building blocks in the synthetic toolbox of advanced photodriven molecular devices. When the central ion is paramagnetic, the relaxation pathways within the manifold of excited states are highly intricate so that unravelling the intramolecular energy and electron transfer processes is usually a very complex task. This fact is critically hampering the development of applications based on the enhanced coupling offered by the electronic exchange interaction. In this work, the dynamics of charge separation in a copper porphyrin-fullerene are studied with several complementary spectroscopic tools across the electromagnetic spectrum (from near-infrared to X-ray wavelengths), each of them providing specific diagnostics. Correlating the various rates clearly demonstrates that the lifetime of the photoinduced charge-separated state exceeds by about 10-fold that of the isolated photoexcited CuII porphyrin. As revealed by the spectral modifications in the XANES region, this stabilization is accompanied by a transient change in covalency around the CuII center, which is induced by an enhanced interaction with the C60 moiety. This experimental finding is further confirmed by state-of-the art calculations using DFT and TD-DFT including dispersion effects that explain the electrostatic and structural origins of this interaction, as the CuIIP cation becomes ruffled and approaches closer to the fullerene in the charge-separated state. From a methodological point of view, these results exemplify the potential of multielectron excitation features in transient X-ray spectra as future diagnostics of subfemtosecond electronic dynamics. From a practical point of view, this work is paving the way for elucidating out-of-equilibrium electron transfer events coupled to magnetic interaction processes on their intrinsic time-scales

Features of Time-independent Wigner Functions

The Wigner phase-space distribution function provides the basis for Moyal's deformation quantization alternative to the more conventional Hilbert space and path integral quantizations. General features of time-independent Wigner functions are explored here, including the functional ("star") eigenvalue equations they satisfy; their projective orthogonality spectral properties; their Darboux ("supersymmetric") isospectral potential recursions; and their canonical transformations. These features are illustrated explicitly through simple solvable potentials: the harmonic oscillator, the linear potential, the Poeschl-Teller potential, and the Liouville potential.Comment: 18 pages, plain LaTex, References supplemente