Cross-section Fluctuations in Open Microwave Billiards and Quantum Graphs: The Counting-of-Maxima Method Revisited

The fluctuations exhibited by the cross-sections generated in a compound-nucleus reaction or, more generally, in a quantum-chaotic scattering process, when varying the excitation energy or another external parameter, are characterized by the width Gamma_corr of the cross-section correlation function. In 1963 Brink and Stephen [Phys. Lett. 5, 77 (1963)] proposed a method for its determination by simply counting the number of maxima featured by the cross sections as function of the parameter under consideration. They, actually, stated that the product of the average number of maxima per unit energy range and Gamma_corr is constant in the Ercison region of strongly overlapping resonances. We use the analogy between the scattering formalism for compound-nucleus reactions and for microwave resonators to test this method experimentally with unprecedented accuracy using large data sets and propose an analytical description for the regions of isolated and overlapping resonances

Semiclassical Theory of Chaotic Quantum Transport

We present a refined semiclassical approach to the Landauer conductance and Kubo conductivity of clean chaotic mesoscopic systems. We demonstrate for systems with uniformly hyperbolic dynamics that including off-diagonal contributions to double sums over classical paths gives a weak-localization correction in quantitative agreement with results from random matrix theory. We further discuss the magnetic field dependence. This semiclassical treatment accounts for current conservation.Comment: 4 pages, 1 figur

Dynamical Supersymmetry Breaking in Intersecting Brane Models

In this paper we study dynamical supersymmetry breaking in absence of gravity with the matter content of the minimal supersymmetric standard model. The hidden sector of the theory is a strongly coupled gauge theory, realized in terms of microscopic variables which condensate to form mesons. The supersymmetry breaking scalar potential combines F, D terms with instanton generated interactions in the Higgs-mesons sector. We show that for a large region in parameter space the vacuum breaks in addition to supersymmetry also electroweak gauge symmetry. We furthermore present local D-brane configurations that realize these supersymmetry breaking patterns.Comment: 30 pages, 4 figures, pdflate

Magnetic model for Ba_2Cu_3O_4Cl_2

Ba_2Cu_3O_4Cl_2 consists of two types of copper atoms, Cu(A) and Cu(B). We study the corresponding Heisenberg model with three antiferromagnetic couplings, J_AA, J_BB and J_AB. We find interesting frustration effects due to the coupling J_AB.Comment: 6 pages, LaTeX, 3 eps figures, to appear in JMM

Direct calculation of the spin stiffness on square, triangular and cubic lattices using the coupled cluster method

We present a method for the direct calculation of the spin stiffness by means of the coupled cluster method. For the spin-half Heisenberg antiferromagnet on the square, the triangular and the cubic lattices we calculate the stiffness in high orders of approximation. For the square and the cubic lattices our results are in very good agreement with the best results available in the literature. For the triangular lattice our result is more precise than any other result obtained so far by other approximate method.Comment: 5 pages, 2 figure

Low-temperature properties of the Hubbard model on highly frustrated one-dimensional lattices

We consider the repulsive Hubbard model on three highly frustrated one-dimensional lattices -- sawtooth chain and two kagom\'{e} chains -- with completely dispersionless (flat) lowest single-electron bands. We construct the complete manifold of {\em exact many-electron} ground states at low electron fillings and calculate the degeneracy of these states. As a result, we obtain closed-form expressions for low-temperature thermodynamic quantities around a particular value of the chemical potential $\mu_0$. We discuss specific features of thermodynamic quantities of these ground-state ensembles such as residual entropy, an extra low-temperature peak in the specific heat, and the existence of ferromagnetism and paramagnetism. We confirm our analytical results by comparison with exact diagonalization data for finite systems.Comment: 20 pages, 12 figures, 2 table

Flat-Band Ferromagnetism as a Pauli-Correlated Percolation Problem

We investigate the location and nature of the para-ferro transition of interacting electrons in dispersionless bands using the example of the Hubbard model on the Tasaki lattice. This case can be analyzed as a geometric site-percolation problem where different configurations appear with nontrivial weights. We provide a complete exact solution for the 1D case and develop a numerical algorithm for the 2D case. In two dimensions the paramagnetic phase persists beyond the uncorrelated percolation point, and the grand-canonical transition is via a first-order jump to an unsaturated ferromagnetic phase.Comment: 6 pages, 5 figure

Mechanical Mixing in Nonlinear Nanomechanical Resonators

Nanomechanical resonators, machined out of Silicon-on-Insulator wafers, are operated in the nonlinear regime to investigate higher-order mechanical mixing at radio frequencies, relevant to signal processing and nonlinear dynamics on nanometer scales. Driven by two neighboring frequencies the resonators generate rich power spectra exhibiting a multitude of satellite peaks. This nonlinear response is studied and compared to $n^{th}$-order perturbation theory and nonperturbative numerical calculations.Comment: 5 pages, 7 figure