Weighted Supermembrane Toy Model

A weighted Hilbert space approach to the study of zero-energy states of supersymmetric matrix models is introduced. Applied to a related but technically simpler model, it is shown that the spectrum of the corresponding weighted Hamiltonian simplifies to become purely discrete for sufficient weights. This follows from a bound for the number of negative eigenvalues of an associated matrix-valued Schr\"odinger operator.Comment: 18 pages, 2 figures; to appear in Lett. Math. Phys

Decorrelation estimates for the eigenlevels of the discrete Anderson model in the localized regime

The purpose of the present work is to establish decorrelation estimates for the locally renormalized eigenvalues of the discrete Anderson model near two distinct energies inside the localization region. In dimension one, we prove these estimates at all energies. In higher dimensions, the energies are required to be sufficiently far apart from each other

Equality of the bulk and edge Hall conductances in a mobility gap

We consider the edge and bulk conductances for 2D quantum Hall systems in which the Fermi energy falls in a band where bulk states are localized. We show that the resulting quantities are equal, when appropriately defined. An appropriate definition of the edge conductance may be obtained through a suitable time averaging procedure or by including a contribution from states in the localized band. In a further result on the Harper Hamiltonian, we show that this contribution is essential. In an appendix we establish quantized plateaus for the conductance of systems which need not be translation ergodic.Comment: 38 pages, LaTeX, uses svjour class. Corrected a number of typos and an error in proof of Lemma four. The latter correction appears as a separate erratum in the published version. Additional typos corrected in v

Transport and the Order Parameter of Superconducting Sr2_2RuO4_4

Recent experiments make it appear more likely that the order parameter of the unconventional superconductor Sr$_2$RuO$_4$ has a spin-triplet $f$-wave symmetry. We study ultrasonic absorption and thermal conductivity of superconducting Sr$_2$RuO$_4$ and fit to the recent data for various $f$-wave candidates. It is shown that only $f_{x^2-y^2}$-wave symmetry can account qualitatively for the transport data.Comment: 4 pages, 2 figures, references added and update

Generating Non-Linear Interpolants by Semidefinite Programming

Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model check- ing, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work for discovering interpolants for propositional logic, quantifier-free fragments of first-order theories and their combinations have been proposed. However, little work focuses on discovering polynomial interpolants in the literature. In this paper, we provide an approach for constructing non-linear interpolants based on semidefinite programming, and show how to apply such results to the verification of programs by examples.Comment: 22 pages, 4 figure

Localization criteria for Anderson models on locally finite graphs

We prove spectral and dynamical localization for Anderson models on locally finite graphs using the fractional moment method. Our theorems extend earlier results on localization for the Anderson model on \ZZ^d. We establish geometric assumptions for the underlying graph such that localization can be proven in the case of sufficiently large disorder

Josephson effect test for triplet pairing symmetry

The critical current modulation and the spontaneous flux of the vortex states in corner Josephson junctions between Sr$_2$RuO$_4$ and a conventional s-wave superconductor are calculated as a function of the crystal orientation, and the magnetic field. For Sr$_2$RuO$_4$ we assume two nodeless p-wave pairing states. Also we use the nodal $f$-wave states $B_{1g}\times E_u$ and $B_{2g} \times E_u$, and one special p-wave state having line nodes. It is seen that the critical current depends solely on the topology of the gap.Comment: 22 pages, 12 figure

The scaling limit of the critical one-dimensional random Schrodinger operator

We consider two models of one-dimensional discrete random Schrodinger operators (H_n \psi)_l ={\psi}_{l-1}+{\psi}_{l +1}+v_l {\psi}_l, {\psi}_0={\psi}_{n+1}=0 in the cases v_k=\sigma {\omega}_k/\sqrt{n} and v_k=\sigma {\omega}_k/ \sqrt{k}. Here {\omega}_k are independent random variables with mean 0 and variance 1. We show that the eigenvectors are delocalized and the transfer matrix evolution has a scaling limit given by a stochastic differential equation. In both cases, eigenvalues near a fixed bulk energy E have a point process limit. We give bounds on the eigenvalue repulsion, large gap probability, identify the limiting intensity and provide a central limit theorem. In the second model, the limiting processes are the same as the point processes obtained as the bulk scaling limits of the beta-ensembles of random matrix theory. In the first model, the eigenvalue repulsion is much stronger.Comment: 36 pages, 2 figure

Anderson localization for a class of models with a sign-indefinite single-site potential via fractional moment method

A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated by the sign-indefinite single-site potential, which is however sign-definite at the boundary of its support. For this class of Anderson operators we establish a finite-volume criterion which implies that above mentioned the fractional moment decay property holds. This constructive criterion is satisfied at typical perturbative regimes, e. g. at spectral boundaries which satisfy 'Lifshitz tail estimates' on the density of states and for sufficiently strong disorder. We also show how the fractional moment method facilitates the proof of exponential (spectral) localization for such random potentials.Comment: 29 pages, 1 figure, to appear in AH