Ground Beetles of Islands in the Western Basin of Lake Erie and the Adjacent Mainland (Coleoptera: Carabidae, Including Cicindelini)

We report 241 species representing 63 genera of ground beetles from the islands of the western basin of Lake Erie and selected mainland sites from a 1991-93 survey, plus specimens examined in public and private collections, and previously published sources. Most species are generally distributed; however, a restricted population of Sphaeroderus schaumii schaumii we rediscovered is no doubt imperiled. Comparison of wing morphotype frequencies of the Lake Erie island species with mainland populations from studies in Ohio and Michigan support a hypothesis that vagility is of increased import in the islands. Regression and correlation analysis show a positive relationship between species number and island area, no correlation between species number and distance from the mainland and an improved fit for a multiple regression which includes collecting effort

Solution to the Equations of the Moment Expansions

We develop a formula for matching a Taylor series about the origin and an asymptotic exponential expansion for large values of the coordinate. We test it on the expansion of the generating functions for the moments and connected moments of the Hamiltonian operator. In the former case the formula produces the energies and overlaps for the Rayleigh-Ritz method in the Krylov space. We choose the harmonic oscillator and a strongly anharmonic oscillator as illustrative examples for numerical test. Our results reveal some features of the connected-moments expansion that were overlooked in earlier studies and applications of the approach

Better bound on the exponent of the radius of the multipartite separable ball

We show that for an m-qubit quantum system, there is a ball of radius asymptotically approaching kappa 2^{-gamma m} in Frobenius norm, centered at the identity matrix, of separable (unentangled) positive semidefinite matrices, for an exponent gamma = (1/2)((ln 3/ln 2) - 1), roughly .29248125. This is much smaller in magnitude than the best previously known exponent, from our earlier work, of 1/2. For normalized m-qubit states, we get a separable ball of radius sqrt(3^(m+1)/(3^m+3)) * 2^{-(1 + \gamma)m}, i.e. sqrt{3^{m+1}/(3^m+3)}\times 6^{-m/2} (note that \kappa = \sqrt{3}), compared to the previous 2 * 2^{-3m/2}. This implies that with parameters realistic for current experiments, NMR with standard pseudopure-state preparation techniques can access only unentangled states if 36 qubits or fewer are used (compared to 23 qubits via our earlier results). We also obtain an improved exponent for m-partite systems of fixed local dimension d_0, although approaching our earlier exponent as d_0 approaches infinity.Comment: 30 pp doublespaced, latex/revtex, v2 added discussion of Szarek's upper bound, and reference to work of Vidal, v3 fixed some errors (no effect on results), v4 involves major changes leading to an improved constant, same exponent, and adds references to and discussion of Szarek's work showing that exponent is essentially optimal for qubit case, and Hildebrand's alternative derivation for qubit case. To appear in PR

Graph Games on Ordinals

We consider an extension of Church\'s synthesis problem to ordinals by adding limit transitions to graph games. We consider game arenas where these limit transitions are defined using the sets of cofinal states. In a previous paper, we have shown that such games of ordinal length are determined and that the winner problem is PSPACE-complete, for a subclass of arenas where the length of plays is always smaller than \\omega^\\omega. However, \nthe proof uses a rather involved reduction to classical Muller games, and the resulting strategies need infinite memory. \n \nWe adapt the LAR reduction to prove the determinacy in the general case, and to generate strategies with finite memory, using a reduction to games where the limit transitions are defined by priorities. We provide an algorithm for computing the winning regions of both players in these games, with a complexity similar to parity games. Its analysis yields three results: determinacy without hypothesis on the length of the plays, existence of \nmemoryless strategies, and membership of the winner problem in NP and co-NP

Theory of impedance networks: The two-point impedance and LC resonances

We present a formulation of the determination of the impedance between any two nodes in an impedance network. An impedance network is described by its Laplacian matrix L which has generally complex matrix elements. We show that by solving the equation L u_a = lambda_a u_a^* with orthonormal vectors u_a, the effective impedance between nodes p and q of the network is Z = Sum_a [u_{a,p} - u_{a,q}]^2/lambda_a where the summation is over all lambda_a not identically equal to zero and u_{a,p} is the p-th component of u_a. For networks consisting of inductances (L) and capacitances (C), the formulation leads to the occurrence of resonances at frequencies associated with the vanishing of lambda_a. This curious result suggests the possibility of practical applications to resonant circuits. Our formulation is illustrated by explicit examples.Comment: 21 pages, 3 figures; v4: typesetting corrected; v5: Eq. (63) correcte

General criterion for the entanglement of two indistinguishable particles

We relate the notion of entanglement for quantum systems composed of two identical constituents to the impossibility of attributing a complete set of properties to both particles. This implies definite constraints on the mathematical form of the state vector associated with the whole system. We then analyze separately the cases of fermion and boson systems, and we show how the consideration of both the Slater-Schmidt number of the fermionic and bosonic analog of the Schmidt decomposition of the global state vector and the von Neumann entropy of the one-particle reduced density operators can supply us with a consistent criterion for detecting entanglement. In particular, the consideration of the von Neumann entropy is particularly useful in deciding whether the correlations of the considered states are simply due to the indistinguishability of the particles involved or are a genuine manifestation of the entanglement. The treatment leads to a full clarification of the subtle aspects of entanglement of two identical constituents which have been a source of embarrassment and of serious misunderstandings in the recent literature.Comment: 18 pages, Latex; revised version: Section 3.2 rewritten, new Theorems added, reference [1] corrected. To appear on Phys.Rev.A 70, (2004

Entanglement frustration for Gaussian states on symmetric graphs

We investigate the entanglement properties of multi-mode Gaussian states, which have some symmetry with respect to the ordering of the modes. We show how the symmetry constraints the entanglement between two modes of the system. In particular, we determine the maximal entanglement of formation that can be achieved in symmetric graphs like chains, 2d and 3d lattices, mean field models and the platonic solids. The maximal entanglement is always attained for the ground state of a particular quadratic Hamiltonian. The latter thus yields the maximal entanglement among all quadratic Hamiltonians having the considered symmetry.Comment: 5 pages, 1 figur

Basis-independent methods for the two-Higgs-doublet model II. The significance of tan(beta)

In the most general two-Higgs-doublet model (2HDM), there is no distinction between the two complex hypercharge-one SU(2) doublet scalar fields, Phi_a (a=1,2). Thus, any two orthonormal linear combinations of these two fields can serve as a basis for the Lagrangian. All physical observables of the model must therefore be basis-independent. For example, tan(beta)=/ is basis-dependent and thus cannot be a physical parameter of the model. In this paper, we provide a basis-independent treatment of the Higgs sector with particular attention to the neutral Higgs boson mass-eigenstates, which generically are not eigenstates of CP. We then demonstrate that all physical Higgs couplings are indeed independent of tan(beta). In specialized versions of the 2HDM, tan(beta) can be promoted to a physical parameter of the Higgs-fermion interactions. In the most general 2HDM, the Higgs-fermion couplings can be expressed in terms of a number of physical "tan(beta)--like" parameters that are manifestly basis-independent. The minimal supersymmetric extension of the Standard Model provides a simple framework for exhibiting such effects.Comment: 56 pages, 5 tables, with Eq. (65) corrected (erratum to appear in Physical Review D

Extremal spacings between eigenphases of random unitary matrices and their tensor products

Extremal spacings between eigenvalues of random unitary matrices of size N pertaining to circular ensembles are investigated. Explicit probability distributions for the minimal spacing for various ensembles are derived for N = 4. We study ensembles of tensor product of k random unitary matrices of size n which describe independent evolution of a composite quantum system consisting of k subsystems. In the asymptotic case, as the total dimension N = n^k becomes large, the nearest neighbor distribution P(s) becomes Poissonian, but statistics of extreme spacings P(s_min) and P(s_max) reveal certain deviations from the Poissonian behavior