Lower bounds to the spectral gap of Davies generators

We construct lower bounds to the spectral gap of a family of Lindblad generators known as Davies maps. These maps describe the thermalization of quantum systems weakly coupled to a heat bath. The steady state of these systems is given by the Gibbs distribution with respect to the system Hamiltonian. The bounds can be evaluated explicitly, when the eigenbasis and the spectrum of the Hamiltonian is known. A crucial assumption is that the spectrum of the Hamiltonian is non-degenerate. Furthermore, we provide a counterexample to the conjecture, that the convergence rate is always determined by the gap of the associated Pauli master equation. We conclude, that the full dynamics of the Lindblad generator has to be considered. Finally, we present several physical example systems for which the bound to the spectral gap is evaluated.Comment: 24 pages, 5 figure

Uniform Asymptotic Methods for Integrals

We give an overview of basic methods that can be used for obtaining asymptotic expansions of integrals: Watson's lemma, Laplace's method, the saddle point method, and the method of stationary phase. Certain developments in the field of asymptotic analysis will be compared with De Bruijn's book {\em Asymptotic Methods in Analysis}. The classical methods can be modified for obtaining expansions that hold uniformly with respect to additional parameters. We give an overview of examples in which special functions, such as the complementary error function, Airy functions, and Bessel functions, are used as approximations in uniform asymptotic expansions.Comment: 31 pages, 3 figure

Asymptotics of a 3F2{}_3F_2 polynomial associated with the Catalan-Larcombe-French sequence

The large $n$ behaviour of the hypergeometric polynomial \FFF{-n}{\sfrac12}{\sfrac12}{\sfrac12-n}{\sfrac12-n}{-1} is considered by using integral representations of this polynomial. This ${}_3F_2$ polynomial is associated with the Catalan-Larcombe-French sequence. Several other representations are mentioned, with references to the literature, and another asymptotic method is described by using a generating function of the sequence. The results are similar to those obtained by Clark (2004) who used a binomial sum for obtaining an asymptotic expansion.Comment: 10 pages, 1 figure. Accepted for publication in {\em Analysis and Applications

Thousand to one

Exodus 20:1-1

Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters

We consider the asymptotic behavior of the incomplete gamma functions gamma(-a,-z) and Gamma(-a,-z) as a goes to infinity. Uniform expansions are needed to describe the transition area z~a in which case error functions are used as main approximants. We use integral representations of the incomplete gamma functions and derive a uniform equation by applying techniques used for the existing uniform expansions for gamma(a,z) and Gamma(a,z). The result is compared with Olver's uniform expansion for the generalized exponential integral. A numerical verification of the expansion is given in a final section

American Indians and Christian Missions: Studies in Cultural Conflict

Reviewed Book: Bowden, Henry Warner. American Indians and Christian Missions: Studies in Cultural Conflict. [S.l.]: Univ of Chicago Press, 1981. Chicago History of American Religion

Formative Measurement Models in Covariance Structure Analysis: Specification and Identification

Many researchers seem to be unsure about how to specify formative measurement models in software programs like LISREL or AMOS and to establish identification of the corresponding structural equation model. In order to make identification easier, a new, mainly graphically oriented approach is presented for a specific class of recursive models with formative indicators. Using this procedure it is shown that some models have erroneously been considered underidentified. Furthermore, it is shown that specifying formative indicators as exogenous variables rises serious conceptual and substantial issues in the case that the formative construct is truly endogenous (i. e. influenced by more remote causes). An empirical study on the effects and causes of brand competence illustrates this point.Formative Indicators; Latent Variables; Covariance Structure Analysis; Identification