Electrically and Magnetically Charged States and Particles in the 2+1-Dimensional Z_N-Higgs Gauge Model

Electrically as well as magnetically charged states are constructed in the 2+1-dimensional Euclidean Z_N-Higgs lattice gauge model, the former following ideas of Fredenhagen and Marcu and the latter using duality transformations on the algebra of observables. The existence of electrically and of magnetically charged particles is also established. With this work we prepare the ground for the constructive study of anyonic statistics of multiparticle scattering states of electrically and magnetically charged particles in this model (work in progress).Comment: 57 pages, Sfb 288 Preprint No. 109. To appear in Commun. Math. Phys. About the file: This is a uuencoded, "gzip-ed" postscript file. It is about 300kB large. The original ps file is about 700kB large. All figures are included. The LaTeX sources ou even hard copies can be required to the authors at [email protected] or Freie Universitaet Berlin. Institut fuer Theoretische Physik. Arnimallee 14. Berlin 14195 German

Stability for quasi-periodically perturbed Hill's equations

We consider a perturbed Hill's equation of the form $\ddot \phi + (p_{0}(t) + \epsilon p_{1}(t)) \phi = 0$, where $p_{0}$ is real analytic and periodic, $p_{1}$ is real analytic and quasi-periodic and \eps is a ``small'' real parameter. Assuming Diophantine conditions on the frequencies of the decoupled system, i.e. the frequencies of the external potentials $p_{0}$ and $p_{1}$ and the proper frequency of the unperturbed ($\epsilon=0$) Hill's equation, but without making non-degeneracy assumptions on the perturbing potential $p_{1}$, we prove that quasi-periodic solutions of the unperturbed equation can be continued into quasi-periodic solutions if $\epsilon$ lies in a Cantor set of relatively large measure in $[-\epsilon_0,\epsilon_0]$, where $\epsilon_0$ is small enough. Our method is based on a resummation procedure of a formal Lindstedt series obtained as a solution of a generalized Riccati equation associated to Hill's problem.Comment: 40 pages, 4 figure

Time Evolution of Two-Level Systems Driven by Periodic Fields

In this paper we study the time evolution of a class of two-level systems driven by periodic fields in terms of new convergent perturbative expansions for the associated propagator U(t). The main virtue of these expansions is that they do not contain secular terms, leading to a very convenient method for quantitatively studying the long-time behaviour of that systems. We present a complete description of an algorithm to numerically compute the perturbative expansions. In particular, we applied the algorithm to study the case of an ac-dc field (monochromatic interaction), exploring various situations and showing results on (time-dependent) observable quantities, like transition probabilities. For a simple ac field, we analised particular situations where an approximate effect of dynamical localisation is exhibited by the driven system. The accuracy of our calculations was tested measuring the unitarity of the propagator U(t), resulting in very small deviations, even for very long times compared to the cycle of the driving field.Comment: 1 table, 5 figures. Version 2 contains minor correction

Optimized time-dependent perturbation theory for pulse-driven quantum dynamics in atomic or molecular systems

We present a time-dependent perturbative approach adapted to the treatment of intense pulsed interactions. We show there is a freedom in choosing secular terms and use it to optimize the accuracy of the approximation. We apply this formulation to a unitary superconvergent technique and improve the accuracy by several orders of magnitude with respect to the Magnus expansion.Comment: 4 pages, 2 figure

Location of crossings in the Floquet spectrum of a driven two-level system

Calculation of the Floquet quasi-energies of a system driven by a time-periodic field is an efficient way to understand its dynamics. In particular, the phenomenon of dynamical localization can be related to the presence of close approaches between quasi-energies (either crossings or avoided crossings). We consider here a driven two-level system, and study how the locations of crossings in the quasi-energy spectrum alter as the field parameters are changed. A perturbational scheme provides a direct connection between the form of the driving field and the quasi-energies which is exact in the limit of high frequencies. We firstly obtain relations for the quasi-energies for some common types of applied field in the high-frequency limit. We then show how the locations of the crossings drift as the frequency is reduced, and find a simple empirical formula which describes this drift extremely well in general, and appears to be exact for the specific case of square-wave driving.Comment: 6 pages, 6 figures. Minor changes to text, this version to be published in Physical Review

Charge Transport Through Open, Driven Two-Level Systems with Dissipation

We derive a Floquet-like formalism to calculate the stationary average current through an AC driven double quantum dot in presence of dissipation. The method allows us to take into account arbitrary coupling strengths both of a time-dependent field and a bosonic environment. We numerical evaluate a truncation scheme and compare with analytical, perturbative results such as the Tien-Gordon formula.Comment: 14 pages, 6 figures. To appear in Phys. Rev.

Griffiths' Singularities in Diluted Ising Models on the Cayley Tree

The Griffiths' singularities are fully exhibited for a class of diluted ferromagnetic Ising models defined on the Cayley tree (Bethe lattice). For the deterministic model the Lee-Yang circle theorem is explicitly proven for the magnetization at the origin and it is shown that, in the thermodynamic limit, the Lee-Yang singularities become dense in the entire unit circle for the whole ferromagnetic phase. Smoothness (infinite differentiability) of the quenched magnetization m at the origin with respect to the external magnetic field is also proven for convenient choices of temperature and disorder. From our analysis one also concludes that the existence of metastable states is impossible for the random models in consideration. Key words: Lee-Yang singularities; Griffiths' singularities; infinite differentiability; metastable states. Contents 1 Introduction 2 2 Some Basic Results and Definitions 7 3 Analyticity of m 9 3.1 Analyticity of F in S 2 n S 1 . . . . . . . . . . . . . . . ...

Singularities of the Effective Fugacity on the Ising Model on the Cayley Tree

. Evidence suggesting a connection between Lee--Yang singularities of the magnetization of the Ising model and the singularities of the effective fugacity is presented. 1 Introduction The study of the Griffiths' singularities in random ferromagnetic Ising models [2] (see [3] and [4] for general discussions) remains one of the most living topics of research in Statistical Mechanics of spin systems. Besides its physical relevance, it involves various mathematical difficulties that make a detailed analysis particularly challenging. One of the main difficulties relies in the almost absence of models where a concrete study of the analytic properties of the magnetization and other thermodynamic quantities, as functions of the (complex) fugacity, could be developed. In [6] a detailed rigorous analysis of the presence of Griffiths' singularities has been performed in a class of layered diluted ferromagnetic Ising models on the Cayley tree. This involved the study of the analytic structure of t..