We study the Josephson effect in alkali atomic gases within the two-mode approximation and show that there is a correspondence between the Bogoliubov description and the harmonic limit of the phase representation. We demonstrate that the quanta of the Josephson plasmon can be identified with the Bogoliubov excitations of the two-site Bose fluid. We thus establish a mapping between the Bogoliubo...

Contents Preface v Chapter 1. From i to z: the basics of complex analysis 1 1. The field of complex numbers 1 2. Differentiability and conformality 3 3. Möbius transforms 7 4. Integration 12 5. Harmonic functions 19 6. The winding number 21 7. Problems 24 Chapter 2. From z to the Riemann mapping theorem: some finer points of basic complex analysis 27 1. The winding number version of Cauchy's th...

Using the Schwarz function of an ellipse, it was recently shown that galaxies with density constant on confocal ellipses can produce at most four “bright” images of a single source. The more physically interesting example of an isothermal galaxy has density that is constant on homothetic ellipses. In that case bright images can be seen to correspond to zeros of a certain transcendental harmonic...

‎In this paper‎, ‎we study the convex combinations of harmonic mappings obtained by shearing a class of slit conformal mappings‎. ‎Sufficient conditions for the convex combinations of harmonic mappings of this family to be univalent and convex in the horizontal direction are derived‎. ‎Several examples of univalent harmonic mappings constructed by using these methods are presented to illustrate...

we study the notion of harmonicity in the sense of symplectic geometry, and investigate the geometric properties of harmonic thom forms and distributional thom currents, dual to different types of submanifolds. we show that the harmonic thom form associated to a symplectic submanifold is nowhere vanishing. we also construct symplectic smoothing operators which preserve the harmonicity of distri...

The main aim of this paper is to introduce three classes $H^0_{p,q}$, $H^1_{p,q}$ and $TH^*_p$ of $p$-harmonic mappings and discuss the properties of mappings in these classes. First, we discuss the starlikeness and convexity of mappings in $H^0_{p,q}$ and $H^1_{p,q}$. Then establish the covering theorem for mappings in $H^1_{p,q}$. Finally, we determine the extreme points of the class $TH^*_{p}$.

We describe a general concept of using the spatial information encoded in the time-dependent polarization of high harmonic radiation generated by orthogonally polarized two-color laser fields. The main properties of recolliding electron wave packets driven by such fields are reviewed. It is shown that in addition to the recollision energy the angle of recollision of such wave packets, which is ...

In this paper, we propose a novel approach for cortical mapping that computes a direct map between two cortical surfaces while satisfying constraints on sulcal landmark curves. By computing the map directly, we can avoid conventional intermediate parameterizations and help simplify the cortical mapping process. The direct map in our method is formulated as the minimizer of a flexible variationa...

We show that for any closed surface of genus greater than one and finite weighted graph filling the surface, there exists a hyperbolic metric which realizes least Dirichlet energy harmonic embedding among fixed homotopy class all metrics on surface. give explicit examples such surfaces through new interpretation Nielsen realization problem mapping groups.

Brolin-Lyubich measure λR of a rational endomorphism R : Ĉ → Ĉ with degR ≥ 2 is the unique invariant measure of maximal entropy hλR = htop(R) = log d. Its support is the Julia set J(R). We demonstrate that λR is always computable by an algorithm which has access to coefficients of R, even when J(R) is not computable. In the case when R is a polynomial, BrolinLyubich measure coincides with the h...