Geometric Models of the Relativistic Harmonic Oscillator

A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the non-relativistic limit, even though their relativistic behavior is quite different. Among quantum models we find a set of models with countable energy spectra, and another one having only a finite number of energy levels and in addition a continuous spectrum.Comment: 8 pages, Late

Modeling OpAmp-induced harmonic distortion for switched-capacitor ΣΔ modulator design

This communication reports a new modeling of opamp-induced harmonic distortion in SC ΣΔ modulators, which is aimed to optimum design of this kind of circuit for high-performance applications. We analyze incomplete transfer of charge in a SC integrator and use power expansion and nonlinear fitting to obtain analytical models to represent harmonic distortion as function of the opamp finite gain-bandwidth (GB), slew-rate (SR) and nonlinear DC gain. Calculated models apply for all modulator architectures where harmonic distortion is dominated by the first integrator in the chain. We show that results provided by the new analytical models fit well to that obtained by simulation in time domain and have accuracy levels much larger than that provided by previously reported modeling approaches

Bipolar Harmonic encoding of CMB correlation patterns

Deviations from statistical isotropy can be modeled in various ways, for instance, anisotropic cosmological models (Bianchi models), compact topologies and presence of primordial magnetic field. Signature of anisotropy manifests itself in CMB correlation patterns. Here we explore the symmetries of the correlation function and its implications on the observable measures constructed within the Bipolar harmonic formalism for these variety of models. Different quantifiers within the Bipolar harmonic representation are used to distinguish between plausible models of breakdown of statistical isotropy and as a spectroscopic tool for discriminating between distinct cosmic topology.Comment: Revised version, accepted for publication in Phys. Rev.