This paper is partly a report on current knowledge concerning the structure of (generic) quantized coordinate rings and their prime spectra, and partly propaganda in support of the conjecture that since these algebras share many common properties, there must be a common basis on which to treat them. The first part of the paper is expository. We survey a number of classes of quantized coordinate...

The renormalization of the two dimensional light-front quantized φ theory is discussed. The mass renormalization condition and the renormalized constraint equation are shown to contain all the information to describe the phase transition in the theory, which is found to be of the second order. We argue that the same result would also be obtained in the conventional equal-time formulation.

A generalized standard map is quantized as a model of quantum chaos. We show that, only in hyperbolic chaotic regime, second moment of quantum level velocity is ∼ 1/h̄ as predicted by the random matrix theory. As a semiclassical implication, all higher order classical time correlations are insignificant in this regime.

We give an introductory review of quantum physics on the noncommutative space-time called the Groenewold-Moyal plane. Basic ideas like star products, twisted statistics , second quantized fields and discrete symmetries are discussed. We also outline some of the recent developments in these fields and mention where one can search for experimental signals.

Many ac quantized Hall resistance experiments have measured significant values of ac longitudinal resistances under temperature and magnetic field conditions in which the dc longitudinal resistance values were negligible. We investigate the effect of non-vanishing ac longitudinal resistances on measurements of the quantized Hall resistances by analyzing equivalent circuits of quantized Hall eff...

We explore a generalization of quantum secret sharing (QSS) in which classical shares play a complementary role to quantum shares, exploring further consequences of an idea first studied by Nascimento, Mueller-Quade and Imai (Phys. Rev. A64 042311 (2001)). We examine three ways, termed inflation, compression and twin-thresholding, by which the proportion of classical shares can be augmented. Th...

This paper presents a systematic approach to designing a naïve quantized control law that combines a regular round-to-nearest quantizer with a closed-loop dynamic system to generate a coarsely quantized control force for reference tracking. The naïve quantized control law is derived from minimizing an instantaneous absolute value of a performance-index signal. The stability and performance of t...

We consider quantized chaotic dynamics for a spiking oscillator with two periodic inputs. As the first input is applied, the oscillator generates various periodic and chaotic pulse-trains governed by a pulse position map. As the second input is added, the oscillator produces pulse positions restricted on a lattice, and the pulse position map is quantized. Then the oscillator generates a set of ...