A class of theoretical models seeks to explain rhythmic single cell data by postulating that they are generated by intrinsic noise in biochemical systems whose deterministic models exhibit only damped oscillations. The main features of such noise-induced oscillations are quantified by the power spectrum which measures the dependence of the oscillatory signal's power with frequency. In this pape...

There are a number of applications in which linear noise models are inappropriate. In this paper, the use of bilinear noise modela in circuits and devices is considered. Several physical problems are studied in this framework. These include circuils involving varying parameters (such as variable resistance circuits constructed using Jieldeffect transistors), the effect of switching jitter on sa...

A similarity transformation is constructed through which a system of particles interacting with inverse-square two-body and harmonic potentials in one dimension, can be mapped identically, to a set of free harmonic oscillators. This equivalence enables us to write down the complete set of eigenfunctions. We find the exact constants of motion and a linear W1+∞ algebra associated with this model....

We propose a quantity, A?, as measure describing the nonadiabaticity of thermodynamic process. For this purpose, we use schematic method to find ‘degree nonadiabaticity’. The utilizes an ‘invariant’ thermal state constructed from Ermakov-Lewis-Riesenfeld invariant. Specifically, study frequency-modulated quantum harmonic oscillator system. Naturally, write first law thermodynamics with A? measu...

After reviewing the main features of anomalous energy transport in 1D systems, we report simulations performed with chains of noisy anharmonic oscillators. The stochastic terms are added in such a way to conserve total energy and momentum, thus keeping the basic hydrodynamic features of these models. The addition of this ”conservative noise” allows to obtain a more efficient estimate of the pow...

The relativistic harmonic oscillator is one of the most important quantum system, as it is one of the very few that can be solved exactly. The Dirac relativistic oscillator (DO) interaction is an important potential both for theory and application. It was for the first time studied by Ito et al [1]. They considered a Dirac equation in which the momentum p is replaced by p − imβω r, with r being...