Model of the telegraph line and its numerical solution

This paper deals with a model of the telegraph line that consists of system of ordinary differential equations, rather than partial differential telegraph equation. Numerical solution is then based on an original mathematical method. This method uses the Taylor series for solving ordinary differential equations with initial condition - initial value problems in a non-traditional way. Systems of ordinary differential equations are solved using variable order, variable step-size Modern Taylor Series Method. The Modern Taylor Series Method is based on a recurrent calculation of the Taylor series terms for each time interval. The second part of paper presents the solution of linear problems which comes from the model of telegraph line. All experiments were performed using MATLAB software, the newly developed linear solver that uses Modern Taylor Series Method. Linear solver was compared with the state of the art solvers in MATLAB and SPICE software.Web of Science81171

Large current noise in nanoelectromechanical systems close to continuous mechanical instabilities

We investigate the current noise of nanoelectromechanical systems close to a continuous mechanical instability. In the vicinity of the latter, the vibrational frequency of the nanomechanical system vanishes, rendering the system very sensitive to charge fluctuations and, hence, resulting in very large (super-Poissonian) current noise. Specifically, we consider a suspended single-electron transistor close to the Euler buckling instability. We show that such a system exhibits an exponential enhancement of the current noise when approaching the Euler instability which we explain in terms of telegraph noise.Comment: 11 pages, 12 figures; v2: minor changes, published versio

Narrow Spectral Feature In Resonance Fluorescence With A Single Monochromatic Laser Field

We describe the resonance fluorescence spectrum of an atomic three-level system where two of the states are coupled by a single monochromatic laser field. The influence of the third energy level, which interacts with the two laser-coupled states only via radiative decays, is studied in detail. For a suitable choice of parameters, this system gives rise to a very narrow structure at the laser frequency in the fluorescence spectrum which is not present in the spectrum of a two-level atom. We find those parameter ranges by a numerical analysis and use the results to derive analytical expressions for the additional narrow peak. We also derive an exact expression for the peak intensity under the assumption that a random telegraph model is applicable to the system. This model and a simple spring model are then used to describe the physical origins of the additional peak. Using these results, we explain the connection between our system, a three-level system in V-configuration where both transitions are laser driven, and a related experiment which was recently reported.Comment: 14 pages, 15 figures, extension of the spring mode