Path integral quantization corresponding to the deformed Heisenberg algebra

In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.     

Estimation of power density in IMPATT using different materials

ABSTRACT

The RF output power dissipated per unit area is calculated using Runge-Kutta method for the high-moderate-moderate-high (n⁺-n-p-p⁺) doping profile of double drift region (DDR)-based impact avalanche transit time (IMPATT) diode by taking different substrate at Ka band. Those substrates are silicon, gallium arsenide, germanium, wurtzite gallium nitride, indium phosphide and 4H-silicon carbide. A comparative study regarding power dissipation ability by the IMPATT using different material is being presented thereby modelling the DDR IMPATT diode in a one-dimensional structure. The IMPATT based on 4H-SiC element has highest power density in the order of 10¹⁰ Wm^?2 and the Si-based counterpart has lowest power density of order 10⁶ Wm^?2 throughout the Ka band. So, 4H-SiC-based IMPATT should be preferable over others for the power density preference based application. This result will be helpful to estimate the power density of the IMPATT for any doping profile and to select the proper element for the optimum design of the IMPATT as far as power density is concerned in the Ka band. Also, we have focused on variation of power density with different junction temperatures and modelled the heat sink with analysis of thermal resistances.     

Magnetic field effect on indole exciplexes: an anomalous dielectric dependence

Individual exciplex formation between various aromatic hydrocarbons, anthracene, pyrene, all-s-trans-1,4-diphenylbuta-1,3-diene and a heteroaromatic amine, 1,2-dimethylindole, was investigated by steady-state fluorescence and magnetic field effect (MFE). A comparative study was carried out with two other exciplex systems 9-cyanophenanthrene-1,2-dimethylindole and 9-cyanophenanthrene-N-methylindole. The extent of charge transfer and dielectric dependence of MFE reveals the potential role of specific interactions related to exciplex geometry.     

The moduli space of flat SU (2) and SO (3) connections over surfaces

All the connected components of the moduli space of flat connections on SU (2) and SO (3) (trivial and non-trivial) bundles over closed oriented surfaces are determined. The symplectic structure and volumes of the non-maximal strata of the moduli space are also determined.     

The Efficiency Distribution Approach in Data Envelopment Analysis: An Application

A method is developed here for characterizing the empirical distribution of the efficient units in data envelopment analysis. Two empirical applications illustrate the various uses of the distribution approach. One involves the cost frontier which exhibits increasing returns to scale and the other involves a dynamic production frontier, where technological change causes a shift of the production frontier over time.     

Tunable circular patch antennas

A method to control the resonant or operating frequencies of circular patch antennas has been investigated experimentally and theoretically. It consists of the placement of passive metallic or tuning posts at approximate locations within the input region of the antenna. Comparison of measured and analytical results seems to establish the validity of a theoretical model proposed to determine the input performance of such circular patch antennas.     

Monopole charge quantization or why electromagnetism is a U(1)-gauge theory

We obtain Dirac’s classic monopole charge quantization from the point of view of geometric quantization and demonstrate how this leads to the conclusion that the electromagnetic field is a U(1)-gauge field.     

Spiking and Bursting in Josephson Junction

This brief reports spiking and bursting in numerical simulations of the resistive-capacitive-inductive shunted Josephson junction model. Regular spiking, intrinsic bursting, and fast spiking, which are usually seen in the mammalian neocortex, are observed in the junction dynamics under external dc bias. The junction voltage is amplitude and frequency modulated when forced by weaker sinusoidal forcing of frequency much lower than the junction resonant frequency. For stronger forcing, bursting is observed. The autonomous junction also shows bursting in the high inductive regime. Bifurcation scenarios of bursting are discussed for both autonomous and nonautonomous cases