Search results for "equation"
showing 10 items of 4219 documents
Generation of even harmonics of sub-THz radiation in bulk GaAs in the presence of a static electric field
2007
The static electric field effects on nonlinear carrier dynamics in low-doped GaAs bulk under the influence of an intense sub-terahertz field are studied by a three-dimensional multivalleys Monte Carlo simulation. The conversion efficiency is calculated by using the appropriate Maxwell equation for the propagation of an electromagnetic wave along a given direction in the medium. Production of odd and even harmonics due to the nonlinearity of the velocity-field relation is investigated.
Rigorous investigation of RF breakdown effects in high power microstrip passive circuits
2009
This work presents a new rigorous investigation of corona effects in microstrip components. To carry out the investigation, a new software tool has been developed. The new tool first calculates the electromagnetic fields in complex microstrip structures using a Volume Integral Equation (VIE) formulation. Novel numerical techniques have been incorporated in the VIE to increase the accuracy during the computation of the electromagnetic fields. This includes novel techniques introduced to treat the singularities of the Green's functions. Once the electromagnetic fields are computed accurately, corona effects in the relevant structures are investigated. For this, a numerical solution of the fre…
A method of variation of boundaries for waveguide grating couplers
2008
We describe a method for calculating the solution of the electromagnetic field in a non-rectilinear open waveguide by using a series expansion, starting from the field of a rectilinear waveguide. Our approach is based on a method of variation of boundaries. We prove that the obtained series expansion converges and we provide a radiation condition at infinity in such a way that the problem has a unique solution. Our approach can model several kinds of optical devices which are used in optical integrated circuits. Numerical examples will be shown for the case of finite aperiodic waveguide grating couplers.
"Dynamical" interactions and gauge invariance
2009
Appreciating the classical understanding of the elementary particle the "dynamical" Poincare algebra is developed. It is shown that the "dynamical" Poincare algebra and the equations of motion of particles with arbitrary spin are gauge invariant and that gauge invariance and relativistic invariance stand on equal footings. A "dynamical" non-minimal interaction is constructed explicitly and the Rarita-Schwinger equation is considered in the framework of this "dynamical" interaction.
The electromagnetic and Proca fields revisited: A unified quantization
1997
Quantizing the electromagnetic field with a group formalism faces the difficulty of how to turn the traditional gauge transformation of the vector potential, Aμ(x) → Aμ(x) + ∂μφ(x), into a group law. In this paper, it is shown that the problem can be solved by looking at gauge transformations in a slightly different manner which, in addition, does not require introducing any BRST-like parameter. This gauge transformation does not appear explicitly in the group law of the symmetry but rather as the trajectories associated with generalized equations of motion generated by vector fields with null Noether invariants. In the new approach the parameters of the local group, U(1)(x, t), acquire dyn…
Motion of an electric charge in a terrestrial laboratory.
1995
The equation of motion for a charge in an electromagnetic field is written in the Fermi coordinates of an observer moving with a constant acceleration g=9.8 m/${\mathrm{s}}^{2}$ (${10}^{\mathrm{\ensuremath{-}}18}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ in units such that c=1). This is involved in the equation of motion not only as a Newtonian term g\ensuremath{\rightarrow}, but also as a relativistic correction of the form ``-2(g\ensuremath{\rightarrow}\ensuremath{\cdot}v\ensuremath{\rightarrow})v\ensuremath{\rightarrow}.'' We have studied the effect of this term under the conditions of an accelerator of particles. To this end, we have considered a constant and uniform magnetic field, a…
Noncoaxial Inductance Calculations Without the Vector Potential for Axisymmetric Coils and Planar Coils
2008
This paper presents an exact method for calculating the mutual inductance between a general axisymmetric coil and a second planar coil consisting of either a disk coil or a planar loop of essentially arbitrary shape. The approach is based directly on the magnetic field rather than the vector potential . The paper gives detailed results for two circular loops, a circular loop and an elliptic loop, and a circular loop and an annular disk coil. The method can be extended to cover the cases where all these loops and coils are extruded in the axial direction to give the corresponding solenoids. The method is also applicable to calculations for nuclear radiation detectors.
Exactly solvable relativistic model with the anomalous interaction
2010
A special class of Dirac-Pauli equations with time-like vector potentials of an external field is investigated. An exactly solvable relativistic model describing the anomalous interaction of a neutral Dirac fermion with a cylindrically symmetric external electromagnetic field is presented. The related external field is a superposition of the electric field generated by a charged infinite filament and the magnetic field generated by a straight line current. In the nonrelativistic approximation the considered model is reduced to the integrable Pron'ko-Stroganov model.
Green’s Function of a Spin- 1 2 $$\tfrac {1}{2}$$ Particle in a Constant External Magnetic Field
2020
Our objective here is to find the Green’s function of a spin-\(\tfrac {1}{2}\) particle in an external electromagnetic field. Accordingly we start with the defining equation
Exact solution of generalized Tavis - Cummings models in quantum optics
1996
Quantum inverse methods are developed for the exact solution of models which describe N two-level atoms interacting with one mode of the quantized electromagnetic field containing an arbitrary number of excitations M. Either a Kerr-type nonlinearity or a Stark-shift term can be included in the model, and it is shown that these two cases can be mapped from one to the other. The method of solution provides a general framework within which many related problems can similarly be solved. Explicit formulae are given for the Rabi splitting of the models for some N and M, on- and off-resonance. It is also shown that the solution of the pure Tavis - Cummings model can be reduced to solving a homogen…