Gaussian software harmonic osscialtor approximation

#Gaussian software harmonic osscialtor approximation free#

It has 2 parameters only Р В Р вЂ Р В РІР‚С™Р Р†Р вЂљРЎС™ the plasma frequency is directly related to the concentration of charge carriers whereas the damping constant is connected to the mobility (or the inverse mean free path). The absorption of light by the acceleration of free charges in a metal or doped semiconductor can be described by the classical Drude model. The so-called Р В Р вЂ Р В РІР‚С™Р вЂ™Р’ВKim oscillatorР В Р вЂ Р В РІР‚С™Р Р†РІР‚С›РЎС› model uses a Gaussian decay of the damping with distance from the center of the oscillator and it fits many absorption bands very nicely, much better than the harmonic oscillator:Р В РІР‚СњР вЂ™Р’В«esides describing vibrational modes the Kim oscillator can also model high energy interband transitions above the OJL model and the broad band absorption of confined charge carriers (which are almost free but are blocked to leave a microcrystal). So whatever causes the damping will be stronger close to the resonance frequency and weaker far away from it Р В Р вЂ Р В РІР‚С™Р Р†Р вЂљРЎС™ at least this is very likely. As the amplitude of whatever vibration we might have is certainly stronger in the resonance region the interaction with the outside world is certainly stronger. the vibration is slowed down in the same way in the center (where the absorption is strong) as in the regions of small absorption. The reason is that the harmonic oscillator has a constant damping parameter, i.e. The model is ok but the overall shape of the absorption bands is not reproduced very well. Here is an attempt to describe 2 strong and a weak side band of molecules on a metal surface: Vibrational modesР В РІР‚СњР В РІР‚С›lthough harmonic oscillators should be the right tool to describe vibrating parts of molecules or crystal lattices they are simplifying too much. In addition, the band gap parameter as well as the tail state exponent (also called Р В Р вЂ Р В РІР‚С™Р вЂ™Р’Вdisorder parameterР В Р вЂ Р В РІР‚С™Р Р†РІР‚С›РЎС›) have physical meaning and characterize the state of the material. This makes fitting optical constants rather easy. It is based on some very simple assumptions about the interband transition and states within the band gap which are caused by disorder:Р В РІР‚СњР В РІР‚РЋor many materials the OJL model produces the correct shape of n and k with a few parameters only: For band transitions of crystalline materials the Tauc-Lorentz model is appropriate:Р В РІР‚СњР вЂ™Р’В«e prepared to superimpose several of these terms since crystalline materials may have feature many interband transitions, like AlGaAs:Р В РІР‚СњР В РІР‚С›morphous semiconductors and almost all oxides and nitrides used in thin film applications can be described by the so-called OJL model. However, these are not very realistic and should be used far away from the resonance frequency of the oscillator only. lifting up electrons from an occupied electronic state to an empty state (interband transitions)Р В РІР‚СњР вЂ™Р’В®lectronic transitions can be roughly described by simple harmonic oscillators.exciting oscillations of bound charges (vibrational modes).acceleration of free charge carriers in conductive materials (free charge carrier absorption).

Optical constant models describe the response of matter to the electric fields of a light wave. Combined with todayР В Р вЂ Р В РІР‚С™Р Р†РІР‚С›РЎС›s fast computer hardware they provide the basis of high quality modelling.

They explain some model improvements that were implemented a long time ago. The results of the paper are applicable to the design of suboptimal controllers and filters for nonlinear quantum systems.Answering some recent questions about optical modelling, I dug out some old slides. We demonstrate the proposed Hamiltonian-based Gaussian linearization for the quantum Duffing oscillator whose Hamiltonian is a quadro-quartic polynomial of the momentum and position operators. This approximation is carried out in a mean square optimal sense with respect to a Gaussian reference quantum state and leads to a self-consistent linearization procedure where the mean vector and quantum covariance matrix of the system observables evolve in time according to the effective linear dynamics. The linearization proceeds by approximating the actual Hamiltonian of the quantum system by a quadratic function of its observables which corresponds to the Hamiltonian of a quantum harmonic oscillator.

This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential equations with non-quadratic Hamiltonians.

Gaussian software harmonic osscialtor approximation