Vector model, dynamic processes density matrix

Contents 1. Introduction 176 2. Static NMR Spectra and the Description of Dynamic Exchange Processes 178 2.1. Simulation of static NMR spectra 178 2.2. Simulation of DNMR spectra with average density matrix method 180 3. Calculation of DNMR Spectra with the Kinetic Monte Carlo Method 182 3.1. Kinetic description of the exchange processes 183 3.2. Kinetic Monte Carlo simulation of DNMR spectra for uncoupled spin systems 188 3.3. Kinetic Monte Carlo simulation of coupled spin systems 196 3.4. The individual density matrix 198 3.5. Calculating the FID of a coupled spin system 200 3.6. Vector model and density matrix in case of dynamic processes 205 4. Summary 211 Acknowledgements 212 References 212... 

Vector model and density matrix in case of dynamic processes... 

The same types of graphic analysis for any choice of the matrix V are used. Here an example of the graphic analysis based on an industrial on-line data is presented. The figures illustrate results of static linear PLS model, in which NIR data fix>m an oil refinery is used to model density of the product The vectors in the algorithm are displayed graphically to illustrate the structure and variation in data. The basic plots are 1. ta versus it, The vectors (t,) decompose the data matrix X. Therefore the plots of t, versus tb show us the sample (time) variation in data. Fig 1 reveals that the process (samples) is changing with the time. Arrows in Fig 1 visualise the drift on 1.-4. PLS components. The dynamic behaviour can be clearly seen even on the first two score vectors. Therefore, it cannot be expected that the same model will be valid at the... 

Now consider the quantum dynamics of the same system. If the discs scatter a plane wave of wave vector k, the same matrix describes the scattering processes in the classical and semiclassical descriptions, but in the latter the parameters must be fixed as follows z = -ik,r = -l for Dirichlet boundary conditions,and P = 1/2 because the square of the wave function is the density of probabilityTherefore, we can analyze both the classical and the quantum dynamics of this model system with the same formalism, keeping in mind the different definitions of the parameters z, P and r. In the following we shall consider only the case lrl = l. 

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See also in sourсe #XX -- [ ]

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