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CPP: Fachverband Chemische Physik und Polymerphysik

CPP 11: Poster: New Instruments and Methods

CPP 11.2: Poster

Montag, 22. März 2010, 16:30–18:00, Poster C

Replacement of Density Matrix Calculations by Observable Equations — •Günter Hempel — Martin-Luther-Universität, Institut für Physik, Betty-Heimann-Str, 7, 06120 Halle

The density matrix formalism is used frequently for calculations of the time evolution of spin systems, e.g. in magnetic resonance spectroscopy. The dimension of the density matrix, however, increases strongly if the number of participating spins grows. As an example, the still small system of three protons and one carbon-13 nucleus generates a 16-dimensional Hilbert space of wave functions leading to a density matrix of 256 elements. Often symmetry relations allow to conclude that some of the elements are constant or zero, others might be linearely dependent on anothers again, but nevertheless the number of differential equations we are left with might be very large. To obtain shorter systems of differential equations a method is proposed which transforms the Liouville-von Neumann-equation into a system of differential equations of observables (instead into one of matrix elements). Generally the number of differential equations of observables is essentially smaller that that of density-element equations. Examples are given which demonstrate the handling of the method and the reduction of the system of differential equations. Applications concern the spin dynamics during polarization transfer within ensembles of spin systems as well as elementary processes of spin diffusion.