A classification of involutive automorphisms of an affine Kac-Moody lie algebra

AbstractIn this thesis we classify the conjugacy classes of involutions in Aut g, where g is an affine Kac-Moody Lie Algebra. We distinguish between two kinds of involutions, those which preserve the conjugacy class of a Borel subalgebra and those which don't.We give a complete and non-redundant list of representatives of involutions of the first kind and we compute their fixed points sets. We prove that any involution of the first kind has a conjugate which leaves invariant the components of the Gauss decomposition g = n− ⊕h⊕n+. We also give a complete list of representatives of the conjugacy classes of involutions of the second kind

Gaussian to Exponential Crossover in the Attenuation of Polarization Echoes in NMR

An ingenious pulse sequence devised by S. Zhang, B. H. Meier, and R. R. Ernst (Phys. Rev. Lett. {\bf 69}, 2149 (1992)) reverses the time evolution (``spin diffusion'') of the local polarization in a dipolar coupled $^{1}$H spin system. This refocusing originates a Polarization Echo whose amplitude attenuates by increasing the time $t_R$ elapsed until the dynamics is reversed. Different functional attenuations are found for a set of dipolar coupled systems: ferrocene, (C$_5$H$_5$)$_2$Fe, cymantrene, (C$_5$H$_5$)Mn(CO)$_3$, and cobaltocene, (C$_5$H$_5$)$_2$Co. To control a relevant variable involved in this attenuation a pulse sequence has been devised to progressively reduce the dipolar dynamics. Since it reduces the evolution of the polarization echo it is referred as REPE sequence. Two extreme behaviors were found while characterizing the materials: In systems with a strong source of relaxation and slow dynamics, the attenuation follows an exponential law (cymantrene). In systems with a strong dipolar dynamics the attenuation is mainly Gaussian. By the application of the REPE sequence the characteristic time of the Gaussian decay is increased until the presence of an underlying dissipative mechanism is revealed (cobaltocene). For ferrocene, however, the attenuation remains Gaussian within the experimental time scale. These two behaviors suggest that the many body quantum dynamics presents an extreme intrinsic instability which, in the presence of small perturbations, leads to the onset of irreversibility. This experimental conclusion is consistent with the tendencies displayed by the numerical solutions of model systems.Comment: 7 pages + 7 Postscript figure

CSI4FS - A Markerless Augmented Reality Application for Forensic Science Crime Scene Investigation Training

A capstone submitted in partial fulfillment of the requirements for the degree of Doctor of Education in the College of Education at Morehead State University by Ian Levstein on April 9, 2018

Spin projection chromatography

We formulate the many-body spin dynamics at high temperature within the non-equilibrium Keldysh formalism. For the simplest XY interaction, analytical expressions in terms of the one particle solutions are obtained for linear and ring configurations. For small rings of even spin number, the group velocities of excitations depend on the parity of the total spin projection. This should enable a dynamical filtering of spin projections with a given parity i.e. a Spin projection chromatography.Comment: 13 pages, 3 figure

Attenuation of polarization echoes in NMR: A study of the emergence of dynamical irreversibility in many-body quantum systems

The reversal of the time evolution of the local polarization in an interacting spin system involves a sign change of the effective dipolar Hamiltonian which refocuses the 'spin diffusion' process generating a polarization echo. Here, the attenuation of these echo amplitudes as a function of evolution time is presented for cymantrene and ferrocene polycrystalline samples, involving one and two five spin rings per molecule respectively. We calculate the fraction of polarization which is not refocused because only the secular part of the dipolar Hamiltonian is inverted. The results indicate that, as long as the spin dynamics is restricted to a single ring, the non-inverted part of the Hamiltonian is notable by itself to explain the whole decay of the polarization echoes. A cross over from exponential (cymantrene) to Gaussian (ferrocene) attenuation is experimentally observed. This is attributed to an increase of the relative importance of the spin dynamics, as compared with irreversible interactions, which favors dynamical irreversibility.Comment: 6 pages in Revtex, 11 Postscript figures. Final versio