A new look at C*-simplicity and the unique trace property of a group

We characterize when the reduced C*-algebra of a group has unique tracial state, respectively, is simple, in terms of Dixmier-type properties of the group C*-algebra. We also give a simple proof of the recent result by Breuillard, Kalantar, Kennedy and Ozawa that the reduced C*-algebra of a group has unique tracial state if and only if the amenable radical of the group is trivial.Comment: 8 page

Multiple Quantum NMR and Entanglement Dynamics in Dipolar Coupling Spin

We investigate numerically the time dependence of the multiple quantum coherences and entanglement in linear chains up to nine nuclear spins of 1/2 coupled by the dipole-dipole interactions. Two models are considered: (1) a spin chain with nearest-neighbor dipole -dipole interactions; (2) a more realistic model with interactions between all spins. It is shown that the entangled states appear between remote particles which do not interact directly (model 1), while the interaction between all spins (model 2) not always results in entanglement between remote spins.Comment: 14 pages, 3 figures. accepted for publication in Physical Review

Multiple Quantum NMR Dynamics in Dipolar Ordered Spin Systems

We investigate analytically and numerically the Multiple Quantum (MQ) NMR dynamics in systems of nuclear spins 1/2 coupled by the dipole-dipole interactions in the case of the dipolar ordered initial state. We suggest two different methods of MQ NMR. One of them is based on the measurement of the dipolar temperature in the quasi-equilibrium state which establishes after the time of order T2 after the MQ NMR experiment. The other method uses an additional resonance 45^0 -pulse after the preparation period of the standard MQ NMR experiment in solids. Many-spin clusters and correlations are created faster in such experiments than in the usual MQ NMR experiments and can be used for the investigation of many-spin dynamics of nuclear spins in solids.Comment: 11 pages, 3 figures. accepted for publication in Physical Review

An inquiry-based learning approach to teaching information retrieval

The study of information retrieval (IR) has increased in interest and importance with the explosive growth of online information in recent years. Learning about IR within formal courses of study enables users of search engines to use them more knowledgeably and effectively, while providing the starting point for the explorations of new researchers into novel search technologies. Although IR can be taught in a traditional manner of formal classroom instruction with students being led through the details of the subject and expected to reproduce this in assessment, the nature of IR as a topic makes it an ideal subject for inquiry-based learning approaches to teaching. In an inquiry-based learning approach students are introduced to the principles of a subject and then encouraged to develop their understanding by solving structured or open problems. Working through solutions in subsequent class discussions enables students to appreciate the availability of alternative solutions as proposed by their classmates. Following this approach students not only learn the details of IR techniques, but significantly, naturally learn to apply them in solution of problems. In doing this they not only gain an appreciation of alternative solutions to a problem, but also how to assess their relative strengths and weaknesses. Developing confidence and skills in problem solving enables student assessment to be structured around solution of problems. Thus students can be assessed on the basis of their understanding and ability to apply techniques, rather simply their skill at reciting facts. This has the additional benefit of encouraging general problem solving skills which can be of benefit in other subjects. This approach to teaching IR was successfully implemented in an undergraduate module where students were assessed in a written examination exploring their knowledge and understanding of the principles of IR and their ability to apply them to solving problems, and a written assignment based on developing an individual research proposal

Vortex State of Tl2_2Ba2_2CuO6+δ_{6+\delta} via 205^{205}Tl NMR at 2 Tesla

We report a $^{205}$Tl NMR study of vortex state for an aligned polycrystalline sample of an overdoped high-$T_c$ superconductor Tl$_2$Ba$_2$CuO$_{6+\delta}$ ($T_{c}\sim$85 K) with magnetic field 2 T along the c axis. We observed an imperfect vortex lattice, so-called Bragg glass at $T$=5 K, coexistence of vortex solid with liquid between 10 and 60 K, and vortex melting between 65 and 85 K. No evidence for local antiferromagnetic ordering at vortex cores was found for our sample.Comment: 4 pages with 5 figure

Non-Abelian Geometric Phase, Floquet Theory, and Periodic Dynamical Invariants

For a periodic Hamiltonian, periodic dynamical invariants may be used to obtain non-degenerate cyclic states. This observation is generalized to the degenerate cyclic states, and the relation between the periodic dynamical invariants and the Floquet decompositions of the time-evolution operator is elucidated. In particular, a necessary condition for the occurrence of cyclic non-adiabatic non-Abelian geometrical phase is derived. Degenerate cyclic states are obtained for a magnetic dipole interacting with a precessing magnetic field.Comment: Plain LaTeX, 13 pages, accepted for publication in J. Phys. A: Math. Ge

The multiple quantum NMR dynamics in systems of equivalent spins with the dipolar ordered initial state

The multiple quantum (MQ) NMR dynamics in the system of equivalent spins with the dipolar ordered initial state is considered. The high symmetry of the MQ Hamiltonian is used in order to develop the analytical and numerical methods for an investigation of the MQ NMR dynamics in the systems consisting of hundreds of spins from "the first principles". We obtain the dependence of the intensities of the MQ NMR coherences on their orders (profiles of the MQ NMR coherences) for the systems of $200 - 600$ spins. It is shown that these profiles may be well approximated by the exponential distribution functions. We also compare the MQ NMR dynamics in the systems of equivalent spins having two different initial states, namely the dipolar ordered state and the thermal equilibrium state in the strong external magnetic field.Comment: 11 pages 4 figure

Radiation in Lorentz violating electrodynamics

Synchrotron radiation is analyzed in the classical effective Lorentz invariance violating model of Myers-Pospelov. Within the full far-field approximation we compute the electric and magnetic fields, the angular distribution of the power spectrum and the total emitted power in the m-th harmonic, as well as the polarization. We find the appearance of rather unexpected and large amplifying factors, which go together with the otherwise negligible naive expansion parameter. This opens up the possibility of further exploring Lorentz invariance violations by synchrotron radiation measurements in astrophysical sources where these amplifying factors are important.Comment: Presented at the Second Mexican Meeting on Theoretical and Experimental Physics, El Colegio Nacional, Mexico City, 6-10 September 200