Comparison theory and smooth minimal C*-dynamics

We prove that the C*-algebra of a minimal diffeomorphism satisfies Blackadar's Fundamental Comparability Property for positive elements. This leads to the classification, in terms of K-theory and traces, of the isomorphism classes of countably generated Hilbert modules over such algebras, and to a similar classification for the closures of unitary orbits of self-adjoint elements. We also obtain a structure theorem for the Cuntz semigroup in this setting, and prove a conjecture of Blackadar and Handelman: the lower semicontinuous dimension functions are weakly dense in the space of all dimension functions. These results continue to hold in the broader setting of unital simple ASH algebras with slow dimension growth and stable rank one. Our main tool is a sharp bound on the radius of comparison of a recursive subhomogeneous C*-algebra. This is also used to construct uncountably many non-Morita-equivalent simple separable amenable C*-algebras with the same K-theory and tracial state space, providing a C*-algebraic analogue of McDuff's uncountable family of II_1 factors. We prove in passing that the range of the radius of comparison is exhausted by simple C*-algebras.Comment: 30 pages, no figure

Twisted k-graph algebras associated to Bratteli diagrams

Given a system of coverings of k-graphs, we show that the cohomology of the resulting (k+1)-graph is isomorphic to that of any one of the k-graphs in the system. We then consider Bratteli diagrams of 2-graphs whose twisted C*-algebras are matrix algebras over noncommutative tori. For such systems we calculate the ordered K-theory and the gauge-invariant semifinite traces of the resulting 3-graph C*-algebras. We deduce that every simple C*-algebra of this form is Morita equivalent to the C*-algebra of a rank-2 Bratteli diagram in the sense of Pask-Raeburn-R{\o}rdam-Sims.Comment: 28 pages, pictures prepared using tik

Information entropy in fragmenting systems

The possibility of facing critical phenomena in nuclear fragmentation is a topic of great interest. Different observables have been proposed to identify such a behavior, in particular, some related to the use of information entropy as a possible signal of critical behavior. In this work we critically examine some of the most widespread used ones comparing its performance in bond percolation and in the analysis of fragmenting Lennard Jones Drops.Comment: 3 pages, 3 figure

Nuclear multifragmentation and fission: similarity and differences

Thermal multifragmentation of hot nuclei is interpreted as the nuclear liquid--fog phase transition deep inside the spinodal region. The experimental data for p(8.1GeV) + Au collisions are analyzed. It is concluded that the decay process of hot nuclei is characterized by two size parameters: transition state and freeze-out volumes. The similarity between dynamics of fragmentation and ordinary fission is discussed. The IMF emission time is related to the mean rupture time at the multi-scission point, which corresponds to the kinetic freeze-out configuration.Comment: 7 pages, 3 Postscript figures, Proceedings of IWM 2005, Catani

Determination of the parameters of semiconducting CdF2:In with Schottky barriers from radio-frequency measurements

Physical properties of semiconducting CdF_2 crystals doped with In are determined from measurements of the radio-frequency response of a sample with Schottky barriers at frequencies 10 - 10^6 Hz. The dc conductivity, the activation energy of the amphoteric impurity, and the total concentration of the active In ions in CdF_2 are found through an equivalent-circuit analysis of the frequency dependencies of the sample complex impedance at temperatures from 20 K to 300 K. Kinetic coefficients determining the thermally induced transitions between the deep and the shallow states of the In impurity and the barrier height between these states are obtained from the time-dependent radio-frequency response after illumination of the material. The results on the low-frequency conductivity in CdF_2:In are compared with submillimeter (10^{11} - 10^{12} Hz) measurements and with room-temperature infrared measurements of undoped CdF_2. The low-frequency impedance measurements of semiconductor samples with Schottky barriers are shown to be a good tool for investigation of the physical properties of semiconductors.Comment: 9 pages, 7 figure

Approximation of excitonic absorption in disordered systems using a compositional component weighted CPA

Employing a recently developed technique of component weighted two particle Green's functions in the CPA of a binary substitutional alloy $A_cB_{1-c}$ we extend the existing theory of excitons in such media using a contact potential model for the interaction between electrons and holes to an approximation which interpolates correctly between the limits of weak and strong disorder. With our approach we are also able to treat the case where the contact interaction between carriers varies between sites of different types, thus introducing further disorder into the system. Based on this approach we study numerically how the formation of exciton bound states changes as the strengths of the contact potentials associated with either of the two site types are varied through a large range of parameter values.Comment: 27 pages RevTeX (preprint format), 13 Postscript figure file

Production of Neutron-rich Heavy Residues and the Freeze-out Temperature in the Fragmentation of Relativistic 238U Projectiles Determined by the Isospin Thermometer

Isotope yields of heavy residues produced in collisions of 238U with lead at 1AGeV show indications for a simultaneous break-up process. From the average N-over-Z ratio of the final residues up to Z = 70, the average limiting temperature of the break-up configuration at freeze out was determined to T approximately 5 MeV using the isospin-thermometer method. Consequences for the understanding of other phenomena in highly excited nuclear systems are discussed.Comment: 22 pages, 9 figures, accepted by Nucl. Phys.

Rokhlin Dimension for Flows

This research was supported by GIF Grant 1137/2011, SFB 878 Groups, Geometry and Actions and ERC Grant No. 267079. Part of the research was conducted at the Fields institute during the 2014 thematic program on abstract harmonic analysis, Banach and operator algebras, and at the Mittag–Leffler institute during the 2016 program on Classification of Operator Algebras: Complexity, Rigidity, and Dynamics.Peer reviewedPostprin

Classification of graph C*-algebras with no more than four primitive ideals

We describe the status quo of the classification problem of graph C*-algebras with four primitive ideals or less