Semiprojectivity with and without a group action

The equivariant version of semiprojectivity was recently introduced by the first author. We study properties of this notion, in particular its relation to ordinary semiprojectivity of the crossed product and of the algebra itself. We show that equivariant semiprojectivity is preserved when the action is restricted to a cocompact subgroup. Thus, if a second countable compact group acts semiprojectively on a C*-algebra $A$, then $A$ must be semiprojective. This fails for noncompact groups: we construct a semiprojective action of the integers on a nonsemiprojective C*-algebra. We also study equivariant projectivity and obtain analogous results, however with fewer restrictions on the subgroup. For example, if a discrete group acts projectively on a C*-algebra $A$, then $A$ must be projective. This is in contrast to the semiprojective case. We show that the crossed product by a semiprojective action of a finite group on a unital C*-algebra is a semiprojective C*-algebra. We give examples to show that this does not generalize to all compact groups.Comment: 38 page

Nearest-neighbour Attraction Stabilizes Staggered Currents in the 2D Hubbard Model

Using a strong-coupling approach, we show that staggered current vorticity does not obtain in the repulsive 2D Hubbard model for large on-site Coulomb interactions, as in the case of the copper oxide superconductors. This trend also persists even when nearest-neighbour repulsions are present. However, staggered flux ordering emerges {\bf only} when attractive nearest-neighbour Coulomb interactions are included. Such ordering opens a gap along the $(\pi,0)-(0,\pi)$ direction and persists over a reasonable range of doping.Comment: 5 pages with 5 .eps files (Typos in text are corrected

Strain dependence of the acoustic properties of amorphous metals below 1K: Evidence for the interaction between tunneling states

We have conducted a thorough study of the acoustic properties between 10^-4 and 1 Kelvin for the amorphous metal Zr_x Cu_1-x (x=0.3 and x=0.4), by measuring the relative change of sound velocity dv/v and internal friction Q^-1 as a function of temperature and also of the applied strain, in both superconducting and normal state. We have found that when plotted versus the ratio of strain energy to thermal energy, all measurements display the same behavior: a crossover from a linear regime of ``independent'' tunneling systems at very low strains and/or high enough temperatures to a nonlinear regime where dv/v and Q^-1 depend on applied strain and the tunneling systems cannot be considered as independent.Comment: 4 pages, 4 figures (submitted to PRL

UCT-Kirchberg algebras have nuclear dimension one

We prove that every Kirchberg algebra in the UCT class has nuclear dimension 1. We first show that Kirchberg 2-graph algebras with trivial $K_0$ and finite $K_1$ have nuclear dimension 1 by adapting a technique developed by Winter and Zacharias for Cuntz algebras. We then prove that every Kirchberg algebra in the UCT class is a direct limit of 2-graph algebras to obtain our main theorem.Comment: 21 pages. Version 2: reference [2] has been added, and the discussion in the introduction updated; a small but important typo has been corrected in the definition of the graph E_T. Version 3: Some typo's corrected and references updated; reference [2] corrected as we had accidentally omitted one of the authors' names in the previous version (sorry Aaron!); this version to appear in Adv. Mat

A Solvable Model of a Glass

An analytically tractable model is introduced which exhibits both, a glass--like freezing transition, and a collection of double--well configurations in its zero--temperature potential energy landscape. The latter are generally believed to be responsible for the anomalous low--temperature properties of glass-like and amorphous systems via a tunneling mechanism that allows particles to move back and forth between adjacent potential energy minima. Using mean--field and replica methods, we are able to compute the distribution of asymmetries and barrier--heights of the double--well configurations {\em analytically}, and thereby check various assumptions of the standard tunneling model. We find, in particular, strong correlations between asymmetries and barrier--heights as well as a collection of single--well configurations in the potential energy landscape of the glass--forming system --- in contrast to the assumptions of the standard model. Nevertheless, the specific heat scales linearly with temperature over a wide range of low temperatures.Comment: 11 pages, latex, including 5 figures, talk presented at the XIV Sitges Conferenc

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

Is weak temperature dependence of electron dephasing possible?

The first-principle theory of electron dephasing by disorder-induced two state fluctuators is developed. There exist two mechanisms of dephasing. First, dephasing occurs due to direct transitions between the defect levels caused by inelastic electron-defect scattering. The second mechanism is due to violation of the time reversal symmetry caused by time-dependent fluctuations of the scattering potential. These fluctuations originate from an interaction between the dynamic defects and conduction electrons forming a thermal bath. The first contribution to the dephasing rate saturates as temperature decreases. The second contribution does not saturate, although its temperature dependence is rather weak, $\propto T^{1/3}$. The quantitative estimates based on the experimental data show that these mechanisms considered can explain the weak temperature dependence of the dephasing rate in some temperature interval. However, below some temperature dependent on the model of dynamic defects the dephasing rate tends rapidly to zero. The relation to earlier studies of the dephasing caused by the dynamical defects is discussed.Comment: 14 pages, 6 figures, submitted to PR

Moving Atom-Field Interaction: Correction to Casimir-Polder Effect from Coherent Back-action

The Casimir-Polder force is an attractive force between a polarizable atom and a conducting or dielectric boundary. Its original computation was in terms of the Lamb shift of the atomic ground state in an electromagnetic field (EMF) modified by boundary conditions along the wall and assuming a stationary atom. We calculate the corrections to this force due to a moving atom, demanding maximal preservation of entanglement generated by the moving atom-conducting wall system. We do this by using non-perturbative path integral techniques which allow for coherent back-action and thus can treat non-Markovian processes. We recompute the atom-wall force for a conducting boundary by allowing the bare atom-EMF ground state to evolve (or self-dress) into the interacting ground state. We find a clear distinction between the cases of stationary and adiabatic motions. Our result for the retardation correction for adiabatic motion is up to twice as much as that computed for stationary atoms. We give physical interpretations of both the stationary and adiabatic atom-wall forces in terms of alteration of the virtual photon cloud surrounding the atom by the wall and the Doppler effect.Comment: 16 pages, 2 figures, clarified discussions; to appear in Phys. Rev.

Heavy Carriers and Non-Drude Optical Conductivity in MnSi

Optical properties of the weakly helimagnetic metal MnSi have been determined in the photon energy range from 2 meV to 4.5 eV using the combination of grazing incidence reflectance at 80 degrees (2 meV to 0.8 eV) and ellipsometry (0.8 to 4.5 eV). As the sample is cooled below 100 K the effective mass becomes strongly frequency dependent at low frequencies, while the scattering rate developes a linear frequency dependence. The complex optical conductivity can be described by the phenomenological relation \sigma(\omega,T) \propto (\Gamma(T)+i\omega)^{-1/2} used for cuprates and ruthenates.Comment: 5 pages, ReVTeX 4, 5 figures in eps forma

Origin of strange metallic phase in cuprate superconductors

The origin of strange metallic phase is shown to exist due to these two conditions---(i) the electrons are strongly interacting such that there are no band and Mott-Hubbard gaps, and (ii) the electronic energy levels are crossed in such a way that there is an electronic energy gap between two energy levels associated to two different wave functions. The theory is also exploited to explain (i) the upward- and downward-shifts in the $T$-linear resistivity curves, and (ii) the spectral weight transfer observed in the soft X-ray absorption spectroscopic measurements of the La-Sr-Cu-O Mott insulator.Comment: To be published in J. Supercond. Nov. Mag