Series Expansion of the Off-Equilibrium Mode Coupling Equations

We show that computing the coefficients of the Taylor expansion of the solution of the off-equilibrium dynamical equations characterizing models with quenched disorder is a very effective way to understand the long time asymptotic behavior. We study the $p=3$ spherical spin glass model, and we compute the asymptotic energy (in the critical region and down to $T=0$) and the coefficients of the time decay of the energy.Comment: 9 pages, LaTeX, 3 uuencoded figure

On multi-dimensional hypocoercive BGK models

We study hypocoercivity for a class of linearized BGK models for continuous phase spaces. We develop methods for constructing entropy functionals that enable us to prove exponential relaxation to equilibrium with explicit and physically meaningful rates. In fact, we not only estimate the exponential rate, but also the second time scale governing the time one must wait before one begins to see the exponential relaxation in the L1 distance. This waiting time phenomenon, with a long plateau before the exponential decay "kicks in" when starting from initial data that is well-concentrated in phase space, is familiar from work of Aldous and Diaconis on Markov chains, but is new in our continuous phase space setting. Our strategies are based on the entropy and spectral methods, and we introduce a new "index of hypocoercivity" that is relevant to models of our type involving jump processes and not only diffusion. At the heart of our method is a decomposition technique that allows us to adapt Lyapunov's direct method to our continuous phase space setting in order to construct our entropy functionals. These are used to obtain precise information on linearized BGK models. Finally, we also prove local asymptotic stability of a nonlinear BGK model.Comment: 55 pages, 2 figure

Novel protein crystal growth technology: Proof of concept

A technology for crystal growth, which overcomes certain shortcomings of other techniques, is developed and its applicability to proteins is examined. There were several unknowns to be determined: the design of the apparatus for suspension of crystals of varying (growing) diameter, control of the temperature and supersaturation, the methods for seeding and/or controlling nucleation, the effect on protein solutions of the temperature oscillations arising from the circulation, and the effect of the fluid shear on the suspended crystals. Extensive effort was put forth to grow lysozyme crystals. Under conditions favorable to the growth of tetragonal lysozyme, spontaneous nucleation could be produced but the number of nuclei could not be controlled. Seed transfer techniques were developed and implemented. When conditions for the orthorhombic form were tried, a single crystal 1.5 x 0.5 x 0.2 mm was grown (after in situ nucleation) and successfully extracted. A mathematical model was developed to predict the flow velocity as a function of the geometry and the operating temperatures. The model can also be used to scaleup the apparatus for growing larger crystals of other materials such as water soluble non-linear optical materials. This crystal suspension technology also shows promise for high quality solution growth of optical materials such as TGS and KDP

4D-XY quantum criticality in a doped Mott insulator

A new phenomenology is proposed for the superfluid density of strongly underdoped cuprate superconductors based on recent data for ultra-clean single crystals of YBCO. The data feature a puzzling departure from Uemura scaling and a decline of the slope as the T_c = 0 quantum critical point is approached. We show that this behavior can be understood in terms of the renormalization of quasiparticle effective charge by quantum fluctuations of the superconducting phase as described by a (3+1)-dimensional XY model. We calculate the renormalization of the superfluid density and its slope, explain the new phenomenology, and predict its eventual demise close to the QCP.Comment: Version published in PRL. For additional info and related work visit http://www.physics.ubc.ca/~fran

Two-pion exchange and strong form-factors in covariant field theories

In this work improvements to the application of the Gross equation to nuclear systems are tested. In particular we evaluate the two pion exchange diagrams, including the crossed-box diagram, using models developed within the spectator-on-mass-shell covariant formalism. We found that the form factors used in these models induce spurious contributions that violate the unitary cut requirement. We tested then some alternative form-factors in order to preserve the unitarity condition. With this new choice, the difference between the exact and the spectator-on-mass-shell amplitudes is of the order of the one boson scalar exchange, supporting the idea that this difference may be parameterized by this type of terms.Comment: RevTeX, 21 pages, 19 figures (PostScript

First steps of a nucleation theory in disordered systems

We devise a field theoretical formalism for a microscopic theory of nucleation processes and phase coexistence in finite dimensional glassy systems. We study disordered $p$-spin models with large but finite range of interaction. We work in the framework of glassy effective potential theory which in mean-field is a non-convex, two minima function of the overlap. We will associate metastability and phase coexistence with the existence of space inhomogeneous solution of suitable field equations and we will study the simplest of such solutions.Comment: 31 pages, 4 figures. Content revised, typos correcte

Metastable States, Relaxation Times and Free-energy Barriers in Finite Dimensional Glassy Systems

In this note we discuss metastability in a long-but-finite range disordered model for the glass transition. We show that relaxation is dominated by configuration belonging to metastable states and associate an in principle computable free-energy barrier to the equilibrium relaxation time. Adam-Gibbs like relaxation times appear naturally in this approach.Comment: 4 pages, 2 figures. Typos correcte

Majorana Fermions in Proximity-coupled Topological Insulator Nanowires

A topological insulator nanowire, proximity-coupled to an ordinary bulk s-wave superconductor and subject to a longitudinal applied magnetic field, is shown to realize a one-dimensional topological superconductor with unpaired Majorana fermions localized at both ends. This situation occurs under a wide range of conditions and constitutes what is possibly the most easily accessible physical realization of the elusive Majorana particles in a solid-state system.Comment: 4 pages + 4 figures. v2 to appear in PRB/RC. For related work and info visit http://www.physics.ubc.ca/~franz