Solvable Examples of Drift and Diffusion of Ions in Non-uniform Electric Fields

The drift and diffusion of a cloud of ions in a fluid are distorted by an inhomogeneous electric field. If the electric field carries the center of the distribution in a straight line and the field configuration is suitably symmetric, the distortion can be calculated analytically. We examine the specific examples of fields with cylindrical and spherical symmetry in detail assuming the ion distributions to be of a generally Gaussian form. The effects of differing diffusion coefficients in the transverse and longitudinal directions are included

Pressure dependence of the magnetization in the ferromagnetic superconductor UGe_2

The recent discovery that superconductivity occurs in several clean itinerant ferromagnets close to low temperature magnetic instabilities naturally invites an interpretation based on a proximity to quantum criticality. Here we report measurements of the pressure dependence of the low temperature magnetisation in one of these materials, UGe_2. Our results show that both of the magnetic transitions observed in this material as a function of pressure are first order transitions and do not therefore correspond to quantum critical points. Further we find that the known pressure dependence of the superconducting transition is not reflected in the pressure dependence of the static susceptibility. This demonstrates that the spectrum of excitations giving superconductivity is not that normally associated with a proximity to quantum criticality in weak itinerant ferromagnets. In contrast our data suggest that instead the pairing spectrum might be related to a sharp spike in the electronic density of states that also drives one of the magnetic transitions.Comment: to appear in Phys. Rev. Let

A scanning drift tube apparatus for spatio-temporal mapping of electron swarms

A "scanning" drift tube apparatus, capable of mapping of the spatio-temporal evolution of electron swarms, developing between two plane electrodes under the effect of a homogeneous electric field, is presented. The electron swarms are initiated by photoelectron pulses and the temporal distributions of the electron flux are recorded while the electrode gap length (at a fixed electric field strength) is varied. Operation of the system is tested and verified with argon gas, the measured data are used for the evaluation of the electron bulk drift velocity. The experimental results for the space-time maps of the electron swarms - presented here for the first time - also allow clear observation of deviations from hydrodynamic transport. The swarm maps are also reproduced by particle simulations

Microscopic theories for cubic and tetrahedral superconductors: application to PrOs_4Sb_{12}

We examine weak-coupling theory for unconventional superconducting states of cubic or tetrahedral symmetry for arbitrary order parameters and Fermi surfaces and identify the stable states in zero applied field. We further examine the possibility of having multiple superconducting transitions arising from the weak breaking of a higher symmetry group to cubic or tetrahedral symmetry. Specifically, we consider two higher symmetry groups. The first is a weak crystal field theory in which the spin-singlet Cooper pairs have an approximate spherical symmetry. The second is a weak spin orbit coupling theory for which spin-triplet Cooper pairs have a cubic orbital symmetry and an approximate spherical spin rotational symmetry. In hexagonal UPt_3, these theories easily give rise to multiple transitions. However, we find that for cubic materials, there is only one case in which two superconducting transitions occur within weak coupling theory. This sequence of transitions does not agree with the observed properties of PrOs_4Sb_{12}. Consequently, we find that to explain two transitions in PrOs_4Sb_{12} using approximate higher symmetry groups requires a strong coupling theory. In view of this, we finally consider a weak coupling theory for which two singlet representations have accidentally nearly degenerate transition temperatures (not due to any approximate symmetries). We provide an example of such a theory that agrees with the observed properties of PrOs_4Sb_{12}.Comment: 11 pages,1 figur

An Experimental Investigation of the Scaling of Columnar Joints

Columnar jointing is a fracture pattern common in igneous rocks in which cracks self-organize into a roughly hexagonal arrangement, leaving behind an ordered colonnade. We report observations of columnar jointing in a laboratory analog system, desiccated corn starch slurries. Using measurements of moisture density, evaporation rates, and fracture advance rates as evidence, we suggest an advective-diffusive system is responsible for the rough scaling behavior of columnar joints. This theory explains the order of magnitude difference in scales between jointing in lavas and in starches. We investigated the scaling of average columnar cross-sectional areas due to the evaporation rate, the analog of the cooling rate of igneous columnar joints. We measured column areas in experiments where the evaporation rate depended on lamp height and time, in experiments where the evaporation rate was fixed using feedback methods, and in experiments where gelatin was added to vary the rheology of the starch. Our results suggest that the column area at a particular depth is related to both the current conditions, and hysteretically to the geometry of the pattern at previous depths. We argue that there exists a range of stable column scales allowed for any particular evaporation rate.Comment: 12 pages, 11 figures, for supporting online movies, go to http://www.physics.utoronto.ca/nonlinear/movies/starch_movies.htm

Force Dependence of the Michaelis Constant in a Two-State Ratchet Model for Molecular Motors

We present a quantitative analysis of recent data on the kinetics of ATP hydrolysis, which has presented a puzzle regarding the load dependence of the Michaelis constant. Within the framework of coarse grained two-state ratchet models, our analysis not only explains the puzzling data, but provides a modified Michaelis law, which could be useful as a guide for future experiments.Comment: 4 pages, 3 eps figures, accepted for publication on Physical Review Letter

The Magnetic Phase Diagram and the Pressure and Field Dependence of the Fermi Surface in UGe2_2

The ac susceptibility and de Haas-van Alphen (dHvA) effect in UGe$_2$ are measured at pressures {\it P} up to 17.7 kbar for the magnetic field {\it B} parallel to the {\it a} axis, which is the easy axis of magnetization. Two anomalies are observed at {\it B$_x$}({\it P}) and {\it B}$_m$({\it P}) ({\it B$_x$} $>$ {\it B}$_m$ at any {\it P}), and the {\it P}-{\it B} phase diagram is presented. The Fermi surface and quasiparticle mass are found to vary smoothly with pressure up to 17.7 kbar unless the phase boundary {\it B$_x$}({\it P}) is crossed. The observed dHvA frequencies may be grouped into three according to their pressure dependences, which are largely positive, nearly constant or negative. It is suggested that the quasiparticle mass moderately increases as the boundary {\it B$_x$}({\it P}) is approached. DHvA effect measurements are also performed across the boundary at 16.8 kbar.Comment: to be published in Phys. Rev.

Nodal domains of Maass forms I

This paper deals with some questions that have received a lot of attention since they were raised by Hejhal and Rackner in their 1992 numerical computations of Maass forms. We establish sharp upper and lower bounds for the $L^2$-restrictions of these forms to certain curves on the modular surface. These results, together with the Lindelof Hypothesis and known subconvex $L^\infty$-bounds are applied to prove that locally the number of nodal domains of such a form goes to infinity with its eigenvalue.Comment: To appear in GAF