Infinite compressibility states in the Hierarchical Reference Theory of fluids. II. Numerical evidence

Continuing our investigation into the Hierarchical Reference Theory of fluids for thermodynamic states of infinite isothermal compressibility kappa[T] we now turn to the available numerical evidence to elucidate the character of the partial differential equation: Of the three scenarios identified previously, only the assumption of the equations turning stiff when building up the divergence of kappa[T] allows for a satisfactory interpretation of the data. In addition to the asymptotic regime where the arguments of part I (cond-mat/0308467) directly apply, a similar mechanism is identified that gives rise to transient stiffness at intermediate cutoff for low enough temperature. Heuristic arguments point to a connection between the form of the Fourier transform of the perturbational part of the interaction potential and the cutoff where finite difference approximations of the differential equation cease to be applicable, and they highlight the rather special standing of the hard-core Yukawa potential as regards the severity of the computational difficulties.Comment: J. Stat. Phys., in press. Minor changes to match published versio

Capture and release of a conditional state of a cavity QED system by quantum feedback

Detection of a single photon escaping an optical cavity QED system prepares a nonclassical state of the electromagnetic field. The evolution of the state can be modified by changing the drive of the cavity. For the appropriate feedback, the conditional state can be captured (stabilized) and then released. This is observed by a conditional intensity measurement that shows suppression of vacuum Rabi oscillations for the length of the feedback pulse and their subsequent return

Determination of the resistivity anisotropy of SrRuO3_{3} by measuring the planar Hall effect

We have measured the planar Hall effect in epitaxial thin films of the itinerant ferromagnet SrRuO3 patterned with their current paths at different angles relative to the crystallographic axes. Based on the results, we have determined that SrRuO3 exhibits small resistivity anisotropy in the entire temperature range of our measurements (between 2 to 300 K); namely, both above and below its Curie temperature (~150 K). It means that in addition to anisotropy related to magnetism, the resistivity anisotropy of SrRuO3 has an intrinsic, nonmagnetic source. We have found that the two sources of anisotropy have competing effects

Uniaxial magnetocrystalline anisotropy in CaRuO3{\rm CaRuO_3}

${\rm CaRuO_3}$ is a paramagnetic metal and since its low temperature resistivity is described by $\rho=\rho_0+AT^\gamma$ with $\gamma \sim 1.5$, it is also considered a non-Fermi liquid (NFL) metal. We have performed extensive magnetoresistance and Hall effect measurements of untwinned epitaxial films of ${\rm CaRuO_3}$. These measurements reveal that ${\rm CaRuO_3}$ exhibits uniaxial magnetocrystalline anisotropy. In addition, the low-temperature NFL behavior is most effectively suppressed when a magnetic field is applied along the easy axis, suggesting that critical spin fluctuations, possibly due to proximity of a quantum critical phase transition, are related to the NFL behavior.Comment: 7 figure

Towards a unification of HRT and SCOZA. Analysis of exactly solvable mean-spherical and generalized mean-spherical models

The hierarchical reference theory (HRT) and the self-consistent Ornstein-Zernike approximation (SCOZA) are two liquid state theories that both furnish a largely satisfactory description of the critical region as well as the phase coexistence and equation of state in general. Furthermore, there are a number of similarities that suggest the possibility of a unification of both theories. Earlier in this respect we have studied consistency between the internal energy and free energy routes. As a next step toward this goal we here consider consistency with the compressibility route too, but we restrict explicit evaluations to a model whose exact solution is known showing that a unification works in that case. The model in question is the mean spherical model (MSM) which we here extend to a generalized MSM (GMSM). For this case, we show that the correct solutions can be recovered from suitable boundary conditions through either of SCOZA or HRT alone as well as by the combined theory. Furthermore, the relation between the HRT-SCOZA equations and those of SCOZA and HRT becomes transparent.Comment: Minimal correction of some typos found during proof reading. Accepted for publication in Phys. Rev.

A Tableaux Calculus for Reducing Proof Size

A tableau calculus is proposed, based on a compressed representation of clauses, where literals sharing a similar shape may be merged. The inferences applied on these literals are fused when possible, which reduces the size of the proof. It is shown that the obtained proof procedure is sound, refutationally complete and allows to reduce the size of the tableau by an exponential factor. The approach is compatible with all usual refinements of tableaux.Comment: Technical Repor

Paramagnetic anisotropic magnetoresistance in thin films of SrRuO3

SrRuO3 is an itinerant ferromagnet and in its thin film form when grown on miscut SrTiO3 it has Tc of ~ 150 K and strong uniaxial anisotropy. We measured both the Hall effect and the magnetoresistance (MR) of the films as a function of the angle between the applied field and the normal to the films at temperatures above Tc. We extracted the extraordinary Hall effect that is proportional to the perpendicular component of the magnetization and thus the MR for each angle of the applied field could be correlated with the magnitude and orientation of the induced magnetization. We successfully fit the MR data with a second order magnetization expansion, which indicates large anisotropic MR in the paramagnetic state. The extremum values of resistivity are not obtained for currents parallel or perpendicular to the magnetization, probably due to the crystal symmetry.Comment: 3 pages, 3 figure

Quaternion algebras with the same subfields

G. Prasad and A. Rapinchuk asked if two quaternion division F -algebras that have the same subfields are necessarily isomorphic. The answer is known to be "no" for some very large fields. We prove that the answer is "yes" if F is an extension of a global field K so that F /K is unirational and has zero unramified Brauer group. We also prove a similar result for Pfister forms and give an application to tractable fields