Gaussian Belief with dynamic data and in dynamic network

In this paper we analyse Belief Propagation over a Gaussian model in a dynamic environment. Recently, this has been proposed as a method to average local measurement values by a distributed protocol ("Consensus Propagation", Moallemi & Van Roy, 2006), where the average is available for read-out at every single node. In the case that the underlying network is constant but the values to be averaged fluctuate ("dynamic data"), convergence and accuracy are determined by the spectral properties of an associated Ruelle-Perron-Frobenius operator. For Gaussian models on Erdos-Renyi graphs, numerical computation points to a spectral gap remaining in the large-size limit, implying exceptionally good scalability. In a model where the underlying network also fluctuates ("dynamic network"), averaging is more effective than in the dynamic data case. Altogether, this implies very good performance of these methods in very large systems, and opens a new field of statistical physics of large (and dynamic) information systems.Comment: 5 pages, 7 figure

On peak phenomena for non-commutative H∞H^\infty

A non-commutative extension of Amar and Lederer's peak set result is given. As its simple applications it is shown that any non-commutative $H^\infty$-algebra $H^\infty(M,\tau)$ has unique predual,and moreover some restriction in some of the results of Blecher and Labuschagne are removed, making them hold in full generality.Comment: final version (the presentation of some part is revised and one reference added

Universal Behavior of Heavy-Fermion Metals Near a Quantum Critical Point

The behavior of the electronic system of heavy fermion metals is considered. We show that there exist at least two main types of the behavior when the system is nearby a quantum critical point which can be identified as the fermion condensation quantum phase transition (FCQPT). We show that the first type is represented by the behavior of a highly correlated Fermi-liquid, while the second type is depicted by the behavior of a strongly correlated Fermi-liquid. If the system approaches FCQPT from the disordered phase, it can be viewed as a highly correlated Fermi-liquid which at low temperatures exhibits the behavior of Landau Fermi liquid (LFL). At higher temperatures $T$, it demonstrates the non-Fermi liquid (NFL) behavior which can be converted into the LFL behavior by the application of magnetic fields $B$. If the system has undergone FCQPT, it can be considered as a strongly correlated Fermi-liquid which demonstrates the NFL behavior even at low temperatures. It can be turned into LFL by applying magnetic fields $B$. We show that the effective mass $M^*$ diverges at the very point that the N\'eel temperature goes to zero. The $B-T$ phase diagrams of both liquids are studied. We demonstrate that these $B-T$ phase diagrams have a strong impact on the main properties of heavy-fermion metals such as the magnetoresistance, resistivity, specific heat, magnetization, volume thermal expansion, etc.Comment: Revtex, 11 pages, revised and accepted by JETP Let

Behavior of Fermi Systems Approaching Fermion Condensation Quantum Phase Transition from Disordered Phase

The behavior of Fermi systems which approach the fermion condensation quantum phase transition (FCQPT) from the disordered phase is considered. We show that the quasiparticle effective mass $M^*$ diverges as $M^*\propto 1/|x-x_{FC}|$ where $x$ is the system density and $x_{FC}$ is the critical point at which FCQPT occurs. Such a behavior is of general form and takes place in both three dimensional (3D) systems and two dimensional (2D) ones. Since the effective mass $M^*$ is finite, the system exhibits the Landau Fermi liquid behavior. At $|x-x_{FC}|/x_{FC}\ll 1$, the behavior can be viewed as a highly correlated one, because the effective mass is large and strongly depends on the density. In case of electronic systems the Wiedemann-Franz law is held and Kadowaki-Woods ratio is preserved. Beyond the region $|x-x_{FC}|/x_{FC}\ll 1$, the effective mass is approximately constant and the system becomes conventional Landau Fermi liquid.Comment: 9 pages, revtex, no figure

Universal behavior of CePd1−xRhx\rm CePd_{1-x}Rh_x Ferromagnet at Quantum Critical Point

The heavy-fermion metal $\rm CePd_{1-x}Rh_x$ can be tuned from ferromagnetism at $x=0$ to non-magnetic state at some critical concentration $x_c$. The non-Fermi liquid behavior (NFL) at $x\simeq x_c$ is recognized by power low dependence of the specific heat $C(T)$ given by the electronic contribution, magnetic susceptibility $\chi(T)$ and volume expansion coefficient $\alpha(T)$ at low temperatures: $C/T\propto\chi(T)\propto\alpha(T)/T\propto1/\sqrt{T}$. We also demonstrate that the behavior of normalized effective mass $M^*_N$ observed in $\rm CePd_{1-x}Rh_x$ at $x\simeq 0.8$ agrees with that of $M^*_N$ observed in paramagnetic $\rm CeRu_2Si_2$ and conclude that these alloys exhibit the universal NFL thermodynamic behavior at their quantum critical points. We show that the NFL behavior of $\rm CePd_{1-x}Rh_x$ can be accounted for within frameworks of quasiparticle picture and fermion condensation quantum phase transition, while this alloy exhibits a universal thermodynamic NFL behavior which is independent of the characteristic features of the given alloy such as its lattice structure, magnetic ground state, dimension etc.Comment: 5 pages, 3 figure

Nodes of the Gap Function and Anomalies in Thermodynamic Properties of Superfluid 3^3He

Departures of thermodynamic properties of three-dimensional superfluid $^3$He from the predictions of BCS theory are analyzed. Attention is focused on deviations of the ratios $\Delta(T=0)/T_c$ and $[C_s(T_c)-C_n(T_c)]/C_n(T_c)$ from their BCS values, where $\Delta(T=0)$ is the pairing gap at zero temperature, $T_c$ is the critical temperature, and $C_s$ and $C_n$ are the superfluid and normal specific heats. We attribute these deviations to the momentum dependence of the gap function $\Delta(p)$, which becomes well pronounced when this function has a pair of nodes lying on either side of the Fermi surface. We demonstrate that such a situation arises if the P-wave pairing interaction $V(p_1,p_2)$, evaluated at the Fermi surface, has a sign opposite to that anticipated in BCS theory. Taking account of the momentum structure of the gap function, we derive a closed relation between the two ratios that contains no adjustable parameters and agrees with the experimental data. Some important features of the effective pairing interaction are inferred from the analysis.Comment: 17 pages, 4 figure

Energy scales and the non-Fermi liquid behavior in YbRh2Si2

Multiple energy scales are detected in measurements of the thermodynamic and transport properties in heavy fermion metals. We demonstrate that the experimental data on the energy scales can be well described by the scaling behavior of the effective mass at the fermion condensation quantum phase transition, and show that the dependence of the effective mass on temperature and applied magnetic fields gives rise to the non-Fermi liquid behavior. Our analysis is placed in the context of recent salient experimental results. Our calculations of the non-Fermi liquid behavior, of the scales and thermodynamic and transport properties are in good agreement with the heat capacity, magnetization, longitudinal magnetoresistance and magnetic entropy obtained in remarkable measurements on the heavy fermion metal YbRh2Si2.Comment: 8 pages, 8 figure

The Shape and Figure Rotation of NGC 2915's Dark Halo

NGC 2915 is a blue compact dwarf galaxy with a very extended HI disk showing a short central bar and extended spiral arms, both reaching far beyond the optical component. We use Tremaine & Weinberg (1984) method to measure the pattern speed of the bar from HI radio synthesis data. Our measurements yield a pattern speed of 0.21+/-0.06 km/s/arcsec (8.0+/-2.4 km/s/kpc for D=5.3 Mpc), in disagreement with the general view that corotation in barred disks lies just outside the end of the bar, but consistent with recent models of barred galaxies with dense dark matter halos. Our adopted bar semi-length puts corotation at more than 1.7 bar radii. The existence of the pattern is also problematic. Because NGC 2915 is isolated, interactions cannot account for the structure observed in the HI disk. We also demonstrate that the low observed disk surface density and the location of the pseudo-rings make it unlikely that swing amplification or bar-driven spiral arms could explain the bar and spiral pattern. Based on the similarity of the dark matter and HI surface density profiles, we discuss the possibility of dark matter distributed in a disk and following closely the HI distribution. The disk then becomes unstable and can naturally form a bar and spiral pattern. However, this explanation is hard to reconcile with some properties of NGC 2915. We also consider the effect of a massive and extended triaxial dark matter halo with a rotating figure. The existence of such halos is supported by CDM simulations showing strongly triaxial dark halos with slow figure rotation. The observed structure of the HI disk can then arise through forcing by the rotating triaxial figure. We associate the measured pattern speed in NGC 2915 with the figure rotation of its dark halo.Comment: 37 pages, including 8 figures and 2 tables (AASTeX, aaspp4.sty). Fig.1 and 2 available as jpg. Accepted for publication in The Astronomical Journal. Online manuscript with PostScript figures available at: http://www.strw.leidenuniv.nl/~bureau/pub_list.htm