Stochastic modelling with randomized Markov bridges

We consider the filtering problem of estimating a hidden random variable X by noisy observations. The noisy observation process is constructed by a randomized Markov bridge (RMB) (Zt)t∈[0,T] of which terminal value is set to ZT=X. That is, at the terminal time T, the noise of the bridge process vanishes and the hidden random variable X is revealed. We derive the explicit filtering formula, governing the dynamics of the conditional probability process, for a general RMB. It turns out that the conditional probability is given by a function of current time t, the current observation Zt, the initial observation Z0, and the a priori distribution ν of X at t = 0. As an example for an RMB, we explicitly construct the skew-normal randomized diffusion bridge and show how it can be utilized to extend well-known commodity pricing models and how one may propose novel stochastic price models for financial instruments linked to greenhouse gas emissions

Anomalous elastic softening of SmRu_{4}P_{12} under high pressure

The filled skutterudite compound SmRu_4P_{12} undergoes a complex evolution from a paramagnetic metal (phase I) to a probable multipolar ordering insulator (phase II) at T_{MI} = 16.5 K, then to a magnetically ordered phase (phase III) at T_{N} = 14 K. Elastic properties under hydrostatic pressures were investigated to study the nature of the ordering phases. We found that distinct elastic softening above T_{MI} is induced by pressure, giving evidence of quadrupole degeneracy of the ground state in the crystalline electric field. It also suggests that quadrupole moment may be one of the order parameters below T_{MI} under pressure. Strangely, the largest degree of softening is found in the transverse elastic constant C_{T} at around 0.5-0.6 GPa, presumably having relevancy to the competing and very different Gruneisen parameters \Omega of T_{MI} and T_{N}. Interplay between the two phase transitions is also verified by the rapid increase of T_{MI} under pressure with a considerably large \Omega of 9. Our results can be understood on the basis of the proposed octupole scenario for SmRu_4P_{12}.Comment: 7 pages, 7 figure

Possible Kondo resonance in PrFe4P12 studied by bulk-sensitive photoemission

Pr 4f electronic states in Pr-based filled skutterudites PrT4X12(T=Fe and Ru; X=P and Sb) have been studied by high-resolution bulk-sensitive Pr 3d-4f resonance photoemission. A very strong spectral intensity is observed just below the Fermi level in the heavy-fermion system PrFe4P12. The increase of its intensity at lower temperatures is observed. We speculate that this is the Kondo resonance of Pr, the origin of which is attributed to the strong hybridization between the Pr 4f and the conduction electrons.Comment: 4 pages(camera ready format), 4 figures, ReVTeX

XANES study of rare-earth valency in LRu4P12 (L = Ce and Pr)

Valency of Ce and Pr in LRu4P12 (L = Ce and Pr) was studied by L2,3-edge x-ray absorption near-edge structure (XANES) spectroscopy. The Ce-L3 XANES spectrum suggests that Ce is mainly trivalent, but the 4f state strongly hybridizes with ligand orbitals. The band gap of CeRu4P12 seems to be formed by strong hybridization of 4f electrons. Pr-L2 XANES spectra indicate that Pr exists in trivalent state over a wide range in temperature, 20 < T < 300 K. We find that the metal-insulator (MI) transition at TMI = 60 K in PrRu4P12 does not originate from Pr valence fluctuation.Comment: 4 page

Diffraction from Ordered States of Higher Multipoles

Possible ways of identification are discussed of an electronic order of higher multipoles such as octupoles and hexadecapoles. A particularly powerful method is resonant X-ray scattering (RXS) using quadrupolar resonance processes called E2.The characteristic azimuthal angle dependence of Ce$_{0.7}$La$_{0.3}$B$_6$ is interpreted as evidence of antiferro-octupole order. For PrRu$_4$P$_{12}$, eightfold pattern against azimuthal angle is predicted if its metal-insulator transition is a consequence of a hexadecapole order. In non-resonant superlattice Bragg scattering, hexadecapole contribution may also be identified because of absence of quadrupole component.Comment: Invited paper to be published in Proc. Hiroshima Workshop on Novel Functional Materials with Multinary Freedoms (Physica B, 2006

31P-NMR and muSR Studies of Filled Skutterudite Compound SmFe4P12: Evidence for Heavy Fermion Behavior with Ferromagnetic Ground State

The 31P-NMR (nuclear magnetic resonance) and muSR (muon spin relaxation) measurements on the filled skutterudite system SmFe4P12 have been carried out. The temperature T dependence of the 31P-NMR spectra indicates the existence of the crystalline electric field effect splitting of the Sm3+$ (J = 5/2) multiplet into a ground state and an excited state of about 70 K. The spin-lattice relaxation rate 1/T1 shows the typical behavior of the Kondo system, i.e., 1/T1 is nearly T independent above 30 K, and varies in proportion to T (the Korringa behavior, 1/T1 \propto T) between 7.5 K and 30 K. The T dependence deviated from the Korringa behavior below 7 K, which is independent of T in the applied magnetic field of 1 kOe, and suppressed strongly in higher fields. The behavior is explained as 1/T1is determined by ferromagnetic fluctuations of the uncovered Sm3+ magnetic moments by conduction electrons. The muSR measurements in zero field show the appearance of a static internal field associated with the ferromagnetic order below 1.6 K.Comment: 6 pages, 9 figures, to be published in J. Phys. Soc. Jpn. 75 (2006

Two Sizes of Superconducting Gaps on an Under-doped Bi2.1Sr1.9Ca2Cu3O10+δ with TC ∼ 101K by Tunneling Spectroscopy

AbstractWe measured tunneling conductances on an under-doped trilayer cuprate Bi2.1Sr1.9Ca2Cu3O10+≏ (Bi2223) with TC ∼ 101K by a point contact method, which has three CuO2 planes in a unit cell. The tunneling conductances on Bi2223 exhibited two sizes of gaps originated from outer and inner CuO2 plane (OP and IP). The estimated size of superconducting gap from OP ΔOP is 34 ± 6 meV, and the ΔIP from IP is 51 ± 5 meV, respectively. We also observed tunneling conductances which simultaneously displayed two superconducting peaks of OP and IP. Moreover, we propose the model of two superconductor-insulator-normal metal junctions which exhibit two sizes gaps of OP and IP

Collision condition indicted by High Pressure Phases in a Chondrite.

第3回極域科学シンポジウム/第35回南極隕石シンポジウム 11月29日（木）、30日（金） 国立国語研究所 2階講

Strong Valence Fluctuation Effects in SmTr2Tr_2Al20_{20}(Tr=Tr=Ti, V, Cr)

We present a single crystal study of low temperature magnetism and transport in Sm$Tr_2$Al$_{20}$ ($Tr =$ Ti, V and Cr). Strong valence fluctuation is manifested as Kondo effects including a large Sommerfeld coefficient $\gamma$, a weak temperature dependence of magnetic susceptibility and a $-\ln T$ dependent resistivity. All the systems order antiferromagnetically at $T_{\rm N}=$ 6.4 K (Ti), 2.3 K (V) and 1.8 K (Cr). Systematic change in the susceptibility, specific heat, and resistivity indicates that stronger $c$-$f$ hybridization in SmV$_2$Al$_{20}$ and SmCr$_2$Al$_{20}$ than in SmTi$_2$Al$_{20}$ suppresses $T_{\rm N}$ and induces the valence fluctuations and moreover field insensitive heavy fermion states