Location of the Multicritical Point for the Ising Spin Glass on the Triangular and Hexagonal Lattices

A conjecture is given for the exact location of the multicritical point in the phase diagram of the +/- J Ising model on the triangular lattice. The result p_c=0.8358058 agrees well with a recent numerical estimate. From this value, it is possible to derive a comparable conjecture for the exact location of the multicritical point for the hexagonal lattice, p_c=0.9327041, again in excellent agreement with a numerical study. The method is a variant of duality transformation to relate the triangular lattice directly with its dual triangular lattice without recourse to the hexagonal lattice, in conjunction with the replica method.Comment: 9 pages, 1 figure; Minor corrections in notatio

High Orbital Eccentricities of Extrasolar Planets Induced by the Kozai Mechanism

One of the most remarkable properties of extrasolar planets is their high orbital eccentricities. Observations have shown that at least 20% of these planets, including some with particularly high eccentricities, are orbiting a component of a wide binary star system. The presence of a distant binary companion can cause significant secular perturbations to the orbit of a planet. In particular, at high relative inclinations, a planet can undergo a large-amplitude eccentricity oscillation. This so-called "Kozai mechanism" is effective at a very long range, and its amplitude is purely dependent on the relative orbital inclination. In this paper, we address the following simple question: assuming that every host star with a detected giant planet also has a (possibly unseen, e.g., substellar) distant companion, with reasonable distributions of orbital parameters and masses, how well could secular perturbations reproduce the observed eccentricity distribution of planets? Our calculations show that the Kozai mechanism consistently produces an excess of planets with very high (e >0.6) and very low (e < 0.1) eccentricities. The paucity of near-circular orbits in the observed sample cannot be explained solely by the Kozai mechanism, because, even with high enough inclinations, the Kozai mechanism often fails to produce significant eccentricity perturbations when there are other competing sources of orbital perturbations on secular timescales, such as general relativity. On the other hand, the Kozai mechanism can produce many highly eccentric orbits. Indeed the overproduction of high eccentricities observed in our models could be combined with plausible circularizing mechanisms (e.g., friction from residual gas) to create more intermediate eccentricities (e=0.1-0.6).Comment: 24 pages, 6 figures, ApJ, in press, minor changes to reflect the accepted versio

Scalable Spin Amplification with a Gain over a Hundred

We propose a scalable and practical implementation of spin amplification which does not require individual addressing nor a specially tailored spin network. We have demonstrated a gain of 140 in a solid-state nuclear spin system of which the spin polarization has been increased to 0.12 using dynamic nuclear polarization with photoexcited triplet electron spins. Spin amplification scalable to a higher gain opens the door to the single spin measurement for a readout of quantum computers as well as practical applications of nuclear magnetic resonance (NMR) spectroscopy to infinitesimal samples which have been concealed by thermal noise.Comment: 6 pages, 7 figure

Duality in finite-dimensional spin glasses

We present an analysis leading to a conjecture on the exact location of the multicritical point in the phase diagram of spin glasses in finite dimensions. The conjecture, in satisfactory agreement with a number of numerical results, was previously derived using an ansatz emerging from duality and the replica method. In the present paper we carefully examine the ansatz and reduce it to a hypothesis on analyticity of a function appearing in the duality relation. Thus the problem is now clearer than before from a mathematical point of view: The ansatz, somewhat arbitrarily introduced previously, has now been shown to be closely related to the analyticity of a well-defined function.Comment: 12 pages, 3 figures; A reference added; to appear in J. Stat. Phy

Strong Resonance of Light in a Cantor Set

The propagation of an electromagnetic wave in a one-dimensional fractal object, the Cantor set, is studied. The transfer matrix of the wave amplitude is formulated and its renormalization transformation is analyzed. The focus is on resonant states in the Cantor set. In Cantor sets of higher generations, some of the resonant states closely approach the real axis of the wave number, leaving between them a wide region free of resonant states. As a result, wide regions of nearly total reflection appear with sharp peaks of the transmission coefficient beside them. It is also revealed that the electromagnetic wave is strongly enhanced and localized in the cavity of the Cantor set near the resonant frequency. The enhancement factor of the wave amplitude at the resonant frequency is approximately $6/|\eta_\mathrm{r}|$, where $\eta_\mathrm{r}$ is the imaginary part of the corresponding resonant eigenvalue. For example, a resonant state of the lifetime $\tau_\mathrm{r}=4.3$ms and of the enhancement factor $M=7.8\times10^7$ is found at the resonant frequency $\omega_\mathrm{r}=367$GHz for the Cantor set of the fourth generation of length L=10cm made of a medium of the dielectric constant $\epsilon=10$.Comment: 20 pages, 11 figures, to be published in Journal of the Physical Society of Japa

Development of an Analytical Method for Nitric Oxide Radical Determination in Natural Waters

The measurement of photochemically generated nitric oxide radicals (NO) in natural waters has long been an arduous task because of a lack of simple analytical techniques, even though the environmental significance of this radical is paramount. We have developed a simple analytical method for the determination of photochemically generated NO in natural waters using 4,5-diaminofluorescein (DAF-2) as a probe compound. This method is based on the reaction of photoformed NO with DAF-2 in air-saturated solution to produce a highly fluorescent triazolofluorescein (DAF-2T) product. DAF-2T was determined by using reversed-phase HPLC with fluorescence detection, with excitation and emission wavelengths of 495 and 515 nm, respectively. Under optimum conditions, the calibration curve exhibited linearity in the range of 0.025−10 nM DAF-2T. The coefficients of variance for the measurements of the signal intensities of DAF-2T (from the photolysis of 0.5 μM and 5 μM NO2− with DAF-2) were less than 5% and 3%, respectively. For a total irradiation time of 30 min, the detection limit of the photoformation rate of NO was 1.65 × 10−13 M s−1, defined as 3σ of the lowest measured DAF-2T concentration (0.025 nM). The proposed method is relatively unaffected by potential interferents in seawater. The method was employed to determine the photoformation rate of NO in the Seto Inland Sea and the Kurose River in Hiroshima Prefecture, Japan. The measured NO photoformation rates in seawater and river water samples ranged from (5.3−32) × 10−12 M s−1 and (9.4−300) × 10−12 M s−1, respectively

Photochemical Production and Consumption Mechanisms of Nitric Oxide in Seawater

Nitric oxide (NO•) is an active odd-nitrogen species that plays a critical role in determining the levels of ozone (O3) and other nitrogen species in the troposphere. Here, we provide experimental evidence for photochemical formation of NO• in seawater. Photoproduction rates and overall scavenging rate constants were measured by irradiation of surface seawater samples collected from the Seto Inland Sea, Japan. Photoproduction rates of NO• ranged from 8.7 × 10−12 M s−1 to 38.8 × 10−12 M s−1 and scavenging rate constants were 0.05−0.33 s−1. The steady state concentrations of NO• in seawater, which were calculated from the photoproduction rates and scavenging rate constants were in the range 2.4−32 × 10−11 M. Estimation from the scavenging rate constant showed that the NO• lifetime in seawater was a few seconds. Our results indicate that nitrite photolysis plays a crucial role in the formation of NO•, even though we cannot exclude minor contributions from other sources. Analysis of filtered and unfiltered seawater samples showed no significant difference in NO• photoformation rates, which suggests a negligible contribution of NO• produced by photobiological processes. Using an estimated value of the Henry’s law constant (kH ≈ 0.0019 M atm−1), a supersaturation of surface seawater of 2 to 3 orders of magnitude was estimated. On the basis of the average values of the surface seawater concentration and the atmospheric NO• concentration, a sea-to-air NO• flux was estimated