Classical Analogue of Weak Value in Stochastic Process

One of the remarkable notions in the recent development of quantum physics is the weak value related to weak measurements. We emulate it as a two-time conditional expectation in a classical stochastic model. We use the well known symmetrized form of the master equation, which is formally equivalent to the wave equation in quantum mechanics apart from the fact that wave functions are always real. The origin of the unusual behaviors of the weak value such as the negative probability and the abnormal enhancement of some expectations becomes clearer in the present case, where the two-time conditional probability has no ambiguity of imaginary/complex values.Comment: Revised version from Arxiv:1109.4302. To appear in the proceedings of the Symposium on 'Interface between Quantum Information and Statistical Physics', to be published by World Scientifi

An Explicit Form of the Equation of Motion of the Interface in Bicontinuous Phases

The explicit form of the interface equation of motion derived assuming a minimal surface is extended to general bicontinuous interfaces that appear in the diffusion limited stage of the phase separation process of binary mixtures. The derivation is based on a formal solution of the equivalent simple layer for the Dirichlet problem of the Laplace equation with an arbitrary boundary surface. It is shown that the assumption of a minimal surface used in the previous linear theory is not necessary, but its bicontinuous nature is the essential condition required for us to rederive the explicit form of the simple layer. The de- rived curvature flow equation has a phenomenological cut-off length, i.e., an `electro-static' screening length. That is re- lated to the well-known scaling length characterizing the spatial pattern size of a homogeneously growing bicontinuous phase. The corresponding equation of the level function in this scheme is given in a one-parameter form also.Comment: 18 page

Irreversible Circulation of Fluctuation and Entropy Production

Physical and chemical stochastic processes described by the master equation are investigated. In this paper, we examine the entropy production both for the master equation and for the corresponding Fokker-Planck equation. For the master equation, the exact expression of the entropy production was recently derived by Gaspard using the Kolmogorov-Sinai entropy ({\em J.Stat.Phys.}, \textbf{117} (2004), 599; [Errata; \textbf{126} (2006), 1109 ]). Although Gaspard's expression is derived from a stochastic consideration, it should be noted that Gaspard's expression conincides with the thermodynamical expression. For the corresponding Fokker-Planck equation, by using the detailed imbalance relation which appears in the derivation process of the fluctuation theorem through the Onsger-Machlup theory, the entropy production is expressed in terms of the {\em irreversible circulation of fluctuation}, which was proposed by Tomita and Tomita ({\em Prog.Theor.Phys.}, \textbf{51} (1974), 1731). However, this expression for the corresponding Fokker-Planck equation differs from that of the entropy production for the master equation. This discrepancy is due to the difference between the master equation and the corresponding Fokker-Planck equation, namely the former treats discrete events, but the latter equation is an approximation of the former one. In fact, in the latter equation, the original discrete events are smoothed out. To overcome this difficulty, we propose the {\em path weight principle}. By using this principle, the modified expression of the entropy production for the corresponding Fokker-Planck equation coincides with that of the master equation (i.e., the thermodynamical expression) for a simple chemical reaction system and a diffusion system.Comment: 17pages, no figures, to appear in Progreess of Theoretical Physics, Vol. 119, No.

Recovery in quantum error correction for general noise without measurement

It is known that one can do quantum error correction without syndrome measurement, which is often done in operator quantum error correction (OQEC). However, the physical realization could be challenging, especially when the recovery process involves high-rank projection operators and a superoperator. We use operator theory to improve OQEC so that the implementation can always be done by unitary gates followed by a partial trace operation. Examples are given to show that our error correction scheme outperforms the existing ones in various scenarios.Comment: 10 page

Metamaterials with magnetism and chirality

This review introduces and overviews electromagnetism in structured metamaterials which undergo simultaneous time-reversal and space-inversion symmetry breaking due to magnetism and chirality. Direct experimental observation of optical magnetochiral effects in a single metamolecule with magnetism and chirality is demonstrated at microwave frequencies. Numerical simulations based on a finite element method reproduce the experimental results well, and predict the emergence of giant magnetochiral effects, by combining resonances in the metamolecule. Toward the realization of magnetochiral effects at higher frequencies than microwaves, a metamolecule is miniaturized in the presence of ferromagnetic resonance in a cavity and coplanar waveguide. This work opens the door to the realization of a one-way mirror and synthetic gauge fields for electromagnetic waves

Calibration of AGN Reverberation Distance Measurements

In Yoshii et al. (2014), we described a new method for measuring extragalactic distances based on dust reverberation in active galactic nuclei (AGNs), and we validated our new method with Cepheid variable stars. In this paper, we validate our new method with Type Ia supernovae (SNe Ia) which occurred in two of the AGN host galaxies during our AGN monitoring program: SN 2004bd in NGC 3786 and SN 2008ec in NGC 7469. Their multicolor light curves were observed and analyzed using two widely accepted methods for measuring SN distances, and the distance moduli derived are $\mu=33.47\pm 0.15$ for SN 2004bd and $33.83\pm 0.07$ for SN 2008ec. These results are used to obtain independently the distance measurement calibration factor, $g$. The $g$ value obtained from the SN Ia discussed in this paper is $g_{\rm SN} = 10.61\pm 0.50$ which matches, within the range of 1$\sigma$ uncertainty, $g_{\rm DUST} = 10.60$, previously calculated ab initio in Yoshii et al. (2014). Having validated our new method for measuring extragalactic distances, we use our new method to calibrate reverberation distances derived from variations of H$\beta$ emission in the AGN broad line region (BLR), extending the Hubble diagram to $z\approx 0.3$ where distinguishing between cosmologies is becoming possible.Comment: Astrophysical Journal Letters accepte

Variation of Inner Radius of Dust Torus in NGC4151

The long-term optical and near infrared monitoring observations for a type 1 act ive galactic nucleus NGC 4151 were carried out for six years from 2001 to 2006 b y using the MAGNUM telescope, and delayed response of flux variations in the $K(2.2\mu m)$ band to those in the $V(0.55\mu m)$ band was clearly detected. Based on cross correlation analysis, we precisely measured a lag time $\Delta t$ for eight separate periods, and we found that $\Delta t$ is not constant changing be tween 30 and 70 days during the monitoring period. Since $\Delta t$ is the ligh t travel time from the central energy source out to the surrounding dust torus, this is the first convincing evidence that the inner radius of dust torus did ch ange in an individual AGN. In order to relate such a change of $\Delta t$ with a change of AGN luminosity $L$, we presented a method of taking an average of th e observed $V$-band fluxes that corresponds to the measured value of $\Delta t$, and we found that the time-changing track of NGC 4151 in the $\Delta t$ versus $L$ diagram during the monitoring period deviates from the relation of $\Delta t \propto L^{0.5}$ expected from dust reverberation. This result, combined with t he elapsed time from period to period for which $\Delta t$ was measured, indicat es that the timescale of dust formation is about one year, which should be taken into account as a new constraint in future studies of dust evolution in AGNs.Comment: 5 pages, 3 figures, To appear in the ApJ Lette

JHK' Imaging Photometry of Seyfert 1 AGNs and Quasars I: Multi-Aperture Photometry

Near-infrared $JHK'$ imaging photometry was obtained of 331 AGNs consisting mainly of Seyfert 1 AGNs and quasars (QSOs). This sample was selected to cover a range of radio emission strength, redshift from $z=0$ to 1, and absolute $B$-magnitude from $M_B=-29$ mag to -18 mag. Among low-$z$ AGNs with $z<0.3$, Seyfert $1-1.5$ AGNs are distributed over a region from a location typical of ``galaxies'' to a location typical of ``QSOs'' in the two-color $J-H$ to $H-K'$ diagram, but Seyfert $1.8-2$ AGNs are distributed around the location of ``galaxies''. Moreover, bright AGNs with respect to absolute $B$-magnitude are distributed near the location of ``QSOs'', while faint AGNs are near the location of ``galaxies''. The distribution of such low-$z$ AGNs in this diagram was found to have little dependence on their 6 cm radio flux. The near-infrared colors of the AGNs observed with an aperture of 7 pixels ($7.49''$) are more QSO-like than those observed with larger apertures up to 15 pixels ($16.1''$). This aperture effect may be explained by contamination from the light of host galaxies within larger apertures. This effect is more prominent for less luminous AGNs