Relation between fundamental estimation limit and stability in linear quantum systems with imperfect measurement

From the noncommutative nature of quantum mechanics, estimation of canonical observables $\hat{q}$ and $\hat{p}$ is essentially restricted in its performance by the Heisenberg uncertainty relation, \mean{\Delta \hat{q}^2}\mean{\Delta \hat{p}^2}\geq \hbar^2/4. This fundamental lower-bound may become bigger when taking the structure and quality of a specific measurement apparatus into account. In this paper, we consider a particle subjected to a linear dynamics that is continuously monitored with efficiency $\eta\in(0,1]$. It is then clarified that the above Heisenberg uncertainty relation is replaced by \mean{\Delta \hat{q}^2}\mean{\Delta \hat{p}^2}\geq \hbar^2/4\eta if the monitored system is unstable, while there exists a stable quantum system for which the Heisenberg limit is reached.Comment: 4 page

SuprimeCam Observation of Sporadic Meteors during Perseids 2004

We report the serendipitous findings of 13 faint meteors and 44 artificial space objects by Subaru SuprimeCam imaging observations during 11-16 August 2004. The meteors, at about 100km altitude, and artificial satellites/debris in orbit, at 500km altitude or higher, were clearly discriminated by their apparent defocused image sizes. CCD photometry of the 13 meteors, including 1 Perseid, 1 Aquarid, and 11 sporadic meteors, was performed. We defined a peak video-rate magnitude by comparing the integrated photon counts from the brightest portion of the track traversed within 33ms to those from a 0-mag star during the same time duration. This definition gives magnitudes in the range 4.0< V_{vr} <6.4 and 4.1< I_{vr}<5.9 for these 13 meteors. The corresponding magnitude for virtual naked-eye observers could be somewhat fainter especially for the V-band observation, in which the [OI] 5577 line lasting about 1 sec as an afterglow could contribute to the integrated flux of the present 5-10 min CCD exposures. Although the spatial resolution is insufficient to resolve the source size of anything smaller than about 1 m, we developed a new estimate of the collisionally excited column diameter of these meteors. A diameter as small as a few mm was derived from their collisionally excited photon rates, meteor speed, and the volume density of the oxygen atoms at the 100km altitude. The actual column diameter of the radiating zone, however, could be as large as few 100m because the excited atoms travel that distance before they emit forbidden lines in 0.7 sec of its average lifetime. Among the 44 artificial space objects, we confirmed that 17 were cataloged satellites/space debris.Comment: 14 pages, 13 figures, 5 tables, submitted to PAS

Fermi arc in doped high-Tc cuprates

We propose a $d$-density wave induced by the spin-orbit coupling in the CuO plane. The spectral function of high-temperature superconductors in the under doped and lightly doped regions is calculated in order to explain the Fermi arc spectra observed recently by angle-resolved photoemission spectroscopy. We take into account the tilting of CuO octahedra as well as the on-site Coulombrepulsive interaction; the tilted octahedra induce the staggered transfer integral between $p_{x,y}$ orbitals and Cu $t_{2g}$ orbitals, and bring about nontrivial effects of spin-orbit coupling for the $d$ electrons in the CuO plane. The spectral weight shows a peak at around ($\pi/2$,$\pi/2$) for light doping and extends around this point forming an arc as the carrier density increases, where the spectra for light doping grow continuously to be the spectra in the optimally doped region. This behavior significantly agrees with that of the angle-resolved photoemissionspectroscopy spectra. Furthermore, the spin-orbit term and staggered transfer effectively induce a flux state, a pseudo-gap with time-reversal symmetry breaking. We have a nodal metallic state in the light-doping case since the pseudogap has a $d_{x^2-y^2}$ symmetry.Comment: 5 pages, 7 figure

Off-diagonal Wave Function Monte Carlo Studies of Hubbard Model I

We propose a Monte Carlo method, which is a hybrid method of the quantum Monte Carlo method and variational Monte Carlo theory, to study the Hubbard model. The theory is based on the off-diagonal and the Gutzwiller type correlation factors which are taken into account by a Monte Carlo algorithm. In the 4x4 system our method is able to reproduce the exact results obtained by the diagonalization. An application is given to investigate the half-filled band case of two-dimensional square lattice. The energy is favorably compared with quantum Monte Carlo data.Comment: 9 pages, 11 figure

Earliest detection of the optical afterglow of GRB 030329 and its variability

We report the earliest detection of an extremely bright optical afterglow of the gamma-ray burst (GRB) 030329 using a 30cm-telescope at Tokyo Institute of Technology (Tokyo, JAPAN). Our observation started 67 minutes after the burst, and continued for succeeding two nights until the afterglow faded below the sensitivity limit of the telescope (approximately 18 mag). Combining our data with those reported in GCN Circulars, we find that the early afterglow light curve of the first half day is described by a broken power-law (t^{- alpha}) function with indices alpha_{1} = 0.88 +/- 0.01 (0.047 < t < t_{b1} days), alpha_{2} = 1.18 +/- 0.01 (t_{b1} < t < t_{b2} days), and alpha_{3} = 1.81 +/- 0.04 (t_{b2} < t < 1.2 days), where t_{b1} ~ 0.26 days and t_{b2} ~ 0.54 days, respectively. The change of the power-law index at the first break at t ~ 0.26 days is consistent with that expected from a ``cooling-break'' when the cooling frequency crossed the optical band. If the interpretation is correct, the decay index before the cooling-break implies a uniform ISM environment.Comment: 13 pages, 1 table and 2 figures. Accepted to the Astrophysical Journal Letter

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Superconductivity, magnetic order, and quadrupolar order in the filled skutterudite system Pr1−x_{1-x}Ndx_{x}Os4_4Sb12_{12}

Superconductivity, magnetic order, and quadrupolar order have been investigated in the filled skutterudite system Pr$_{1-x}$Nd$_{x}$Os$_4$Sb$_{12}$ as a function of composition $x$ in magnetic fields up to 9 tesla and at temperatures between 50 mK and 10 K. Electrical resistivity measurements indicate that the high field ordered phase (HFOP), which has been identified with antiferroquadruoplar order, persists to $x$ $\sim$ 0.5. The superconducting critical temperature $T_c$ of PrOs$_4$Sb$_{12}$ is depressed linearly with Nd concentration to $x$ $\sim$ 0.55, whereas the Curie temperature $T_{FM}$ of NdOs$_4$Sb$_{12}$ is depressed linearly with Pr composition to ($1-x$) $\sim$ 0.45. In the superconducting region, the upper critical field $H_{c2}(x,0)$ is depressed quadratically with $x$ in the range 0 $<$ $x$ $\lesssim$ 0.3, exhibits a kink at $x$ $\approx$ 0.3, and then decreases linearly with $x$ in the range 0.3 $\lesssim$ $x$ $\lesssim$ 0.6. The behavior of $H_{c2}(x,0)$ appears to be due to pair breaking caused by the applied magnetic field and the exhange field associated with the polarization of the Nd magnetic moments, in the superconducting state. From magnetic susceptibility measurements, the correlations between the Nd moments in the superconducting state appear to change from ferromagnetic in the range 0.3 $\lesssim$ $x$ $\lesssim$ 0.6 to antiferromagnetic in the range 0 $<$ $x$ $\lesssim$ 0.3. Specific heat measurements on a sample with $x$ $=$ 0.45 indicate that magnetic order occurs in the superconducting state, as is also inferred from the depression of $H_{c2}(x,0)$ with $x$.Comment: 7 pages, 7 figures, currently submitted to Phys. Rev.