How to Measure the Quantum State of Collective Atomic Spin Excitation

The spin state of an atomic ensemble can be viewed as two bosonic modes, i.e., a quantum signal mode and a $c$-numbered ``local oscillator'' mode when large numbers of spin-1/2 atoms are spin-polarized along a certain axis and collectively manipulated within the vicinity of the axis. We present a concrete procedure which determines the spin-excitation-number distribution, i.e., the diagonal elements of the density matrix in the Dicke basis for the collective spin state. By seeing the collective spin state as a statistical mixture of the inherently-entangled Dicke states, the physical picture of its multi-particle entanglement is made clear.Comment: 6 pages, to appear in Phys. Rev.

Effects of the Zero-Mode Landau Level on Inter-Layer Magnetoresistance in Multilayer Massless Dirac Fermion Systems

We report on the experimental results of interlayer magnetoresistance in multilayer massless Dirac fermion system $\alpha$-(BEDT-TTF)$_2$I$_3$ under hydrostatic pressure and its interpretation. We succeeded in detecting the zero-mode Landau level (n=0 Landau level) that is epected to appear at the contact points of Dirac cones in the magnetic field normal to the two-dimensional plane. The characteristic feature of zero-mode Landau carriers including the Zeeman effect is clearly seen in the interlayer magnetoresistance.Comment: 2 pages, 2 figure

On the two-dataset problem

This paper considers the two-dataset problem, where data are collected from two potentially different populations sharing common aspects. This problem arises when data are collected by two different types of researchers or from two different sources. We may reach invalid conclusions without using knowledge about the data collection process. To address this problem, this paper develops statistical models focusing on the difference in measurement and proposes two prediction errors that help to evaluate the underlying data collection process. As a consequence, it is possible to discuss the heterogeneity/similarity of data in terms of prediction. Two real datasets are selected to illustrate our method

Growth rate analysis of scalar gradients in generalized surface quasigeostrophic equations of ideal fluids

The growth rates of scalar gradients are studied numerically and analytically in a family of two-dimensional (2D) incompressible fluid equations related to the surface quasigeostrophic (SQG) equation. The active scalar is related to the stream function ψ by θ=(−△)α/2ψ (0⩽α⩽2). A notable difference is observed in a comparison of the instantaneous growth rates in Lp and in L∞ norms, depending on the stage of the time evolution. The crux is the phase-shift effect of singular integral operators, which displaces the peak location of the scalar gradient from that of the strain rate. On this basis, a method of detecting such a dislocation is proposed in view of the importance of their coalescence needed for a possible blow-up. Moreover, it is found in the long-time evolution that a solution of the SQG equation (whose regularity is not known) is less singular than that of the 2D Euler equations (known to be regular) on the time interval covered by this computation. This consistently expands an earlier observation by Majda and Tabak [Physica D 98, 515 (1996).] in some detail. A 1D model problem is discussed to illustrate the present method, and extensions to the 3D case are also are briefly discussed

Glassy dynamics in thin films of polystyrene

Glassy dynamics was investigated for thin films of atactic polystyrene by complex electric capacitance measurements using dielectric relaxation spectroscopy. During the isothermal aging process the real part of the electric capacitance increased with time, whereas the imaginary part decreased with time. It follows that the aging time dependences of real and imaginary parts of the electric capacitance were primarily associated with change in volume (film thickness) and dielectric permittivity, respectively. Further, dielectric permittivity showed memory and rejuvenation effects in a similar manner to those observed for poly(methyl methacrylate) thin films. On the other hand, volume did not show a strong rejuvenation effect.Comment: 7 pages, 7 figures. Phys. Rev. E (in press

On the direct indecomposability of infinite irreducible Coxeter groups and the Isomorphism Problem of Coxeter groups

In this paper we prove, without the finite rank assumption, that any irreducible Coxeter group of infinite order is directly indecomposable as an abstract group. The key ingredient of the proof is that we can determine, for an irreducible Coxeter group, the centralizers of the normal subgroups that are generated by involutions. As a consequence, we show that the problem of deciding whether two general Coxeter groups are isomorphic, as abstract groups, is reduced to the case of irreducible Coxeter groups, without assuming the finiteness of the number of the irreducible components or their ranks. We also give a description of the automorphism group of a general Coxeter group in terms of those of its irreducible components.Comment: 30 page

An X-ray measurement of Titan's atmospheric extent from its transit of the Crab Nebula

Saturn's largest satellite, Titan, transited the Crab Nebula on 5 January 2003. We observed this astronomical event with the {\it Chandra} X-ray Observatory. An ``occultation shadow'' has clearly been detected and is found to be larger than the diameter of Titan's solid surface. The difference gives a thickness for Titan's atmosphere of 880 $\pm$ 60 km. This is the first measurement of Titan's atmospheric extent at X-ray wavelengths. The value measured is consistent with or slightly larger than those estimated from earlier Voyager observations at other wavelengths. We discuss the possibility of temporal variations in the thickness of Titan's atmosphere.Comment: 14 pages, 5 figures, AASTeX preprint. Accepted for publication in the Astrophysical Journa