A generalization of contact metric manifolds

We give a characterization of a contact metric manifold as a special almost contact metric manifold and discuss an almost contact metric manifold which is {a} natural generalization of the contact metric manifolds introduced by Y. Tashiro.Comment: 15 page

A proof of the Chern-Gauss-Bonnet theorem for indefinite signature metrics using analytic continuation

We derive the Chern-Gauss-Bonnet Theorem for manifolds with smooth non-degenerate boundary in the pseudo-Riemannian context from the corresponding result in the Riemannian setting by examining the Euler-Lagrange equations associated to the Pfaffian of a complex "metric" on the tangent space and then applying analytic continuation.Comment: This paper has been withdrawn by the authors. A later improved version is available upon request from the authors but will not be posted to the arXi

Nanoscale Topographical Replication of Graphene Architecture by Artificial DNA nanostructures

Despite many studies on how geometry can be used to control the electronic properties of graphene, certain limitations to fabrication of designed graphene nanostructures exist. Here, we demonstrate controlled topographical replication of graphene by artificial deoxyribonucleic acid (DNA) nanostructures. Owing to the high degree of geometrical freedom of DNA nanostructures, we controlled the nanoscale topography of graphene. The topography of graphene replicated from DNA nanostructures showed enhanced thermal stability and revealed an interesting negative temperature coefficient of sheet resistivity when underlying DNA nanostructures were denatured at high temperatures.Comment: 12 pages, 3 figure

Strong Confinement and Oscillations in Two-Component Bose-Einstein Condensates

We present a new model of BEC dynamics based on strong confinement near the ground state. The model predicts oscillations in a two-component condensate, based on interference of non-spreading wave packets moving within a pair of tilted nearly square potentials. The oscillations are similar to those recently reported for a magnetically trapped $^{87}$Rb condensate, and the model's predictions give good quantitative agreement with the experiments.Comment: 4 pages, 8 figure

Fabrication of Analog Electronics for Serial Readout of Silicon Strip Sensors

A set of analog electronics boards for serial readout of silicon strip sensors was fabricated. A commercially available amplifier is mounted on a homemade hybrid board in order to receive analog signals from silicon strip sensors. Also, another homemade circuit board is fabricated in order to translate amplifier control signals into a suitable format and to provide bias voltage to the amplifier as well as to the silicon sensors. We discuss technical details of the fabrication process and performance of the circuit boards we developed.Comment: minor typos corrected, and additional acknowledgement included. To be submitted to JINS

Correction to "minimal unit vector fields"

The paper "Minimal unit vector fields" by O. Gil-Medrano and E. Llinares-Fuster \cite{GilLli1}. is a seminal paper in the field that has been cited by many authors. It contains, however, a minor technical mistake in Theorem 14 that is important to fix. In this short note, we will provide a correction to that result.Comment: 8page

Complex sine-Gordon Theory for Coherent Optical Pulse Propagation

It is shown that the McCall-Hahn theory of self-induced transparency in coherent optical pulse propagation can be identified with the complex sine-Gordon theory in the sharp line limit. We reformulate the theory in terms of the deformed gauged Wess-Zumino-Witten sigma model and address various new aspects of self-induced transparency.Comment: 8 pages, in Late

Nonabelian sine-Gordon theory and its application to nonlinear optics

Using a field theory generalization of the spinning top motion, we construct nonabelian generalizations of the sine-Gordon theory according to each symmetric spaces. A Lagrangian formulation of these generalized sine-Gordon theories is given in terms of a deformed gauged Wess-Zumino-Witten action which also accounts for integrably perturbed coset conformal field theories. As for physical applications, we show that they become precisely the effective field theories of self-induced transparency in nonlinear optics. This provides a dictionary between field theory and nonlinear optics.Comment: 5 pages, to appear in the Proceedings of the 2nd Sakharov Conference on Physics, Moscow, May, 199

Field Theory for Coherent Optical Pulse Propagation

We introduce a new notion of "matrix potential" to nonlinear optical systems. In terms of a matrix potential $g$, we present a gauge field theoretic formulation of the Maxwell-Bloch equation that provides a semiclassical description of the propagation of optical pulses through resonant multi-level media. We show that the Bloch part of the equation can solved identically through $g$ and the remaining Maxwell equation becomes a second order differential equation with reduced set of variables due to the gauge invariance of the system. Our formulation clarifies the (nonabelian) symmetry structure of the Maxwell-Bloch equations for various multi-level media in association with symmetric spaces $G/H$. In particular, we associate nondegenerate two-level system for self-induced transparency with $G/H=SU(2)/U(1)$ and three-level \L - or V-systems with $G/H = SU(3)/U(2)$. We give a detailed analysis for the two-level case in the matrix potential formalism, and address various new properties of the system including soliton numbers, effective potential energy, gauge and discrete symmetries, modified pulse area, conserved topological and nontopological charges. The nontopological charge measures the amount of self-detuning of each pulse. Its conservation law leads to a new type of pulse stability analysis which explains nicely earlier numerical results.Comment: 43 pages, Latex, some comments and references are added. postscript file containing 10 figures can be obtained at http://photon.kyunghee.ac.kr/~qhpark

Saturated actions by finite dimensional Hopf *-algebras on C*-algebras

If a finite group action $\alpha$ on a unital $C^*$-algebra $M$ is saturated, the canonical conditional expectation $E:M\to M^\alpha$ onto the fixed point algebra is known to be of index finite type with $Index(E)=|G|$ in the sense of Watatani. More generally if a finite dimensional Hopf $*$-algebra $A$ acts on $M$ and the action is saturated, the same is true with $Index (E)=\dim(A)$. In this paper we prove that the converse is true. Especially in case $M$ is a commutative $C^*$-algebra $C(X)$ and $\alpha$ is a finite group action, we give an equivalent condition in order that the expectation $E:C(X)\to C(X)^\alpha$ is of index finite type, from which we obtain that $\alpha$ is saturated if and only if $G$ acts freely on $X$. Actions by compact groups are also considered to show that the gauge action $\gamma$ on a graph $C^*$-algebra $C^*(E)$ associated with a locally finite directed graph $E$ is saturated.Comment: 18 pages, to be published in Intern. J. Mat