Many-body interband tunneling as a witness of complex dynamics in the Bose-Hubbard model

A perturbative model is studied for the tunneling of many-particle states from the ground band to the first excited energy band, mimicking Landau-Zener decay for ultracold, spinless atoms in quasi-one-dimensional optical lattices subjected to a tunable tilting force. The distributions of the computed tunneling rates provide an independent and experimentally accessible signature of the regular-chaotic transition in the strongly correlated many-body dynamics of the ground band.     

Suspended bridge-like silica 2×2 beam splitter on silicon

We report a successful experimental realization of a 2×2 suspended silica splitter integrated on a silicon substrate. The silica splitter was photo-lithographically patterned, etched, and reflowed to form the suspended and rounded silica waveguide channels. The silica splitter showed a flat splitting ratio and excess loss over a wide wavelength range from 1520 to 1630 nm with a low crosstalk. Additionally, as a result of the very low nonlinear coefficients of silica, the splitting ratio is independent of input power.     

Dirac Operators on Quantum Projective Spaces

We construct a family of self-adjoint operators D _N , ${N\in{\mathbb Z}}We construct a family of self-adjoint operators D _N , N ? \mathbb Z{N\in{\mathbb Z}} , which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space \mathbb CP^l_q{{\mathbb C}{\rm P}^{\ell}_q} , for any ℓ ≥ 2 and 0 < q < 1. They provide 0⁺-dimensional equivariant even spectral triples. If ℓ is odd and N=\frac12(l+1){N=\frac{1}{2}(\ell+1)} , the spectral triple is real with KO-dimension 2ℓ mod 8.     

Reflectometric measurement of birefringence rotation in single-mode optical fibers

We present a novel reflectometric technique for the measurement of orientation and modulus of the linear birefringence vector in single-mode optical fibers. The technique provides information also on circular birefringence, although this component, if present, appears as a rotation of the linear birefringence. A detailed theoretical analysis is reported and validated by experimental results.     

Continuously tunable 1 byte delay in coupled-resonator optical waveguides

A reconfigurable coupled-resonator optical waveguide made of a few directly coupled ring resonators is employed to control the delay of data streams modulated at tens of gigabits per second. A delay of 8 bit lengths (1 optical byte) with a small pulse broadening and 1 dB/bit fractional loss is achieved by using only eight rings. The limiting role of waveguide loss and spurious backreflections is experimentally investigated. The high storage efficiency (1 bit/ring) of the device enables an easy, reliable, hitless, and relatively low-power-consuming management of the delay. A higher storage efficiency is demonstrated to be associated to an unavoidable higher pulse distortion.     

Study on the bubble transport mechanism in an acoustic standing wave field

The use of bubbles in applications such as surface chemistry, drug delivery, and ultrasonic cleaning etc. has been enormously popular in the past two decades. It has been recognized that acoustically-driven bubbles can be used to disturb the flow field near a boundary in order to accelerate physical or chemical reactions on the surface. The interactions between bubbles and a surface have been studied experimentally and analytically. However, most of the investigations focused on violently oscillating bubbles (also known as cavitation bubble), less attention has been given to understand the interactions between moderately oscillating bubbles and a boundary. Moreover, cavitation bubbles were normally generated in situ by a high intensity laser beam, little experimental work has been carried out to study the translational trajectory of a moderately oscillating bubble in an acoustic field and subsequent interactions with the surface. This paper describes the design of an ultrasonic test cell and explores the mechanism of bubble manipulation within the test cell. The test cell consists of a transducer, a liquid medium and a glass backing plate. The acoustic field within the multi-layered stack was designed in such a way that it was effectively one dimensional. This was then successfully simulated by a one dimensional network model. The model can accurately predict the impedance of the test cell as well as the mode shape (distribution of particle velocity and stress/pressure field) within the whole assembly. The mode shape of the stack was designed so that bubbles can be pushed from their injection point onto a backing glass plate. Bubble radial oscillation was simulated by a modified Keller–Miksis equation and bubble translational motion was derived from an equation obtained by applying Newton’s second law to a bubble in a liquid medium. Results indicated that the bubble trajectory depends on the acoustic pressure amplitude and initial bubble size: an increase of pressure amplitude or a decrease of bubble size forces bubbles larger than their resonant size to arrive at the target plate at lower heights, while the trajectories of smaller bubbles are less influenced by these factors. The test cell is also suitable for testing the effects of drag force on the bubble motion and for studying the bubble behavior near a surface.     

Chain geometries over local alternative algebras

In this paper, chain geometries over local alternative algebras are introduced. We determine the isomorphisms between them, and embed them into chain geometries over associative algebras.Dedicated to Professor Rafael Artzy on the occasion of his 80th birthday     

A priori estimates for quasilinear degenerate parabolic equations

We prove some maximum and gradient estimates for classical solutions to a wide class of quasilinear degenerate parabolic equations, including first order ones. The proof is elementary and exploits the smallness of the domain in the time direction.

     

Induced local actions on taut and Stein manifolds

Let act by biholomorphisms on a taut manifold . We show that can be regarded as a -invariant domain in a complex manifold on which the universal complexification of acts. If is also Stein, an analogous result holds for actions of a larger class of real Lie groups containing, e.g., abelian and certain nilpotent ones. In this case the question of Steinness of is discussed.