An analytic approximation to the Diffusion Coefficient for the periodic Lorentz Gas

An approximate stochastic model for the topological dynamics of the periodic triangular Lorentz gas is constructed. The model, together with an extremum principle, is used to find a closed form approximation to the diffusion coefficient as a function of the lattice spacing. This approximation is superior to the popular Machta and Zwanzig result and agrees well with a range of numerical estimates.Comment: 13 pages, 4 figure

Light emission patterns from stadium-shaped semiconductor microcavity lasers

We study light emission patterns from stadium-shaped semiconductor (GaAs) microcavity lasers theoretically and experimentally. Performing systematic wave calculations for passive cavity modes, we demonstrate that the averaging by low-loss modes, such as those realized in multi-mode lasing, generates an emission pattern in good agreement with the ray model's prediction. In addition, we show that the dependence of experimental far-field emission patterns on the aspect ratio of the stadium cavity is well reproduced by the ray model.Comment: 5 pages, 4 figure

Wave Chaos in Rotating Optical Cavities

It is shown that, even when the eigenmodes of an optical cavity are wave-chaotic, the frequency splitting due to the rotation of the cavity occurs and the frequency difference is proportional to the angular velocity although the splitting eigenmodes are still wave-chaotic and do not correspond to any unidirectionally-rotating waves.Comment: 4 pages, 6 figure

Chaos-assisted emission from asymmetric resonant cavity microlasers

We study emission from quasi-one-dimensional modes of an asymmetric resonant cavity that are associated with a stable periodic ray orbit confined inside the cavity by total internal reflection. It is numerically demonstrated that such modes exhibit directional emission, which is explained by chaos-assisted emission induced by dynamical tunneling. Fabricating semiconductor microlasers with the asymmetric resonant cavity, we experimentally demonstrate the selective excitation of the quasi-one-dimensional modes by employing the device structure to preferentially inject currents to these modes and observe directional emission in good accordance with the theoretical prediction based on chaos-assisted emission.Comment: 9 pages, 10 figures, some figures are in reduced qualit

NNI-Form Quark Mass Matrix Expressed by the Observable Quantities

It is pointed out that the phase convention of the CKM matrix V affects texture analysis of the quark mass matrices (M_u, M_d) when we try to describe (M_u, M_d) by the observable quantities (quark masses and CKM matrix parameters) only. This is demonstrated for a case of the non-Hermitian Fritzsch-type mass matrix (tilde{M}_u, tilde{M}_d), which is a general expression of quark mass matrix (M_u, M_d) and is described by twelve parameters. We find that we can always choose a phase convention of V which yields tilde{M}_{u32} = 0, so that the remaining ten parameters in (tilde{M}_u, tilde{M}_d) can completely be expressed by the ten observable quantities.Comment: 11 pages (LaTeX); Title was change

Preparation of amino-substituted indenes and 1,4-dihydronaphthalenes using a one-pot multireaction approach: total synthesis of oxybenzo[c]phenanthridine alkaloids

Allylic trichloroacetimidates bearing a 2-vinyl or 2-allylaryl group have been designed as substrates for a one-pot, two-step multi-bond-forming process leading to the general preparation of aminoindenes and amino-substituted 1,4-dihydronaphthalenes. The synthetic utility of the privileged structures formed from this one-pot process was demonstrated with the total synthesis of four oxybenzo[c]phenanthridine alkaloids, oxychelerythrine, oxysanguinarine, oxynitidine, and oxyavicine. An intramolecular biaryl Heck coupling reaction, catalyzed using the Hermann–Beller palladacycle was used to effect the key step during the synthesis of the natural products

On the duality between periodic orbit statistics and quantum level statistics

We discuss consequences of a recent observation that the sequence of periodic orbits in a chaotic billiard behaves like a poissonian stochastic process on small scales. This enables the semiclassical form factor $K_{sc}(\tau)$ to agree with predictions of random matrix theories for other than infinitesimal $\tau$ in the semiclassical limit.Comment: 8 pages LaTe

Hyperfast pulsars as the remnants of massive stars ejected from young star clusters

Recent proper motion and parallax measurements for the pulsar PSR B1508+55 indicate a transverse velocity of ~1100 km/s, which exceeds earlier measurements for any neutron star. The spin-down characteristics of PSR B1508+55 are typical for a non-recycled pulsar, which implies that the velocity of the pulsar cannot have originated from the second supernova disruption of a massive binary system. The high velocity of PSR B1508+55 can be accounted for by assuming that it received a kick at birth or that the neutron star was accelerated after its formation in the supernova explosion. We propose an explanation for the origin of hyperfast neutron stars based on the hypothesis that they could be the remnants of a symmetric supernova explosion of a high-velocity massive star which attained its peculiar velocity (similar to that of the pulsar) in the course of a strong dynamical three- or four-body encounter in the core of dense young star cluster. To check this hypothesis we investigated three dynamical processes involving close encounters between: (i) two hard massive binaries, (ii) a hard binary and an intermediate-mass black hole, and (iii) a single star and a hard binary intermediate-mass black hole. We find that main-sequence O-type stars cannot be ejected from young massive star clusters with peculiar velocities high enough to explain the origin of hyperfast neutron stars, but lower mass main-sequence stars or the stripped helium cores of massive stars could be accelerated to hypervelocities. Our explanation for the origin of hyperfast pulsars requires a very dense stellar environment of the order of 10^6 -10^7 stars pc^{-3}. Although such high densities may exist during the core collapse of young massive star clusters, we caution that they have never been observed.Comment: 11 pages, 6 figures, 1 table, accepted to MNRA

Billiard Systems in Three Dimensions: The Boundary Integral Equation and the Trace Formula

We derive semiclassical contributions of periodic orbits from a boundary integral equation for three-dimensional billiard systems. We use an iterative method that keeps track of the composition of the stability matrix and the Maslov index as an orbit is traversed. Results are given for isolated periodic orbits and rotationally invariant families of periodic orbits in axially symmetric billiard systems. A practical method for determining the stability matrix and the Maslov index is described.Comment: LaTeX, 19 page

Kink propagation in a two-dimensional curved Josephson junction

We consider the propagation of sine-Gordon kinks in a planar curved strip as a model of nonlinear wave propagation in curved wave guides. The homogeneous Neumann transverse boundary conditions, in the curvilinear coordinates, allow to assume a homogeneous kink solution. Using a simple collective variable approach based on the kink coordinate, we show that curved regions act as potential barriers for the wave and determine the threshold velocity for the kink to cross. The analysis is confirmed by numerical solution of the 2D sine-Gordon equation.Comment: 8 pages, 4 figures (2 in color