Understanding deterministic diffusion by correlated random walks

Low-dimensional periodic arrays of scatterers with a moving point particle are ideal models for studying deterministic diffusion. For such systems the diffusion coefficient is typically an irregular function under variation of a control parameter. Here we propose a systematic scheme of how to approximate deterministic diffusion coefficients of this kind in terms of correlated random walks. We apply this approach to two simple examples which are a one-dimensional map on the line and the periodic Lorentz gas. Starting from suitable Green-Kubo formulas we evaluate hierarchies of approximations for their parameter-dependent diffusion coefficients. These approximations converge exactly yielding a straightforward interpretation of the structure of these irregular diffusion coeficients in terms of dynamical correlations.Comment: 13 pages (revtex) with 5 figures (postscript

The relationship between chaotic behavior and tunneling effect in quantum transport devices(1)Current topics of quantum chaos in nanosciences, Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)

この論文は国立情報学研究所の電子図書館事業により電子化されました。狭い金属ゲート(QPC)を両端に有する開放型量子ドットについて、零磁場近傍の磁気抵抗のピーク形状が、ゲート電圧を変化させることによってローレンツ型とカスプ型が交互に現れる現象が観測された。このローレンツ型とカスプ型が交互に現れる要因としては、QPCによるトンネリング効果と量子ドットによる弱局在の両方が関係しているものではないかと推測され、考察を行った。We have studied transport properties in the low-temperature magnetoresistance through the ballistic narrow path restricted by short width metallic gates, which cause a quantum point contact(QPC) which have a saddle point potential, on the 2 dimensional electron gas(2DEG) system. An alternate and systematic variation between a Lorentzian line fitting and a cusplike line fitting in the zero-field peaks has been observed, as sweeping the gate voltage. It indicates a possibility of existence of chaotic and regular paths on the short gated ballistic/tunneling transport. We will discuss on the quantum chaos behavior on the systematic variation between the Lorentzian and the cusp-like peakshape based on the disordered path system under the short gate, and suggest a relation with level repulsion of energy spectrum

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

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

Uniform approximation for diffractive contributions to the trace formula in billiard systems

We derive contributions to the trace formula for the spectral density accounting for the role of diffractive orbits in two-dimensional billiard systems with corners. This is achieved by using the exact Sommerfeld solution for the Green function of a wedge. We obtain a uniformly valid formula which interpolates between formerly separate approaches (the geometrical theory of diffraction and Gutzwiller's trace formula). It yields excellent numerical agreement with exact quantum results, also in cases where other methods fail.Comment: LaTeX, 41 pages including 12 PostScript figures, submitted to Phys. Rev.