First-passage and extreme-value statistics of a particle subject to a constant force plus a random force

We consider a particle which moves on the x axis and is subject to a constant force, such as gravity, plus a random force in the form of Gaussian white noise. We analyze the statistics of first arrival at point $x_1$ of a particle which starts at $x_0$ with velocity $v_0$. The probability that the particle has not yet arrived at $x_1$ after a time $t$, the mean time of first arrival, and the velocity distribution at first arrival are all considered. We also study the statistics of the first return of the particle to its starting point. Finally, we point out that the extreme-value statistics of the particle and the first-passage statistics are closely related, and we derive the distribution of the maximum displacement $m={\rm max}_t[x(t)]$.Comment: Contains an analysis of the extreme-value statistics not included in first versio

Harmonically confined, semiflexible polymer in a channel: response to a stretching force and spatial distribution of the endpoints

We consider an inextensible, semiflexible polymer or worm-like chain which is confined in the transverse direction by a parabolic potential and subject to a longitudinal force at the ends, so that the polymer is stretched out and backfolding is negligible. Simple analytic expressions for the partition function, valid in this regime, are obtained for chains of arbitrary length with a variety of boundary conditions at the ends. The spatial distribution of the end points or radial distribution function is also analyzed.Comment: 14 pages including figure

Bosonization Theory of Excitons in One-dimensional Narrow Gap Semiconductors

Excitons in one-dimensional narrow gap semiconductors of anti-crossing quantum Hall edge states are investigated using a bosonization method. The excitonic states are studied by mapping the problem into a non-integrable sine-Gordon type model. We also find that many-body interactions lead to a strong enhancement of the band gap. We have estimated when an exciton instability may occur.Comment: 4pages, 1 figure, to appear in Phys. Rev. B Brief Report

Optical control of photon tunneling through an array of nanometer scale cylindrical channels

We report first observation of photon tunneling gated by light at a different wavelength in an artificially created array of nanometer scale cylindrical channels in a thick gold film. Polarization properties of gated light provide strong proof of the enhanced nonlinear optical mixing in nanometric channels involved in the process. This suggests the possibility of building a new class of "gated" photon tunneling devices for massive parallel all-optical signal and image processing.Comment: 4 pages, 4 figure

Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit

In this work we explore the transmission properties of a single slit in a metallic screen. We analyze the dependence of these properties on both slit width and angle of incident radiation. We study in detail the crossover between the subwavelength regime and the geometrical-optics limit. In the subwavelength regime, resonant transmission linked to the excitation of waveguide resonances is analyzed. Linewidth of these resonances and their associated electric field intensities are controlled by just the width of the slit. More complex transmission spectra appear when the wavelength of light is comparable to the slit width. Rapid oscillations associated to the emergence of different propagating modes inside the slit are the main features appearing in this regime.Comment: Accepted for publication in Phys. Rev.

Implications of Recent Measurements of Hadronic Charmless B Decays

Implications of recent CLEO measurements of hadronic charmless B decays are discussed. (i) Employing the Bauer-Stech-Wirbel (BSW) model for form factors as a benchmark, the $B\to\pi^+\pi^-$ data indicate that the form factor $F_0^{B\pi}(0)$ is smaller than that predicted by the BSW model, whereas the data of $B\to\omega\pi, K^*\eta$ imply that the form factors $A_0^{B\omega}(0), A_0^{BK^*}(0)$ are greater than the BSW model's values. (ii) The tree-dominated modes $B\to\pi^+\pi^-, \rho^0\pi^\pm, \omega\pi^\pm$ imply that the effective number of colors N_c(LL) for (V-A)(V-A) operators is preferred to be smaller, while the current limit on $B\to\phi K$ shows that N_c(LR)>3. The data of $B\to K\eta'$ and $K^*\eta$ clearly indicate that $N_c(LR)\gg N_c(LL)$. (iii) In order to understand the observed suppression of $\pi^+\pi^-$ and non-suppression of $K\pi$ modes, both being governed by the form factor $F_0^{B\pi}$, the unitarity angle $\gamma$ is preferred to be greater than $90^\circ$. By contrast, the new measurement of $B^\pm\to\rho^0\pi^\pm$ no longer strongly favors $\cos\gamma<0$. (iv) The observed pattern K^-\pi^+\sim \ov K^0\pi^-\sim {2\over 3}K^-\pi^0 is consistent with the theoretical expectation: The constructive interference between electroweak and QCD penguin diagrams in the $K^-\pi^0$ mode explains why {\cal B}(B^-\to K^-\pi^0)>{1\over 2}{\cal B}(\ov B^0\to K^-\pi^+). (v) The observation \nc(LL)<3<\nc(LR) and our preference for \nc(LL)\sim 2 and \nc(LR)\sim 6 are justified by a recent perturbative QCD calculation of hadronic rare B decays in the heavy quark limit.Comment: 21 pages; CLEO measurements of several charmless B decay modes are updated. Discussion of the unitarity angle gamma in the \rho\pi mode is revise

Study of Bc --> J/psi pi, etac pi decays with perturbative QCD approach

The Bc --> J/psi pi, etac pi decays are studied with the perturbative QCD approach. It is found that form factors and branching ratios are sensitive to the parameters w, v, f_J/psi and f_etac, where w and v are the parameters of the charmonium wave functions for Coulomb potential and harmonic oscillator potential, respectively, f_J/psi and f_etac are the decay constants of the J/psi and etac mesons, respectively. The large branching ratios and the clear signals of the final states make the Bc --> J/psi pi, etac pi decays to be the prospective channels for measurements at the hadron collidersComment: 21 pages, revtex

B→J/ψKB \to J/\psi K Decays in QCD Factorization

The hadronic decays $B\to J/\psi K(K^*)$ are interesting because experimentally they are the only color-suppressed modes which have been measured, and theoretically they are calculable by QCD factorization even the emitted meson $J\psi$ is heavy. We analyze the decay $B\to J\psi K$ within the framework of QCD factorization in the heavy quark limit. We show explicitly the scale and $\gamma_5$-scheme independence of decay amplitudes and infrared safety of nonfactorizable corrections at twist-2 order. Leading-twist contributions from the light-cone distribution amplitudes (LCDAs) of the mesons are too small to accommodate the data; the nonfactorizable corrections to naive factorization are small and not significant. We study the twist-3 effects due to the kaon and find that the coefficient $a_2(J\psi K)$ is largely enhanced by the nonfactorizable spectator interactions arising from the twist-3 kaon LCDA $\phi^K_\sigma$, which are formally power-suppressed but chirally, logarithmically and kinematically enhanced. Therefore, factorization breaks down at twist-3 order. Higher-twist effects of $J\psi$ are briefly discussed. Our result also resolves the long-standing sign ambiguity of $a_2(J\psi K)$, which turns out to be positive for its real part.Comment: 18 pages, 2 figures. Typos in Eqs.(3.4), (3.5), and (3.6) are correcte

Updated Analysis of a_1 and a_2 in Hadronic Two-body Decays of B Mesons

Using the recent experimental data of $B\to D^{(*)}(\pi,\rho)$, $B\to D^{(*)} D_s^{(*)}$, $B\to J/\psi K^{(*)}$ and various model calculations on form factors, we re-analyze the effective coefficients a_1 and a_2 and their ratio. QCD and electroweak penguin corrections to a_1 from $B\to D^{(*)}D_s^{(*)}$ and a_2 from $B\to J/\psi K^{(*)}$ are estimated. In addition to the model-dependent determination, the effective coefficient a_1 is also extracted in a model-independent way as the decay modes $B\to D^{(*)}h$ are related by factorization to the measured semileptonic distribution of $B\to D^{(*)}\ell \bar\nu$ at $q^2=m_h^2$. Moreover, this enables us to extract model-independent heavy-to-heavy form factors, for example, $F_0^{BD}(m_\pi^2)=0.66\pm0.06\pm0.05$ and $A_0^{BD^*}(m_\pi^2)=0.56\pm0.03\pm0.04$. The determination of the magnitude of a_2 from $B\to J/\psi K^{(*)}$ depends on the form factors $F_1^{BK}$, $A_{1,2}^{BK^*}$ and $V^{BK^*}$ at $q^2=m^2_{J/\psi}$. By requiring that a_2 be process insensitive (i.e., the value of a_2 extracted from $J/\psi K$ and $J/\psi K^*$ states should be similar), as implied by the factorization hypothesis, we find that $B\to K^{(*)}$ form factors are severely constrained; they respect the relation $F_1^{BK}(m^2_{J/\psi})\approx 1.9 A_1^{BK^*}(m^2_{J/\psi})$. Form factors $A_2^{BK^*}$ and $V^{BK^*}$ at $q^2=m^2_{J/\psi}$ inferred from the measurements of the longitudinal polarization fraction and the P-wave component in $B\to J/\psi K^*$ are obtained. A stringent upper limit on a_2 is derived from the current bound on \ov B^0\to D^0\pi^0 and it is sensitive to final-state interactions.Comment: 33 pages, 2 figures. Typos in Tables I and IX are corrected. To appear in Phys. Rev.

Reversible Band Gap Engineering in Carbon Nanotubes by Radial Deformation

We present a systematic analysis of the effect of radial deformation on the atomic and electronic structure of zigzag and armchair single wall carbon nanotubes using the first principle plane wave method. The nanotubes were deformed by applying a radial strain, which distorts the circular cross section to an elliptical one. The atomic structure of the nanotubes under this strain are fully optimized, and the electronic structure is calculated self-consistently to determine the response of individual bands to the radial deformation. The band gap of the insulating tube is closed and eventually an insulator-metal transition sets in by the radial strain which is in the elastic range. Using this property a multiple quantum well structure with tunable and reversible electronic structure is formed on an individual nanotube and its band-lineup is determined from first-principles. The elastic energy due to the radial deformation and elastic constants are calculated and compared with classical theories.Comment: To be appear in Phys. Rev. B, Apr 15, 200