Algebraic time-decay for the bipolar quantum hydrodynamic model

The initial value problem is considered in the present paper for bipolar quantum hydrodynamic model for semiconductors (QHD) in $\mathbb{R}^3$. We prove that the unique strong solution exists globally in time and tends to the asymptotical state with an algebraic rate as $t\to+\infty$. And, we show that the global solution of linearized bipolar QHD system decays in time at an algebraic decay rate from both above and below. This means in general, we can not get exponential time-decay rate for bipolar QHD system, which is different from the case of unipolar QHD model (where global solutions tend to the equilibrium state at an exponential time-decay rate) and is mainly caused by the nonlinear coupling and cancelation between two carriers. Moreover, it is also shown that the nonlinear dispersion does not affect the long time asymptotic behavior, which by product gives rise to the algebraic time-decay rate of the solution of the bipolar hydrodynamical model in the semiclassical limit.Comment: 23 page

Exchange effects on electron scattering through a quantum dot embedded in a two-dimensional semiconductor structure

We have developed a theoretical method to study scattering processes of an incident electron through an N-electron quantum dot (QD) embedded in a two-dimensional (2D) semiconductor. The generalized Lippmann-Schwinger equations including the electron-electron exchange interaction in this system are solved for the continuum electron by using the method of continued fractions (MCF) combined with 2D partial-wave expansion technique. The method is applied to a one-electron QD case. Cross-sections are obtained for both the singlet and triplet couplings between the incident electron and the QD electron during the scattering. The total elastic cross-sections as well as the spin-flip scattering cross-sections resulting from the exchange potential are presented. Furthermore, inelastic scattering processes are also studied using a multichannel formalism of the MCF.Comment: 11 pages, 4 figure

Determination of the superconducting gap in near optimally doped Bi_2Sr_{2-x}La_xCuO_{6+\delta} (x ~ 0.4) from low-temperature specific heat

Low-temperature specific heat of the monolayer high-Tc superconductor Bi_2Sr_{2-x}La_xCuO_{6+\delta} has been measured close to the optimal doping point (x ~ 0.4) in different magnetic fields. The identification of both a T^2 term in zero field and a \sqrt{H} dependence of the specific heat in fields is shown to follow the theoretical prediction for d-wave pairing, which enables us to extract the slope of the superconducting gap in the vicinity of the nodes (v_{\Delta}, which is proportional to the superconducting gap \Delta_0 at the antinodes according to the standard d_{x^2-y^2} gap function). The v_{\Delta} or \Delta_0 (~ 12 meV) determined from this bulk measurement shows close agreement with that obtained from spectroscopy or tunneling measurements, which confirms the simple d-wave form of the superconducting gap.Comment: 5 pages, 4 figures, 1 tabl

The Nature of Optical Features in the Inner Region of the 3C48 Host Galaxy

The well-known quasar 3C48 is the most powerful compact steep-spectrum radio-loud QSO at low redshifts. It also has two unusual optical features within the radius of the radio jet (~1"): (1) an anomalous, high-velocity narrow-line component, having several times as much flux as does the narrow-line component coinciding with the broad-line redshift; and (2) a bright continuum peak (3C48A) ~1" northeast of the quasar. Both of these optical features have been conjectured to be related to the radio jet. Here we explore these suggestions. We have obtained Gemini North GMOS integral-field-unit (IFU) spectroscopy of the central region around 3C48. We use the unique features of the IFU data to remove unresolved emission at the position of the quasar. The resolved emission at the wavelength of the high-velocity component is peaked <~0.25" north of the quasar, at virtually the same position angle as the base of the radio jet. These observations appear to confirm that this high-velocity gas is connected with the radio jet. However, most of the emission comes from a region where the jet is still well collimated, rather than from the regions where the radio maps indicate strong interaction with an external medium. We also present the results of HST STIS spectroscopy of 3C48A. We show that 3C48A is dominated by stars with a luminosity-weighted age of ~1.4 X 10^8 years, substantially older than any reasonable estimate for the age of the radio source. Our IFU data indicate a similar age. Thus, 3C48A almost certainly cannot be attributed to jet-induced star formation. The host galaxy of 3C48 is clearly the result of a merger, and 3C48A seems much more likely to be the distorted nucleus of the merging partner, in which star formation was induced during the previous close passage.Comment: 10 pages, accepted by The Astrophysical Journa

Two body non-leptonic Λb\Lambda_b decays in quark model with factorization ansatz

The two body non-leptonic $\Lambda_b$ decays are analyzed in factorization approximation, using quark model, $\xi = 1 / N_c$ as a free parameter. It is shown that the experimental branching ratio for $\Lambda_b \longrightarrow \Lambda {J/\psi}$ restricts $\xi$ and this ratio can be understood for a value of $\xi$ which lies in the range $0 \leq \xi \leq 0.5$ suggested by two body B meson decays. The branching ratios for $\Lambda_b \longrightarrow \Lambda_{c} D^*_s(D_s)$ are predicted to be larger than the previous estimates. Finally it is pointed that CKM-Wolfenstein parameter $\rho^2 + \eta^2$, where $\eta$ is CP phase, can be determined from the ratio of widths of $\Lambda_b \longrightarrow \Lambda \bar{D}$ and $\Lambda_b \longrightarrow \Lambda {J/\psi}$ or that of $\Lambda_b \longrightarrow p D_s$ and $\Lambda_b \longrightarrow \Lambda_c D_s$ independent of the parameter $\xi$.Comment: 18 pages, latex, 1 figure available on request, please send any questions or comments to [email protected]

Two types of generalized integrable decompositions and new solitary-wave solutions for the modified Kadomtsev-Petviashvili equation with symbolic computation

The modified Kadomtsev-Petviashvili (mKP) equation is shown in this paper to be decomposable into the first two soliton equations of the 2N-coupled Chen-Lee-Liu and Kaup-Newell hierarchies by respectively nonlinearizing two sets of symmetry Lax pairs. In these two cases, the decomposed (1+1)-dimensional nonlinear systems both have a couple of different Lax representations, which means that there are two linear systems associated with the mKP equation under the same constraint between the potential and eigenfunctions. For each Lax representation of the decomposed (1+1)-dimensional nonlinear systems, the corresponding Darboux transformation is further constructed such that a series of explicit solutions of the mKP equation can be recursively generated with the assistance of symbolic computation. In illustration, four new families of solitary-wave solutions are presented and the relevant stability is analyzed.Comment: 23 page

Non-deterministic Gates for Photonic Single Rail Quantum Logic

We discuss techniques for producing, manipulating and measureing qubits encoded optically as vacuum and single photon states. We show that a universal set of non-deterministic gates can be constructed using linear optics and photon counting. We investigate the efficacy of a test gate given realistic detector efficiencies.Comment: 8 pages, 6 figure

An SO(10) GUT Model with S4S4 Flavor Symmetry

We present a supersymmetric grand unification model based on SO(10) group with $S4$ flavor symmetry. In this model, the fermion masses are from Yukawa couplings involving $\bf{10}$ and $\bar{\bf{126}}$ Higgs multiplets and the flavor structures of mass matrices of both quarks and leptons are determined by spontaneously broken $S4$. This model fits all of the masses and mixing angles of the quarks and leptons. For the most general CP-violation scenario, this model gives $\sin\theta_{13}$ a wide range of values from zero to the current bound with the most probable values $0.02-0.09$. With certain assumptions where leptonic phases have same CP-violation source as CKM phase, one gets a narrower range $0.03-0.09$ for $\sin\theta_{13}$ with the most probable values $0.04-0.08$. This model gives leptonic Dirac CP phase the most probable values 2-4 radians in the general CP-violation case.Comment: 14 pages,2 figures. Version published in Physical Review