Flavor SU(3) topological diagram and irreducible representation amplitudes for heavy meson charmless hadronic decays:mismatch and equivalence

Flavor SU(3) analysis of B meson charmless hadronic two light pseudoscalar decays can be formulated in two different ways. One is to construct the SU(3) irreducible representation amplitude(IRA) according to effective Hamiltonian transformation properties, and the other is to draw the topological diagrams(TDA). We first point out that previous analyses of TDA and IRA approaches do not match in several aspects, in particular a few SU(3)independent amplitudes have been overlooked in the TDA approach. This has caused confusions in the past and sometimes resulted in incorrect interpretation of data. We then demonstrate that only if these amplitudes are included, a consistent and unified picture can be obtained. With the new TDA amplitudes, all charmless hadronic decays of heavy meson must have nonzero direct CP symmetries as already predicted by the IRA approach. In addition to their notable impact on CP asymmetry, the new amplitudes are also important to extract new physics information.     

Conserved quantities and symmetries related to stochastic Hamiltonian systems

In this paper symmetries and conservation laws for stochastic dynamical systems are discussed in detail. Determining equations for infinitesimal approximate symmetries of Ito and Stratonovich dynamical systems are derived. It shows how to derive conserved quantities for stochastic dynamical systems by using their symmetries without recourse to Noether's theorem.     

Direct-interaction approximation by the modal-interaction perturbation technique

An alternate method is presented of obtaining the direct-interaction equations by combining the heuristic and rigorous derivations of Kraichnan. Within the framework of the model dynamic representation of Kraichnan's rigorous theory, we have developed the irreducible diagram expansion systematically * by formalizing the perturbation argument of his heuristic derivation. It is hoped that the present work will provide a further insight into the analytical structure of the irreducible diagram expansion and bridge the gap apparent in the two original derivations of the direct-interaction equations given by Kraichnan.     

A study of the Al-Cu-Co phase diagram and the solidification of alloys containing decagonal phase

The ternary Al-Cu-Co phase diagram was studied in order to revise the region of 50–75 at.% Al. The study was carried out by optical microscopy, scanning electron microscopy, transmission electron microscopy and powder X-ray diffraction. Isothermal 800°C, 600°C and 540°C sections are presented. The development of the composition range of the decagonal phase with temperature is discussed.     

A general formula for analytic reduction of multi-loop tensor Feynman integrals

We prove a general formula for analytic reduction of tensor integrals which appear in calculations of multi-loop Feynman diagrams in quantum field theory models.     

A variance formula related to a quantum conductance problem

Let t be a block of an Haar-invariant orthogonal (β=1), unitary (β=2) or symplectic (β=4) matrix from the classical compact groups O(n), U(n) or Sp(n), respectively. We obtain a close form for Var(tr(t^∗t)). The case for β=2 is related to a quantum conductance problem, and our formula recovers a result obtained by several authors. Moreover, our result shows that the variance has a limit ⁻¹(8β) for β=1,2 and 4 as the sizes of t go to infinity in a special way. Although t in our formulation comes from a block of an Haar-invariant matrix from the classical compact groups, the above limit is consistent with a formula by Beenakker, where t is a block of a circular ensemble.     

Effect of Microscopic Noise on Front Propagation

We study the effect of the noise due to microscopic fluctuations on the position of a one dimensional front propagating from a stable to an unstable region in the linearly marginal stability case. By simulating a very simple system for which the effective number N of particles can be as large as N=10¹⁵⁰, we measure the N dependence of the diffusion constant D_N of the front and the shift of its velocity v_N. Our results indicate that D_N(log N)^–3. They also confirm our recent claim that the shift of velocity scales like v_min–v_NK(log N)^–2 and indicate that the numerical value of K is very close to the analytical expression K_approx obtained in our previous work using a simple cut-off approximation.     

Phase diagram of the extended hubbard model with pair hopping interaction

A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and pair-hopping interaction W is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin-density wave (SDW) and charge-density wave (CDW) phases for large U and V, respectively, we identify a bond-charge-density-wave (BCDW) phase W < 0, | U - 2V| < | 2W| and a bond-spin-density-wave (BSDW) for W > 0, | U - 2V| < W. The possibility of bond-located ordering results from the site-off-diagonal nature of the pair-hopping term and is a special feature of the half-filled band case. The BCDW phase corresponding to an enhanced Peierls instability in the system. The BdSDW is an unconventional insulating magnetic phase, characterized by a gapless spin excitation spectrum and a staggered magnetization located on bonds between sites. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the η-superconducting phase at | U - 2V| ≪ 2t?W is briefly discussed. Received 20 February 2002 / Received in final form 11 April 2002 Published online 19 July 2002     

A stochastic particle system modeling the Carleman equation

Two species of Brownian particles on the unit circle are considered; both have diffusion coefficient >0 but different velocities (drift), 1 for one species and –1 for the other. During the evolution the particles randomly change their velocity: if two particles have the same velocity and are at distance ( being a positive parameter), they both may simultaneously flip their velocity according to a Poisson process of a given intensity. The analogue of the Boltzmann-Grad limit is studied when goes to zero and the total number of particles increases like ^–1. In such a limit propagation of chaos and convergence to a limiting kinetic equation are proven globally in time, under suitable assumptions on the initial state. If, furthermore, depends on and suitably vanishes when goes to zero, then the limiting kinetic equation (for the density of the two species of particles) is the Carleman equation.Dedicated to the memory of Paola Calderoni.     

随机扩散模型一种新的密度函数统计方法

引入核函数法对随机扩散方程（SDE）样本的密度分布进行统计,希望用核函数来减少统计涨落。由于SDE样本的密度随时间发展,越来越稀疏,所以核函数也应该越来越大,也就是说核函数应该随时间在变化。通过一个瞬时释放的二维扩散问题（具有解析解）,从定性和定量两个角度比较了变带宽核函数法和传统统计方法在密度分布统计中的性能差别,论述了变带宽核函数法的优缺点,变带宽核函数法在牺牲部分峰值的前提下可以很好地解决SDE样本密度分布统计涨落问题,在工程应用中值得推广。     

Phase diagram of the three-dimensional Hubbard model at half filling

We investigate the phase diagram of the three-dimensional Hubbard model at half filling using quantum Monte Carlo (QMC) simulations. The antiferromagnetic Néel temperature is determined from the specific heat maximum in combination with finite-size scaling of the magnetic structure factor. Our results interpolate smoothly between the asymptotic solutions for weak and strong coupling, respectively, in contrast to previous QMC simulations. The location of the metal-insulator transition in the paramagnetic phase above is determined using the electronic compressibility as criterion. Received 11 April 2000 and Revised in final form 29 June 2000     

A diagrammatic derivation of (convective) pattern equations

In complicated bifurcation problems where more than one instability can arise at onset, reasonably sound derivations of the equations that govern the amplitudes of the nearly marginal modes have been developed when the spectrum of the modes is discrete. The basis of these derivations lies in the center manifold theorem of dynamical systems theory. But when the spectrum of the modes is continuous and we no longer have that theorem to fall back on, there is nevertheless an equation (the Swift-Hohenberg equation) that well describes the patterns seen in Rayleigh-Bénard convection. Indeed, several ‘derivations’ of the S-H equation have been offered and here we describe how to obtain the S-H equation using Bogoliubov’s method. We suggest that this procedure clarifies and simplifies (though it does not make rigorous) the derivation of the S-H equation.Looking ahead to the derivation of pattern equations for more complicated problems with continuous spectra, we also describe a diagrammatic procedure that, once mastered, is useful in performing the complicated perturbative developments that are needed in such derivations. Here we illustrate the proposed combination of the ideas of Bogoliubov and Feynman for the standard form of the Rayleigh-Bénard convection problem.The resulting pattern equation is nonlocal but it reduces without approximation to the 1-D Swift-Hohenberg equation in the case of 2-D convection. Like the S-H equation, the nonlocal version admits a Lyapunov functional and we briefly indicate its utility in pattern selection both for the Swift-Hohenberg equation and its nonlocal extension. We conclude by describing the kinds of problems for which we intend the combined method but reserve the exhibition of the required calculations for a future festschrift.     

A Stochastic Mechanics Based on Bohm‧s Theory and its Connection with Quantum Mechanics

We construct a stochastic mechanics by replacing Bohm‧s first-order ordinary differential equation of motion with a stochastic differential equation where the stochastic process is defined by the set of Bohmian momentum time histories from an ensemble of particles. We show that, if the stochastic process is a purely random process with n-th order joint probability density in the form of products of delta functions, then the stochastic mechanics is equivalent to quantum mechanics in the sense that the former yields the same position probability density as the latter. However, for a particular non-purely random process, we show that the stochastic mechanics is not equivalent to quantum mechanics. Whether the equivalence between the stochastic mechanics and quantum mechanics holds for all purely random processes but breaks down for all non-purely random processes remains an open question.     

Quantum Collision Models: A Beginner Guide

In recent years, quantum collision models, sometimes dubbed repeated interaction models, have gained much attention due to their simplicity and their capacity to convey ideas without resorting to technical complications typical of many approaches and techniques used in the field of open quantum systems. In this tutorial, we show how to use these models, highlighting their strengths and some technical subtleties often overlooked in the literature. We do this by deriving the Markovian master equation and comparing the standard collisional derivation with the standard microscopic one. We then use the collision model to derive the master equation of a two-level system interacting with either a bosonic or fermionic bath to give the reader a flavour of the real use of the model.     

Extended Riccati Equation Rational Expansion Method and Its Application to Nonlinear Stochastic Evolution Equations

In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons & Fractals 25 (2005) 1019] to uniformly construct a series of stochastic nontravelling wave solutions for nonlinear stochastic evolution equation. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions including a series of rational formal nontraveling wave and coefficient functions' soliton-like solutions and trigonometric-like function solutions. The method can also be applied to solve other nonlinear stochastic evolution equation or equations.     

随机系统的概率密度函数形状调节

针对受高斯白噪声激励的非线性随机系统,提出了使状态响应的概率密度函数形状跟踪期望形状的调节方法.首先,确立了非线性随机系统的多项式反馈机制,同时对系统中的非线性部分进行多项式展开;然后,以Fokker-Planck-Kolmogorov方程为工具,导出了与控制增益相关的各阶矩递推方程,并根据跟踪问题的要求,构造了矩逼近优化问题,用梯度搜索法求解该优化问题,获得了调节函数;再依据特征函数与概率密度函数构成Fourier对的关系,对状态响应的概率密度函数进行重构;最后,通过两个例子仿真,验证了本文方法的有效性.     

Dynamic phase transitions in the kinetic mixed spin-1/2 and spin-5/2 Ising model under a time-dependent oscillating magnetic field

We calculate the dynamic phase transition (DPT) temperatures and present the dynamic phase diagrams in the kinetic mixed spin-1/2 and spin-5/2 Ising model under the presence of a time-dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the set of mean-field dynamic equations. The time variation of the average magnetizations and the thermal behavior of the dynamic magnetizations are investigated, extensively. The nature (continuous or discontinuous) of the transitions is characterized by studying the thermal behaviors of the dynamic magnetizations. The DPT points are obtained and the phase diagrams are presented in two different planes. Phase diagrams contain four fundamental phases and three coexistence or mixed phases, which strongly depend on interaction parameters. The phase diagrams are discussed and a comparison is made with the results of the other mixed spin Ising systems.