Solution of two-body bound state problems with confining potentials

The homogeneous Lippmann-Schwinger integral equation is solved in momentum space by using confining potentials. Since the confining potentials are unbounded at large distances, they lead to a singularity at small momentum. In order to remove the singularity of the kernel of the integral equation, a regularized form of the potentials is used. As an application of the method, the mass spectra of heavy quarkonia, mesons consisting from heavy quark and antiquark (Υ(bb̄), ψ(cc̄)), are calculated for linear and quadratic confining potentials. The results are in good agreement with configuration space and experimental results. © 2010 American Institute of Physics.

The Nonlinear Phenomena Of Thin Polydimethylsiloxane (Pdms) Films In Electrowetting

Electrowetting (EW) is an effective way to manipulate small volume liquid in micro- and nano-devices, for it can improve its wettability. Since the late 1990s, electrowetting-on-dielectric (EWOD) has been used widely in bio-MEMS, lab-on-a-chip, etc. Polydimethlsiloxane (PDMS) is extensively utilized as base materials in the fabrication of biomedical micro- and nano-devices. The properties of thin PDMS films used as dielectric layer in EW are studied in this paper. The experimental results show that the thin PDMS films exhibit good properties in EWOD. As to PDMS films with different thicknesses, a threshold voltage and a hysteresis were observed in the EIWOD experiments.

An Electrowetting Model For Rough Surfaces Under Low Voltage

Electrowetting is one of the most effective methods to enhance wettability. A significant change of contact angle for the liquid droplet can result from the surface microstructures and the external electric field, without altering the chemical composition of the system. During the electrowetting process on a rough surface, the droplet exhibits a sharp transition from the Cassie-Baxter to the Wenzel regime at a low critical voltage. In this paper, a theoretical model for electrowetting is put forth to describe the dynamic electrical control of the wetting behavior at the low voltage, considering the surface topography. The theoretical results are found to be in good agreement with the existing experimental results. (c) Koninklijke Brill NV, Leiden, 2008.

中能核反应中的统计发射过程及核温度参量

在过去的几年里，利用兰州重离子加速器（HIRFL）提供的束流，以及在OUVERTURE合作研究中，利用意大利国家核物理研究院南方实验室（INFN-LNS）超导回旋提供的束流，进行了多次中能区重离子核反应实验研究工作。如，最初的46.7MeV/u ~(12)C+~(58)Ni，~(115)In，~(197)Au的实验及30MeV/u ~(40)Ar+~(58)Ni，~(64)Ni~(115)In和30MeV/u Ni轰击Ni，Au，Al在MULTICS+MEDEA：4π装置上进行的实验工作。此外，本人还从事过一些理论研究工作，包括多粒子散射形式理论和相关数学物理问题研究，量子分子动力学和量子统计模型计算。本文是从事这些核物理研究工作的积累，主要侧重于实验结果的物理内容分析，而不强调实验技术，数据处理的技巧。主要的物理内容有以下几个方面：1.对于利用双同位素产额比提取同位素核温度的方法进行研究推广，使得对于实验中碰到的仅有部分能谱可以实现很好同位素分辩的情况，即使不能得到总的同位素产额，仅仅通过一段能区的同位素产额也可提取核温度。用于具体的实验研究工作中后，对于46.7MeV/u ~(12)C+~(58)Ni，~(115)In，~(197)Au核反应过程，同一体系利用这种方法得到的同位素核温度和利用粒子非稳态布居提取的核温度一致。2.围绕核反应过程中核温度的参量的提取，对于双同位素产额比与核温度的刻度关系进行了分析研究，通过计算考虑中等质量碎片（IMF）内部激发能后的内部配分函数表明，中等质量碎片的内部激发对刻度关系有重要影响。零阶近似下区域密度近似的结果和Gemini模拟计算的结果反映了相同的情况。3.研究核反应机制，多个粒子散射的形式理论的必需的，对于两体散射，其形式理论已经比较成熟，但是对于多个粒子散射问题出现的严重的困难是多体Lippmann-Schwinger方程无唯一收敛的解。作为一种探索性的研究工作，开展了多体散射理论研究工作，发展了一些具有普遍意义的数学物理方法。在本项研究工作中，通过能基础数学中的约当引理的推广，发现一个特例：对非连接图，Lippmann-Schwingwer方程存在收敛的解，因此多体散射形式理论，有可能重新建立。由于核力和多体问题是当今核物理研究的两大难点，世界各国的科学家都在努力以图攻克它们，而且多体问题还是物理学的其它许多领域的难题，因而多体散射还是引起诸多研究学科广泛兴趣的课题。通过发展一些新的数学理论和方法，我们已得到一些有意义的结果。4.将量子分子动力学这种中高能量区域所用的理论分析方法扩展至较低能区，通过对相空间中初始位置和动量抽样增加限制条件。如结合能和实验值要求一致，平均核势，核内Pauli阻塞更强一些，在演化中能量和动量守恒等等。得到一个很稳定的初始基态。均方半径保持不弥散的时间可达1600fm/c，用于研究10.6MeV/u Ne~(20)+Al~(27)的实验分析过程中。另外，量子统计模型（QSM）主要描述中心核-核碰撞，将它和碎裂模型结合，作一些改进后，可以对核-核碰撞进行统一描述。5.在中能核反应研究中发现，核反应过程中有大量的中子，轻带电粒子以及中等质量碎片发射出来，可以将这些粒子发射机制大致分为两大类。其中一类可以归结为动力学发射过程的产物。另一类则可以归于统计发射的产物。在低能核反应中，其发射能谱的斜率的负倒数，可作为复合核的核温度。而在中能重离子核反应中，其发射能谱变得很复杂，不再具有Maxwell分布。通常的三源拟合所给出的温度参数，已不能反映物理实质。提出多阶矩分析方法用于分析中能核反应中统计发射规律及受动力学过程的影响。

Integral equations of scattering in one dimension

A self-contained discussion of integral equations of scattering is presented in the case of centrally symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and three dimensions. The present discussion illustrates in a simple fashion the concept of partial-wave decomposition, Green's function, Lippmann-Schwinger integral equations of scattering for wave function and transition operator, optical theorem, and unitarity relation. We illustrate the present approach with a Dirac delta potential. (C) 2001 American Association of Physics Teachers.

Strong D* -> D pi and B* -> B pi couplings

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Flavor SU(4) breaking between effective couplings

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

No-pole condition in Landau gauge: Properties of the Gribov ghost form factor and a constraint on the 2d gluon propagator

We study general properties of the Landau-gauge Gribov ghost form factor sigma(p(2)) for SU(N-c) Yang-Mills theories in the d-dimensional case. We find a qualitatively different behavior for d = 3, 4 with respect to the d = 2 case. In particular, considering any (sufficiently regular) gluon propagator D(p(2)) and the one-loop-corrected ghost propagator, we prove in the 2d case that the function sigma(p(2)) blows up in the infrared limit p -> 0 as -D(0) ln(p(2)). Thus, for d = 2, the no-pole condition sigma(p(2)) < 1 (for p(2) > 0) can be satisfied only if the gluon propagator vanishes at zero momentum, that is, D(0) = 0. On the contrary, in d = 3 and 4, sigma(p(2)) is finite also if D(0) > 0. The same results are obtained by evaluating the ghost propagator G(p(2)) explicitly at one loop, using fitting forms for D(p(2)) that describe well the numerical data of the gluon propagator in two, three and four space-time dimensions in the SU(2) case. These evaluations also show that, if one considers the coupling constant g(2) as a free parameter, the ghost propagator admits a one-parameter family of behaviors (labeled by g(2)), in agreement with previous works by Boucaud et al. In this case the condition sigma(0) <= 1 implies g(2) <= g(c)(2), where g(c)(2) is a "critical" value. Moreover, a freelike ghost propagator in the infrared limit is obtained for any value of g(2) smaller than g(c)(2), while for g(2) = g(c)(2) one finds an infrared-enhanced ghost propagator. Finally, we analyze the Dyson-Schwinger equation for sigma(p(2)) and show that, for infrared-finite ghost-gluon vertices, one can bound the ghost form factor sigma(p(2)). Using these bounds we find again that only in the d = 2 case does one need to impose D(0) = 0 in order to satisfy the no-pole condition. The d = 2 result is also supported by an analysis of the Dyson-Schwinger equation using a spectral representation for the ghost propagator. Thus, if the no-pole condition is imposed, solving the d = 2 Dyson-Schwinger equations cannot lead to a massive behavior for the gluon propagator. These results apply to any Gribov copy inside the so-called first Gribov horizon; i.e., the 2d result D(0) = 0 is not affected by Gribov noise. These findings are also in agreement with lattice data.

A Lanczos-powered implementation of the Faber polynomial quantum time propagator for reaction probabilities

Complementing our recent work on subspace wavepacket propagation [Chem. Phys. Lett. 336 (2001) 149], we introduce a Lanczos-based implementation of the Faber polynomial quantum long-time propagator. The original version [J. Chem. Phys. 101 (1994) 10493] implicitly handles non-Hermitian Hamiltonians, that is, those perturbed by imaginary absorbing potentials to handle unwanted reflection effects. However, like many wavepacket propagation schemes, it encounters a bottleneck associated with dense matrix-vector multiplications. Our implementation seeks to reduce the quantity of such costly operations without sacrificing numerical accuracy. For some benchmark scattering problems, our approach compares favourably with the original. (C) 2004 Elsevier B.V. All rights reserved.

Symmetry contaminations in reactive scattering through long-lived collision complexes

We extend our Lanczos subspace time-independent wave packet method [J. Chem. Phys. 116 (2002) 2354] to investigate the issue of symmetry contaminations for the challenging deep-well H + O-2 reaction. Our central objective is to address the issue of whether significant symmetry contamination can occur if a wavepacket initially possessing the correct O-O exchange symmetry is propagated over tens of thousands of recursive steps using a basis which does not explicitly enforce the correct symmetry, and if so how seriously this affects the results. We find that symmetry contamination does exist where the symmetry constraint is not explicitly enforced in the basis. While it affects individual resonances and the associated peak amplitudes, the overall shape of the more averaged quantities such as total reaction probabilities and vibrational branching ratios are not seriously affected. (C) 2004 Elsevier B.V. All rights reserved.

Unimolecular Rovibrational Bound and Resonance States for Large Angular Momentum: J=20 Calculations for HO2

We explore the calculation of unimolecular bound states and resonances for deep-well species at large angular momentum using a Chebychev filter diagonalization scheme incorporating doubling of the autocorrelation function as presented recently by Neumaier and Mandelshtam [Phys. Rev. Lett. 86, 5031 (2001)]. The method has been employed to compute the challenging J=20 bound and resonance states for the HO2 system. The methodology has firstly been tested for J=2 in comparison with previous calculations, and then extended to J=20 using a parallel computing strategy. The quantum J-specific unimolecular dissociation rates for HO2-> H+O-2 in the energy range from 2.114 to 2.596 eV have been reported for the first time, and comparisons with the results of Troe and co-workers [J. Chem. Phys. 113, 11019 (2000) Phys. Chem. Chem. Phys. 2, 631 (2000)] from statistical adiabatic channel method/classical trajectory calculations have been made. For most of the energies, the reported statistical adiabatic channel method/classical trajectory rate constants agree well with the average of the fluctuating quantum-mechanical rates. Near the dissociation threshold, quantum rates fluctuate more severely, but their average is still in agreement with the statistical adiabatic channel method/classical trajectory results.

Freezing of the QCD coupling constant and solutions of Schwinger-Dyson equations

We compare phenomenological values of the frozen QCD running coupling constant (alpha(s)) with two classes of infrared finite solutions obtained through nonperturbative Schwinger-Dyson equations. We use these same solutions with frozen coupling constants as well as their respective nonperturbative gluon propagators to compute the QCD prediction for the asymptotic pion form factor. Agreement between theory and experiment on alpha(s)(0) and F (pi)(Q(2)) is found only for one of the Schwinger-Dyson equation solutions.

HIGHER-DERIVATIVE SCHWINGER MODEL

Using the operator formalism, we obtain the bosonic representation for the free fermion field satisfying an equation of motion with higher-order derivatives. Then, we consider the operator solution of a generalized Schwinger model with higher-derivative coupling. Since the increasing of the derivative order implies the introduction of an equivalent number of extra fermionic degrees of freedom, the mass acquired by the gauge field is bigger than the one for the standard two-dimensional QED. An analysis of the problem from the functional integration point of view corroborates the findings of canonical quantization, and corrects certain results previously announced in the literature on the basis of Fujikawa's technique.

SELF-CONSISTENT SOLUTION OF THE SCHWINGER-DYSON EQUATIONS FOR THE NUCLEON AND MESON PROPAGATORS

The Schwinger-Dyson equations for the nucleon and meson propagators are solved self-consistently in an approximation that goes beyond the Hartree-Fock approximation. The traditional approach consists in solving the nucleon Schwinger-Dyson equation with bare meson propagators and bare meson-nucleon vertices; the corrections to the meson propagators are calculated using the bare nucleon propagator and bare nucleon-meson vertices. It is known that such an approximation scheme produces the appearance of ghost poles in the propagators. In this paper the coupled system of Schwinger-Dyson equations for the nucleon and the meson propagators are solved self-consistently including vertex corrections. The interplay of self-consistency and vertex corrections on the ghosts problem is investigated. It is found that the self-consistency does not affect significantly the spectral properties of the propagators. In particular, it does not affect the appearance of the ghost poles in the propagators.

Schwinger-dyson equations and dynamical gluon mass generation

We discuss the solutions obtained for the gluon propagador in Landau gauge within two distinct approximations for the Schwinger-Dyson equations (SDE). The first, named Mandelstam's approximation, consist in neglecting all contributions that come from fermions and ghosts fields while in the second, the ghosts fields are taken into account leading to a coupled system of integral equations. In both cases we show that a dynamical mass for the gluon propagator can arise as a solution. © 2005 American Institute of Physics.