Weinbergʼs approach to nucleon–nucleon scattering revisited

We propose a new, renormalizable approach to nucleon–nucleon scattering in chiral effective field theory based on the manifestly Lorentz invariant form of the effective Lagrangian without employing the non-relativistic expansion. For the pion-less case and for the formulation based on perturbative pions, the new approach reproduces the known results obtained by Kaplan, Savage and Wise. Contrary to the standard formulation utilizing the non-relativistic expansion, the non-perturbatively resummed one-pion exchange potential can be renormalized by absorbing all ultraviolet divergences into the leading S-wave contact interactions. We explain in detail the differences to the non-relativistic formulation and present numerical results for two-nucleon phase shifts at leading order in the low-momentum expansion.     

Effective potential of the O(N) linear sigma-model at finite temperature

We study the O(N) symmetric linear sigma-model at finite temperature as the low-energy effective models of quantum chromodynamics (QCD) using the Cornwall-Jackiw-Tomboulis (CJT) effective action for composite operators. It has so far been claimed that the Nambu-Goldstone theorem is not satisfied at finite temperature in this framework unless the large-N limit in the O(N) symmetry is taken. We show that this is not the case. The pion is always massless below the critical temperature, if one determines the propagator within the form such that the symmetry of the system is conserved, and defines the pion mass as the curvature of the effective potential. We use a regularization for the CJT effective potential in the Hartree approximation, which is analogous to the renormalization of auxiliary fields. A numerical study of the Schwinger-Dyson equation and the gap equation is carried out including the thermal and quantum loops. We point out a problem in the derivation of the sigma meson mass without quantum correction at finite temperature. A problem about the order of the phase transition in this approach is also discussed. Received: 21 June 2000 / Accepted: 13 September 2000     

Some Aspects of Nuclear Structure in Relativistic Approach

The nucleon effective interaction in the nuclear medium is investigated in the framework of the DiracBrueckner-Hartree-Fock (DBHF) approach. A new decomposition of the Dirac structure of nucleon self-energy in the DBHF is adopted for asymmetric nuclear matter. The properties of finite nuclei are investigated with the nucleon effective interaction. The agreement with the experimental data is satisfactory. The relativistic microscopic optical potential in asymmetric nuclear matter is investigated in the DBHF approach. The proton scattering from nuclei is calculated and compared with the experimental data. A proper treatment of the resonant continuum for exotic nuclei is studied. The width effect of the resonant continuum on the pairing correlation is discussed. The quasiparticle relativistic random phase approximation based on the relativistic mean-field ground state in the response function formalism is also addressed.     

Some Aspects of Nuclear Structure in Relativistic Approach

The nucleon effective interaction in the nuclear medium is investigated in the framework of the DiracBrueckner-Hartree-Fock (DBHF) approach. A new decomposition of the Dirac structure of nucleon self-energy in the DBHF is adopted for asymmetric nuclear matter. The properties of finite nuclei are investigated with the nucleon effective interaction. The agreement with the experimental data is satisfactory. The relativistic microscopic optical potential in asymmetric nuclear matter is investigated in the DBHF approach. The proton scattering from nuclei is calculated and compared with the experimental data. A proper treatment of the resonant continuum for exotic nuclei is studied. The width effect of the resonant continuum on the pairing correlation is discussed. The quasiparticle relativistic random phase approximation based on the relativistic mean-field ground state in the response function formalism is also addressed.     

The Gross-Neveu model at finite temperature at next-to-leading order in the 1/N expansion

We present new results on the Gross-Neveu model at finite temperature and at next-to-leading order in the 1/N expansion. In particular, a new expression is obtained for the effective potential which is explicitly invariant under renormalization group transformations. The model is used as a playground to investigate various features of field theory at finite temperature. For example we verify that, as expected from general arguments, the cancellation of ultraviolet divergences takes place at finite temperature without the need for introducing counterterms beyond those of zero temperature. As well known, the discrete chiral symmetry of the (1+1)-dimensional model is spontaneously broken at zero temperature and restored, in leading order, at some temperature T_c; we find that the 1/N approximation breaks down for temperatures below T_c: as the temperature increases, the fluctuations become eventually too large to be treated as corrections, and a Landau pole invalidates the calculation of the effective potential in the vicinity of its minimum. Beyond T_c, the 1/N expansion becomes again regular: it predicts that in leading order the system behaves as a free gas of massless fermions and that, at the next-to-leading order, it remains weakly interacting. In the limit of large temperature, the pressure coincides with that given by perturbation theory with a coupling constant defined at a scale of the order of the temperature, as expected from asymptotic freedom.     

Instabilities in thermal gravity with a cosmological constant

It is shown that in quantum gravity at finite temperature, the effective potential evaluated in the tadpole approximation can have a local minimum below a certain critical temperature. However, when the leading higher order thermal loop corrections are included, one finds that no static solution exists at high temperature.     

IR renormalization of general effective actions and Hawking flux in 2D gravity theories

The infrared problem of the effective action in 2D is discussed in the framework of the covariant perturbation theory. The divergences are regularized by a mass and the leading term is evaluated up to the third order of perturbation theory. A summation scheme is proposed which isolates the divergences from the finite part of the series and results in a single term. The latter turns out to be equivalent to the coupling to a certain classical external field. This suggests renormalization by factorization. PACS 4.60.-m; 4.60.Kz; 4.70.Dy     

Meson Properties at Finite Temperature in the Linear Sigma Model

The meson masses are investigated at finite temperature in the framework of the linear sigma model with an explicit chiral symmetry breaking term. The imaginary-time thermo-field dynamics and effective potential have been used for the calculation of the meson masses. We found that the behavior of the sigma and pion masses at finite temperature is in agreement with previous works. The critical temperature, the order of the phase transition, and the dependence of the meson fields on the temperature are discussed.     

On a potential-velocity formulation of Navier-Stokes equations

Computational methods in continuum mechanics, especially those encompassing fluid dynamics, have emerged as an essential investigative tool in nearly every field of technology. Despite being underpinned by a well-developed mathematical theory and the existence of readily available commercial software codes, computing solutions to the governing equations of fluid motion remains challenging: in essence due to the non-linearity involved. Additionally, in the case of free surface film flows the dynamic boundary condition at the free surface complicates the mathematical treatment notably. Recently, by introduction of an auxiliary potential field, a first integral of the two-dimensional Navier-Stokes equations has been constructed leading to a set of equations, the differential order of which is lower than that of the original Navier-Stokes equations. In this paper a physical interpretation is provided for the new potential, making use of the close relationship between plane Stokes flow and plane linear elasticity. Moreover, it is shown that by application of this alternative approach to free surface flows the dynamic boundary condition is reduced to a standard Dirichlet-Neumann form, which allows for an elegant numerical treatment. A least squares finite element method is applied to the problem of gravity driven film flow over corrugated substrates in order to demonstrate the capabilities of the new approach. Encapsulating non-Newtonian behaviour and extension to three-dimensional problems is discussed briefly.     

量子化学中有限元法的并行计算

在有限元方法的框架下,将量子化学中的基组展开方法和普通有限元方法结合起来,提出了一个新方案。在曙光1000并行机上,采用新方案,计算了Li₂、LiH、BH分子的基态总能量。新方案在相同计算量下,可获得比普通有限元方法高得多的精度。     

Control of the binding energy by tuning the single dopant position,magnetic field strength and shell thickness in ZnS/CdSe core/shell quantum dot

Recently, the new tunable optoelectronic devices associated to the inclusion of the single dopant are in continuous emergence. Combined to other effects such as magnetic field, geometrical confinement and dielectric discontinuity, it can constitute an approach to adjusting new transitions. In this paper, we present a theoretical investigation of magnetic field, donor position and quantum confinement effects on the ground state binding energy of single dopant confined in ZnS/CdSe core/shell quantum dot. Within the framework of the effective mass approximation, the Schrödinger equation was numerically been solved by using the Ritz variational method under the finite potential barrier. The results show that the binding energy is very affected by the core/shell sizes and by the external magnetic field. It has been shown that the single dopant energy transitions can be controlled by tuning the dopant position and/or the field strength.     

An age-dependent approach to random walks on disordered lattices

We derive a new approach for the stochastic transport in random systems, starting from a phenomenological master equation with random transition rates. Our method combines the effective medium approximation with age-dependent dynamics. Within the framework of our approximation, the static disorder may be described by means of a system of age-dependent master equations. For translationally invariant systems which obey certain separability conditions, the approach is equivalent with the continuous time random walk theory. Moreover, for self-avoiding random walks our effective medium approximation is exact. For non self-avoiding random walks, the approximation neglects the correlations between successive transitions leading to closed paths on the lattice.     

Manning-Oosawa counterion condensation

Counterion condensation is a basic feature of 2D electrostatics exhibited by highly charged rodlike polymers such as DNA. In the framework of the Poisson Boltzmann equation with salt, we show that such a polymer of radius a attracts a condensate of thickness RM=A(axi)1/2 where xi is the Debye length and A depends weakly on the polymer charge density q0. To leading order in 1/ln(xi/a), we derive the condensate structure and show that free ions follow universal density profiles independent of a and q0. Generalizing this approach we calculate ion profiles for finite concentration solutions.     

Magneto-bound polaron in CdSe spherical quantum dots: strong coupling approach

The effect of a magnetic field on the ground-state energy of a donor impurity confined in a polar CdSe spherical quantum dot embedded in a nonpolar matrix is studied theoretically. The interaction between the all charge carriers (electron and ion) and the confined longitudinal optical phonons (LO-phonons) is taken into account by considering the strong coupling method (Landau–Pekar approach). A variational calculation is performed in the framework of the effective mass approximation using a trial wave function deduced from the second-order perturbation and assuming that the quantum dot has a finite depth potential.     

Similarity renormalization group evolution of chiral effective nucleon–nucleon potentials in the subtracted kernel method approach

Methods based on Wilson’s renormalization group have been successfully applied in the context of nuclear physics to analyze the scale dependence of effective nucleon–nucleon (NN) potentials, as well as to consistently integrate out the high-momentum components of phenomenological high-precision NN potentials in order to derive phase-shift equivalent softer forms, the so called V_low-k potentials. An alternative renormalization group approach that has been applied in this context is the similarity renormalization group (SRG), which is based on a series of continuous unitary transformations that evolve hamiltonians with a cutoff on energy differences. In this work we study the SRG evolution of a leading order (LO) chiral effective NN potential in the ¹S₀ channel derived within the framework of the subtracted kernel method (SKM), a renormalization scheme based on a subtracted scattering equation.     

Ordering thermodynamics from generalized potential description

The suggested effective potential approach allows to describe the change in phase relations. The evaluation of the internal mixing energy of alloys is carried out in the framework of the static concentration waves theory of Khachaturyan. The model outlines the technique to calculate the values of the energy parameters of ordering process from the first principles. On the basis of non-empirical pair potential the temperature dependence of the long-range order parameter of NiTi and AuPd are plotted.     

Shear Viscosity of Hot QED at Finite Chemical Potential from Kubo Formula

Within the framework of finite temperature field theory this paper discusses the shear viscosity of hot QED plasma through Kubo formula at one-loop skeleton diagram level with a finite chemical potential. The effective widths (damping rates) are introduced to regulate the pinch singularities and then gives a reliable estimation of the shear viscous coefficient. The finite chemical potential contributes positively compared to the pure temperature case. The result agrees with that from the kinetics theory qualitatively.     

Renormalization of the post-Gaussian effective potential

In order to study the effects of renormalization on the variationally calculated φ⁴ effective potential, we employ the Gaussian-effective-potential formalism, nonlinear canonical transformations, and the loop approximation. A quantitative comparison of physically equivalent potentials is carried out in two dimensions. The renormalization procedure in three dimensions, leading after the nonlinear transformation to a manifestly finite energy expectation, is described. Different from finite-dimensional quantum mechanics, the optimization is meaningful only if all divergent sub-graphs generated by the ansatz are identified and renormalized by the bare parameters.     

A new effective potential for deuteron

We calculate for the first time the static properties of the deuteron, within the framework of supersymmetric quantum mechanics, analytically. A new effective potential and its partner are derived from a superpotential so that all parameters are fitted by the experimental data. An analytical expression is obtained for the deuteron wave function and contributions of the orthogonal ¹³S₁ and ¹³D₁ states are determined, explicitly. Compared to one pion exchange, the superpotential produces an electrostatic as well as two pion exchange terms for the potential. The saddle point radius of the potential and the maximum of the wave function are linearly proportional. In comparison with other methods, the approach presented in this paper is a new and extensible symmetry-based approach that, despite its straightforward calculations and explicit analytical expressions, provides a good explanation for two-body effective interactions such as two-nucleon systems and diatomic molecules.     

A general finite element model for numerical simulation of structure dynamics

A finite element model used to simulate the dynamics with continuum and discontinuum is presented. This new approach is conducted by constructing the general contact model. The conventional discrete element is treated as a standard finite element with one node in this new method. The one-node element has the same features as other finite elements, such as element stress and strain. Thus, a general finite element model that is consistent with the existed finite element model is set up. This new model is simple in mathematical concept and is straightforward to be combined into the existing standard finite element code. Numerical example demonstrates that this new approach is more effective to perform the dynamic process analysis in which the interactions among a large number of discrete bodies and continuum objects are included.