A solution to the non-Abelian duality problem

Dualities uniquely excel at resolving non-perturbative aspects of complex phase diagrams of interacting, Landau or topologically ordered, systems. However, traditional duality transformations fail for systems like the Heisenberg model and non-Abelian gauge theories. The bond-algebraic theory of quantum and classical dualities provides a solution to this long-standing conundrum, the so-called non-Abelian duality problem, by embedding traditional dualities into a more general transformation scheme that always preserves locality in any number of dimensions. Remarkably, it turns out to be unimportant whether a model?s group of symmetries is Abelian or non-Abelian. The capability of the bond-algebraic approach to handle finite and infinite systems with arbitrary boundary conditions has recently led to the discovery of holographic symmetries  , relating topological order, edge states, and generalized order parameters. We discuss the interplay between these distinguished boundary symmetries and our solution to the non-Abelian duality problem. To illustrate our technique we present, among others, novel dualities for the SU(2)$\mathit{SU}(2)$ principal chiral field and both U(1)$U(1)$ and SU(2)$\mathit{SU}(2)$ generalizations of the planar quantum compass model of orbital ordering.     

Variational approach to hydrodynamics: Application to the sonoluminescence gas bubble

We develop a variational approximation allowing to study under realistic physical conditions the interior dynamics of cavitating gas bubbles in liquids. We discuss in some detail the intricacy of the gas bubble dynamics related to the small size of the system. We also show how to formulate the problem in the framework of the energy equation for non-adiabatic processes.     

A new approach to particle confinement

A new approach to permanent confinement of non-relativistic and relativistic particles inside microscopic regions of space is presented. Motion in suitably chosen energy-dependent potentials turns out to be such that the size of orbits of particles bound in such potentials decreases when energy is supplied to them from external sources and there exists a maximum size of these orbits. The energy spectrum is purely discrete without any continuum. The dynamics of such particles requires the introduction of a space-dependent metric in the Hilbert space of states to ensure conservation of probability.     

A new approach to nonrenormalizable models

Nonrenormalizable quantum field theories require counter-terms; and based on the hard-core interpretation of such interactions, it is initially argued, contrary to the standard view, that counter-terms suggested by renormalized perturbation theory are in fact inappropriate for this purpose. Guided by the potential underlying causes of triviality of such models, as obtained by alternative analyses, we focus attention on the ground-state distribution function, and suggest a formulation of such distributions that exhibits nontriviality from the start. Primary discussion is focused on self-interacting scalar fields. Conditions for bounds on general correlation functions are derived, and there is some discussion of the issues involved with the continuum limit.     

A new approach to potential scattering

Potential scattering calculations based onCalogero's equation and given in two former papers are now improved to include unitarity of theS-matrix. It is shown that the method gives results better than the second Born approximation and even reasonable in the two limits of very strong coupling and very low energies. As test examples, the square-well potential and the Yukawa potential are discussed.     

A new approach to Burger's equation

A new approach to Burger's equation is proposed using the decomposition method, eliminating smallness assumptions or linearization.     

A new approach to classical mechanics

A new approach to classical mechanics proposed by Prigogine, George, and Rae, which avoids the nonlinear Hamilton-Jacobi technique and introduces a linear eigenvalue problem involving probabilities as eigenvectors, is illustrated by the study of an exactly soluble model.     

A new approach to peratization technique

The usual method of peratization technique is to expand scattering lengthA(a) in Born series in powers of the coupling constantg. In this paper a new approach to the peratization technique has been discussed starting with the standard equation for the scattering length. As an application of the theory developed, the cases of inverse fourth power and a logarithmic singular potentials have been discussed.     

A new approach to potential scattering

An approximate integral-representation of theS-matrix in partial-wave expansion is derived for a scalar Schrödinger particle in a central field. The method consists of linearizingCalogero's Riccati equation for the interpolatingS-matrix in such a way that the solution of the linearized equation deviates as little as possible from the exact one. TheS-matrix thus obtained exhibits exact crossing-symmetry and uniform convergence independent of the coupling constant of the scattering potential. In the weak coupling limit it is especially shown thatour method is more accurate than the second Born approximation. In the second part of the paper we specialize ourS-matrix to low and large energies. At low energies, a general integral for the scattering length is obtained and at large energies the summation over all angular momenta is carried out yielding an expression for the scattering amplitude.     

Augmented superfield approach to exact nilpotent symmetries for matter fields in non-Abelian theory

We derive the nilpotent (anti-) BRST symmetry transformations for the Dirac (matter) fields of an interacting four (3+1)-dimensional 1-form non-Abelian gauge theory by applying the theoretical arsenal of augmented superfield formalism where (i) the horizontality condition, and (ii) the equality of a gauge invariant quantity, on the six (4,2)-dimensional supermanifold, are exploited together. The above supermanifold is parameterized by four bosonic spacetime coordinates x^μ (with μ=0,1,2,3) and a couple of Grassmannian variables θ and θ̄. The on-shell nilpotent BRST symmetry transformations for all the fields of the theory are derived by considering the chiral superfields on the five (4,1)-dimensional super sub-manifold and the off-shell nilpotent symmetry transformations emerge from the consideration of the general superfields on the full six (4,2)-dimensional supermanifold. Geometrical interpretations for all the above nilpotent symmetry transformations are also discussed within the framework of augmented superfield formalism.     

Green’s function approach to phonon hydrodynamics in solids

In the first part the Green’s function approach developed byKadanoff andBaym is used to derive a transport equation for phonons in a dielectric anharmonic crystal. The approximations which reduce this generalized equation to the Peierls equation are exhibited. In the second part, neglecting Umklapp processes, the linearized equation is applied to hydrodynamic phenomena. In a system close to local thermal equilibrium second sound and Poiseuille flow may exist. The damping through normal processes is approximately calculated by a momentum-dependent relaxation time. The coupling between the phonon and the dilatation fields is discussed.     

一种新型光滑粒子动力学固壁边界施加模型

由于Lagrange粒子法的本质, 固壁边界条件的施加一直是光滑粒子动力学方法的难点之一. 本文从固壁边界的物理原理出发, 应用多层虚粒子表征固壁边界, 提出了一种新型固壁边界施加模型. 将虚粒子看作流体的扩展, 计算中虚粒子密度保持不变, 压力、速度等参数通过对流体粒子的插值获得, 虚粒子有条件的参与控制方程的计算, 对流体的密度/压力产生影响, 通过压力梯度隐式地表征壁面与流体之间的作用强度并对流体粒子施加沿壁面法线方向的斥力作用, 防止流体粒子对壁面的穿透. 数值算例测试结果表明, 与现有固壁边界施加方法相比, 本文方法更加符合流体与固壁边界作用的物理原理, 可以简单、有效地施加固壁边界条件, 方便地应用于具有复杂几何边界的问题, 获得稳定的流场形态、规则的粒子秩序及良好的速度、压力等参量的分布.     

非等温非牛顿黏性流体流动问题的修正光滑粒子动力学方法模拟

为准确、有效地模拟非等温非牛顿黏性流体的流动问题,本文基于一种不含核导数计算的核梯度修正格式和不可压缩条件给出了一种改进光滑粒子动力学(SPH)离散格式,它较传统SPH离散格式具有较高精度和较好稳定性.同时,为准确地描述温度场的演化过程,建立了非牛顿黏性的SPH温度离散模型.通过对等温Poiseuille流、喷射流和非等温Couette流、4:1收缩流进行模拟,并与其他数值结果作对比,分别验证了改进SPH方法模拟非牛顿黏性流动问题的可靠性和提出的SPH温度离散模型求解非等温流动问题的有效性和准确性.随后,运用改进SPH方法结合SPH温度离散模型对环形腔和C形腔内非等温非牛顿黏性流体的充模过程进行了试探性模拟研究,分析了数值模拟的收敛性,讨论了不同位置处热流参数对温度和流动的影响.     

A new approach to melting under pressure

Abstract

A theory is presented that predicts the melting curve and the solid-solid-liquid triple point of a solid. It is based on the elastic properties of the crystal.     

A new approach to the Einstein-Podolsky-Rosen paradox

Some new aspects of the EPR paradox are considered. We first show that the authors' argument, leading to the conclusion that quantum theory is incomplete, is based on a tacit assumption that may be questioned. We then investigate the non-local features of the EPR setup and point out an interesting connection between the nonlocality involved in the quantum correlations of pairs of particles and that of a single particle in quantum theory.