Excited States of the Double sine-Gordon Model

Using the Gaussian wave functional as variational ground state, we study the excited states of the double sine-Gordon model in (D+1) dimensions. We find, i) for D < 3 there exist twoparticle bound states, their energy decreases with increasing coupling; ii) also for D < 3, the phase shift of the two-particle scattering state is always positive; iii) for D ≥ 3 the investigation on the interaction between the particles shows that the theory is trivial.     

Variational Study of the Discrete sine-Gordon Model

By using the Gaussian wave functional method, the (1+1)-dimensional discrete sine-Gordon model is studied. The ground state energy and the one-particle states and the two-particle bound state are calculated.     

THE TWO-BOSON SCATTERING PHASE SHIFTS IN THE GENERAL φ6 THEORY WITH THE GAUSSIAN WAVE-FUNCTIONAL APPROACH

The two-particle scattering phase shifts with a λφ⁴ +ξφ⁶ interaction are com-puted in (1 + 1) and (2 + 1) dimensions using the Gaussian wave-functional approach.Through numerical analysis, we give the phase-shift curves with respect to the scat-tering energy for most cases of this theory. In (1 + 1) and (2 + 1 ) dimensions, for the symmetry vacuum the phase shifts are positive or negative depending on the signs of the renormalized parameter, while for the asymmetric vacuum the phase shifts are negative.     

Variational calculation of the excited states in the sinh-Gordon field theory

The Gaussian wave-functional variational approximation is used to calculate the energy of one-particle state as well as the energy and wave function of two-particle state in the sinh-Gordon model in (1+1) dimensions. We find that there are no bound states in this model. The phase shifts of the scattering states are investigated in detail.     

Equivalence of Bogoliubov Transformations to the Gaussian Wave-Functional Approach in sin-Dordon Model

Through the calculation of the effective potential and the excited state energies for the sinh-Gordon and the sine-Gordon models in (D + 1) dimensions, we show that the variational technique of Bogoliu bov transformations is equivalent to the Gaussian wave-functional approach.     

Variational calculation of the sine-Gordon effective potential

The Gaussian effective potential of the sine-Gordon model is calculated in 1+1 and 2+1 dimensions. Issues like renormalization, vacuum energy and stability of the vacuum are discussed in detail.     

Finite-volume form factors in semi-classical approximation

A semi-classical approach is used to obtain Lorentz covariant expressions for the form factors between the kink states of a quantum field theory with degenerate vacua. Implemented on a cylinder geometry it provides an estimate of the spectral representation of correlation functions in a finite volume. Illustrative examples of the applicability of the method are provided by the sine-Gordon and the broken φ⁴ theories in 1+1 dimensions.     

Mesons, baryons and waves in the baby Skyrmion model

We study various classical solutions of the baby-Skyrmion model in (2+1) dimensions. We point out the existence of higher energy states, interpret them as resonances of Skyrmions and anti-Skyrmions and study their decays. Most of the discussion involves a highly exited Skyrmion-like state with winding number one which decays into an ordinary Skyrmion and a Skyrmion-anti-Skyrmion pair. We also study wave-like solutions of the model and show that some of such solutions can be constructed from the solutions of the sine-Gordon equation. We also show that the baby-Skyrmion model has non-topological stationary solutions. We study their interactions with Skyrmions.     

LargeThe Coleman Phage Transition in Double Sine-Gordon Model

The Gaussian effective potential of the double sine-Gordon mode in 1+1 dimensions is calculated within this approximation, a Coleman phase transition condition is obtained which reduces to the well-known result in sine-Gordon model.     

Dromion Structures of (2+l)-Dimensional sine-Gordon System

Starting from n line soliton solutions of an integrable (2+1)-dimensional sine-Gordon system, one can find a dromion solution which is localized in all directions for a suitable potential. The dromion structures for a special (2+1)-dimensional sine-Gordon equation are studied in detail. The interactions among dromions are not elastic. In addition to a phase shift, the "shape" and the velocity of these dromions may also be changed after interaction.     

A Generalization of the Sine-Gordon Equation to 2 + 1 Dimensions

Abstract

The Singular Manifold Method (SMM) is applied to an equation in 2 + 1 dimensions [13] that can be considered as a generalization of the sine-Gordon equation. SMM is useful to prove that the equation has two Painlevé branches and, therefore, it can be considered as the modified version of an equation with just one branch, that is the AKNS equation in 2 + 1 dimensions. The solutions of the former split as linear superposition of two solutions of the second, related by a B¨acklund-gauge transformation. Solutions of both equations are obtained by means of an algorithmic procedure derived from these transformations.     

High-K multi-particle bands and pairing reduction in 254No

The multi-particle states and rotational properties of the two-particle bands in 254No are investigated by the cranked shell model with pairing correlations treated by the particle number conserving method.The rotational bands on top of the two-particle K^π=3^+,8^− and 10^+ states and the pairing reduction are studied theoretically in 254No for the first time.The experimental excitation energies and moments of inertia of the multi-particle states are reproduced well by the calculations.Better agreement with the data is achieved by including the high-order deformation ε6,which leads to enlarged Z=100 and N=152 deformed shell gaps.An increase of J¹ in these two-particle bands compared with the ground state band is attributed to the pairing reduction due to the Pauli blocking effect.     

Time-dependent variational method for sine-Gordon quantum field theory

The sine-Gordon model in 1+1 dimensions is studied within the Schrödinger framework for field theory. In particular we evaluate the effective potential and examine the finiteness ofm(t), the soliton mass, for allt.     

Bäcklund transformations for the generalized sine-gordon equation in 2+1 and 3+1 dimensions

We construct Bäcklund transformations for the generalized sine-Gordon equations in 2+1 and 3+1 dimensions. The connection of these equations with the nonlinear model is considered.     

Rydberg-Rydberg collisions: resonant enhancement of state mixing and penning ionization

In rubidium Rydberg states, the collision nD_(5/2)+nD_(5/2)-->(n-2)F_(7/2)+(n+2)P_(3/2) is nearly resonant in the vicinity of n=43. As a result, over a short range of n centered around n approximately 43 the Rydberg-Rydberg interaction potential is quite large and turns from repulsive to attractive [Phys. Rev. A 75, 032712 (2007)10.1103/PhysRevA.75.032712]. We use state-selective field ionization to investigate the effect of this resonance on instantaneous excitation of mixed two-particle states, state-mixing collisions, and Penning ionization. We find that these processes depend on the magnitude and sign of the two-particle interaction potential, and thus on n near the resonance. The large magnitude of the observed state mixing provides evidence for many-body effects.     

Separation Transformation and New Exact Solutions of the (N+1)-dimensional Dispersive Double sine-Gordon Equation

In this paper, the separation transformation approach is extended to the (N+1)-dimensional dispersive double sine-Gordon equation arising in many physical systems such as the spin dynamics in the B phase of ³He superfluid. This equation is first reduced to a set of partial differential equations and a nonlinear ordinary differential equation. Then the general solutions of the set of partial differential equations are obtained and the nonlinear ordinary differential equation is solved by F-expansion method. Finally, many new exact solutions of the (N+1)-dimensional dispersive double sine-Gordon equation are constructed explicitly via the separation transformation. For the case of N>2, there is an arbitrary function in the exact solutions, which may reveal more novel nonlinear structures in the high-dimensional dispersive double sine-Gordon equation.     

Soliton equations and pseudospherical surfaces

All the soliton equations in 1 + 1 dimensions that can be solved by the AKNS 2 × 2 inverse scattering method (for example, the sine-Gordon, KdV or modified KdV equations) are shown to describe pseudospherical surfaces, i.e., surfaces of constant negative Gaussian curvature. This result provides a unified picture of all these soliton equations. Geometrical interpretations of characteristic properties like infinite numbers of conservation laws and Bäcklund transformations and of the soliton solutions themselves are presented. The important role of scale transformations as generating one parameter families of pseudospherical surfaces is pointed out.     

Separation Transformation and New Exact Solutions of the (N+1)-dimensional Dispersive Double sine-Gordon Equation

In this paper,the separation transformation approach is extended to the(N + 1)-dimensional dispersive double sine-Gordon equation arising in many physical systems such as the spin dynamics in the B phase of 3 He superfluid.This equation is first reduced to a set of partial differential equations and a nonlinear ordinary differential equation.Then the general solutions of the set of partial differential equations are obtained and the nonlinear ordinary differential equation is solved by F-expansion method.Finally,many new exact solutions of the(N + 1)-dimensional dispersive double sine-Gordon equation are constructed explicitly via the separation transformation.For the case of N 2,there is an arbitrary function in the exact solutions,which may reveal more novel nonlinear structures in the high-dimensional dispersive double sine-Gordon equation.     

PLANE SYMMETRIC GENERAL SOLUTION TO EINSTEIN-MAXWELL EQUATIONS IN HIGHER DIMENSIONS

The plane symmetric general solution to the Einstein-Maxwell equations in D =n+2 dimensions is presented. In addition to the n(n+1)/2 spacelike Killing vector fields characterizing the higher dimensional plane symmetry, there is also an extra Killing vector field in the solution, suggesting that the generalized Birkhoff theorem proved for 4-dimensional spacetimes might also be valid in higher dimensions.