Exact soliton solutions for a spin chain with an easy plane

Controlling soliton excitations in Heisenberg spin chains through the magic angle

We study the nonlinear dynamics of collective excitation in an N -site XXZ quantum spin chain, which is manipulated by an oblique magnetic field. We show that, when the tilted field is applied along the magic angle, theta_{0}=+/-arccossqrt[13] , the anisotropic Heisenberg spin chain becomes isotropic and thus an freely propagating spin wave is stimulated. Also, in the regime of tilted angles larger and smaller than the magic angle, two types of nonlinear excitations appear: bright and dark solitons.

Exact soliton solution and inelastic two-soliton collision in a spin chain driven by a time-dependent magnetic field

We investigate dynamics of exact N-soliton trains in a spin chain driven by a time-dependent magnetic field by means of an inverse scattering transformation. The one-soliton solution indicates obviously the spin precession around the magnetic field and periodic shape variation induced by the time-varying field as well. In terms of the general soliton solutions, N-soliton interaction and particularly various two-soliton collisions are analyzed. The inelastic collision by which we mean the soliton shape change before and after collision appears is generally due to the time-varying field. We, moreover, show that complete inelastic collisions can be achieved by adjusting spectrum and field parameters. This may lead to a potential technique of shape control of soliton.

Density waves in traffic flow of two kinds of vehicles

Through the car-following model, the traffic flow of two types of vehicles (cars and trucks) on a single-lane flow is studied, in which drivers on different vehicles have different sensitivities and the safety distance is assumed to be the same for all vehicles. The linear analysis is carried out to determine the condition of critical stability. With the nonlinear analysis, it proves that the small fluctuation of the vehicle density near the critical stable state satisfies the Korteweg-deVries equation and different sensitivities affect only the soliton evolution. When the headway in the critical state is more than the safety distance, the density around the soliton peak exceeds the density of the critical stable state, which can be explained as the formation of traffic jam. Contrarily, when the headway state is less than the safety distance, drivers will increase the headway to avoid the jam. The direct approach of the soliton perturbation shows that drivers' sensitivity will increase the soliton's amplitude continuously. Moreover, the increase of the number of trucks in the traffic flow will slow down the evolution of the amplitude.

Ratio of canonical and microcanonical temperatures of a vibratory antiferromagnetic ising chain

The ratio of canonical and microcanonical temperatures T(c)/T(&mgr;) of a vibratory antiferromagnetic Ising chain with N spins is given by analytical calculation. The result is T(c)/T(&mgr;)=1+O(N-1), which is consistent with the natural assumption given by Rugh.