Itinerant oscillator model

Fig. 1. Energy distribution of neutrons scattered by hydrogen in liquid argon at 100"K and 26.5 atm, as a function of time of flight for various scattering angles, 6. Solid curve, interpolation model. Dashed curve, Sears itinerant oscillator model. Jagged curve, Experiment. Abscissa is time of flight in usec/m and ordinate is cross section in mb sr-1 usee-1.

Exercise. Consider the following simplified version of the itinerant oscillator model. A body moves in a fluid and contains in its interior a damped oscillator (fig. 22). The equations of motion are... 

Another piece of information that we wanted to extract from our experiments was connected with the dynamic behavior of spatial variables. If we consider three successive particles in the chain and we denote by the distance of the middle one from the center of mass of the other two and by the distance between these two, we can compute the normalized autocorrelation function of these two variables. They are shown in Fig. 9 as can be immediately observed, they decay to zero on a time scale which is much greater than that of the velocity variable. Also, the center of mass decays faster than R . In the next section we shall argue that this suggests that the virtual potential characterizing the itinerant oscillator model has to be assumed to be fluctuating around a mean shape, which, moreover, will be shown to be nonlinear and softer than its harmonic approximation. 

As a final remark we wish to note that the result of the one-dimensional computer simulation shown in Fig. 9 suggests that the nonlinear version of the itinerant oscillator model should be improved by giving a fluctuating character to the virtual potential, since Rq does not turn out to be a very fast variable. Therefore, the potential of (4.9) should be interpreted as an average potential around which an effective potential would fluctuate. 

In the linear case the itinerant oscillator model is well known, and its rigorous foundation has been illustrated in Section II. Its nonlinear version... 

Itinerant Oscillator. The itinerant oscillator model of dielectric response was introduced by Hill." It has considerable attraction as a model of the liquid state, and the name has become well known since Sears " used... 

The first objective of this review is to describe a method of solution of the Langevin equations of motion of the itinerant oscillator model for rotation about a fixed axis in the massive cage limit, discarding the small oscillation approximation in the context of dielectric relaxation of polar molecules, this solution may be obtained using a matrix continued fraction method. The second... 

In order to proceed, we first describe the problem of generalizing the Onsager model to include the frequency dependence of the relative permittivity and how this problem may be linked to the cage or itinerant oscillator model. 

The theory of the Brownian motion on which the itinerant oscillator model is based is distinguished by a characteristic feature, namely, the concept of a collision rate which is the inverse of the time interval between successive collision events of the Brownian particle with its surroundings. In the words of Einstein [71] ... 

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