Specific heat of anharmonic oscillators in one dimension
The specific heats of one-dimension systems are obtained with two different methods, which are achieved in terms of the partition function and the probability density function, respectively. In this thesis, we consider three kinds of anharmonic potentials and calculate numerically the specific heat of a particle moving in a potential in one dimension and also at thermally equilibrium with a heat bath. From the views of classical statistical mechanics, the method from the partition function is standard, direct and simple. In addition, we construct the probability density function of a stochastic variable. Since we can calculate < V > / T and < V > / T , this method can gives us more information. Namely, we can realize the specific heat more deeply. For a symmetric double-well potential, V , we find that at very low temperature the curve of the specific heat has a peak. In addition, we also respectively calculate the specific heats of a symmetric single-well potential, V , and an asymmetric single-well one, V . After comparing the specific heats of these three potentials, we interpret the specific heats of them from the view of the geometry of these potentials. In V and V , we find that there is a region in the potential where the potential curvatures are negative. Finally we suggest that the peak of the specific heat of a one-dimension system, once it appears, is associated with the existence of negative curvature of the potential.
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