Physics NotePublished
The Partition Function for Anharmonic Oscilator in the Strong-Coupling Regime
N.F. Svaiter
2004
Publication details
- Authors
- N.F. Svaiter
- Type
- Physics Note
- Status
- Published
- Publication date
- 2004
- Description
- We consider a single anharmonic oscillator with frequency $\omega$ and coupling constant $\lambda$ respectively, in the strong-coupling regime. We are assuming that the system is in thermal equilibrium with a reservoir at temperature $\beta^{-1}$. Using the strong-coupling perturbative expansion, we obtain the partition function for the oscillator in the regime $\lambda>>\omega$, up to the order $\frac{1}{\sqrt{\lambda}}$. To obtain this result, we follow two steps. First, we must give meaning to the first term of the strong-coupling perturbative expansion, i.e., the static ultra-local generating functional $Q_{\beta}(h)$. Second, we have to regularize and renormalize the kernel $K(\omega,\sigma,\tau-\tau')$ integrated over Euclidean time. In order to solve both problems, we make use of a combination of Klauder representation for the static ultra-local generating functional (Acta Phys. Austr. {\bf 41}, 237 (1975), Ann. Phys. {\bf 117}, 19 (1979)), and the generalized zeta-function method. The free energy and the mean energy, up to the order $\frac{1}{\sqrt{\lambda}}$, are also presented. We are showing that the thermodynamics quantities are nonanalytic in the coupling constant.
- Year
- 2004
- Number
- CBPF-NF-015/04
- Linked to a thesis
- No
- Linked to a grant
- No