Nota de FísicaPublicado
The Partition Function for Anharmonic Oscilator in the Strong-Coupling Regime
N.F. Svaiter
2004
Dados da publicação
- Autores
- N.F. Svaiter
- Tipo
- Nota de Física
- Status
- Publicado
- Data de publicação
- 2004
- Descrição
- 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.
- Ano
- 2004
- Número
- CBPF-NF-015/04
- Vínculo com tese
- Não
- Vínculo com bolsa
- Não