Quantum-statistical mechanics of extended objects. III. Kinks in the one-dimensionalφ4and double-quadratic potential systems

Abstract

Making use of the field-theoretical technique developed in our earlier work, we study kinks in one-dimensional systems with the ${\ensuremath{\varphi}}^{4}$ and double-quadratic (DQ) potentials at finite temperatures. In the ${\ensuremath{\varphi}}^{4}$ system all divergences in the theory are eliminated by the mass renormalization of the $\ensuremath{\varphi}$ field (the phonon). The renormalized phonon mass $m$ becomes temperature dependent. In the DQ system, on the other hand, there exists no mass renormalization of the phonon, and $m$ is dependent of the temperature. The kink energy ${E}_{K}$, the inertial mass of the kink ${E}_{I}$, and the kink density ${n}_{K}$ are determined in both systems. The results obtained here and in our earlier work on the sine-Gordon system seem to indicate that the qualitative behavior of the kink is almost independent of the underlying nonlinear system, while the behavior of the phonon mass is quite sensitive to the details of the nonlinear interaction of the system. Also the present analysis confirms to a large extent the ideal-gas phenomenology for the one-dimensional nonlinear system.