Nonlinear dynamics and thermodynamics of two-component scalar field systems at low temperatures

A model for nonlinear complex, two-component scalar field systems is considered in the continuum limit, with a particular emphasis on competing effects between a symmetric and an asymmetric anisotropy coupling term. The nonlinear excitations of the system are found in terms of kink states (the so-called φ4 kinks) and solitons (the double-sine-Gordon wobblers). Kink states govern the system dynamics when fluctuations are dominated by time and space variation of the amplitude of the order parameters, and solitons in the phase fluctuation regime. Kink states can be observed in structural phase transitions and below the critical temperature, where they play the role of interfaces between adjacent ordered phases. Solitions are also a variety of domain walls observable in structural phase transitions. The influence of these domain walls on the thermodynamics of the model has been investigated. At high temperatures, the correlation length varies as the inverse temperature while at low temperatures the correlation length varies exponentially with temperature. This last behaviour is reminiscent of the contribution of solitons. Because the competition between the symmetric and the asymmetric coupling terms gives rise to more than one type of soliton, the energy between the resulting distinct walls splits and therefore promotes a complex cross-over behaviour from high temperature to low temperature.