Landau theory

About: Landau theory is a research topic. Over the lifetime, 2882 publications have been published within this topic receiving 57078 citations.

Gradient flow of the superconducting Ginzburg–Landau functional on the plane

Abstract: First we prove the existence of global smooth solutions of the gradient flow of the superconducting Ginzburg Landau (or Abelian Higgs) functional on M. It is then proved that in the case of critical coupling, for a large class of initial data of arbitrary winding number AT, each solution converges in temporal gauge to a unique solution of the static equations of the same winding number. The proof has two essential ingredients. Firstly a weighted energy identity is used to obtain spatial exponential decay of certain quantities uniformly in time. This implies the strong subsequential convergence to a static solution in the H norm. Secondly, an adiabatic approximation in the neighbourhood of the static solution space is used to prove that the solution converges without passing to subsequences. Thus the u;-limit set of each solution is a point. The adiabatic approximation consists of finding, at each time, the L-closest point to the solution on the space of static solutions of the same winding number as the initial data. Special cases of the result imply that two vortices of opposite sign will annihilate for a large class of initial data and that a single vortex is asymptotically stable with respect to a large class of perturbations.

Phase transition of pure zirconia under irradiation: A textbook example

Abstract: One of the most important goals in ceramic and materials science is to be able to design materials with specific properties. Irradiation seems to be a powerful tool for the design of advanced ceramics because of its ability to modify over different scales the microstructure of solids. Nowadays, it is clearly proved that irradiation induces order–disorder phase transitions in metallic alloys and in some ceramics. In this paper, we show that a displacive phase transition can also be induced by irradiation. Based on many experimental facts, a microscopic model is proposed to explain the displacive phase transition observed in this material after irradiation. Defects, produced in the oxygen sublattice, induce important strain fields on a nanometric scale. This strain field can be handled as a secondary order parameter within the Landau theory approach, leading to a decrease of the phase transition temperature and thus quenching the high temperature tetragonal phase.

Quantum saturation of the order parameter and the dynamical soft mode in quartz

Abstract: The temperature evolution of the static order parameter of α-quartz and its soft-mode frequencies were determined at temperatures below 300 K. While these parameters follow classic Landau theory at higher temperatures, quantum saturation was found below room temperature with a characteristic quantum temperature of 187 K. A quantitative analysis gave a good agreement with the predictions of a Φ6 model close to the displacive limit and a rather flat dispersion of the soft-mode branch. No indication of any effect of strong mode–mode coupling on the saturation behaviour was observed.