Fluctuations and Landau-Devonshire expansion for barium titanate

The experimentally observed temperature dependence of the quartic coefficients in the Landau-Devonshire expansion for BaTiO_3 is naturally accounted for within a proper fluctuation model. It is explained, in particular, why one of the quartic coefficients varies with temperature above T_c while the second is constant. The tetragonal phase in BaTiO_3 is argued to exist essentially due to the thermal fluctuations, while the true Landau-Devonshire expansion with temperature-independent coefficients favours the rhombohedral ferroelectric phase. Certain conclusions concerning the temperature dependence of the sextic Landau-Devonshire coefficients are also made.Comment: Minor changes, 1 reference added, published versio

Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics

When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials and potentials with finite number of bound states. After the survey of the results existing in the subject the algebraic and analytic properties of hidden-symmetry differential operators are rigorously elaborated in the Theorems and illuminated by several examples