Fil D. Phonon assisted collective phenomena in low-dimensional strongly correlated systems

The object is electron-phonon interaction and collective effects caused by it in low-dimensional strongly correlated electron systems. The aim is to determine interrelations between behavior of phonon excitations and the structure of the ground state. The methods are the microscopic and phenomenological model description, methods of theoretical physics (Chern-Simons Lagrange approach, functional integral method, Ewald's method etc.). The new approaches and results - new models are developed, namely, the microscopic anisotropic model of the co-operative Jahn-Teller effect, the phonon model of the orientational pinning of two-dimensional Wigner crystals and stripe-structures, the theory of interaction of phonons with anyons and composite fermions. The mechanisms of formation of the mixed orbital state, a strong dispersion of the optic phonon modes in HTSC cuprates and the anisotropy of the conductivity in quantum Hall systems are clarified. The new effects of an oscillating dispersion of acoustic phononspectra, a modification of a spatial distribution of the induced charge and a shift of the velocity of elastic modes in systems with anyons and composite fermions are predicted. The field is condensed matter physics.