Physics of cooperative phenomena in condensed matter systems: Non linear dynamics of driven charge density waves; model studies of high temperature superconductivity

This thesis examines four problems of cooperative phenomena in condensed matter physics. The first two topics deal with non-linear dynamics of charge density wave systems. The second two concern superconductivity with unusually high critical temperature.; Firstly, the dynamics of one dimensional charge density waves are studied using models with only a few internal phase degrees of freedom. It is shown that these simple models are sufficient to produce the subharmonic current-lock observed experimentally. The relative simplicity of the model makes it suitable for studying details of the dynamics difficult to obtain with models having larger number of degrees of freedom.; Secondly, it is shown that the introduction of phase-slip centers can account for the diverse dynamical phenomena observed in "switching" charge density wave systems. In particular, the following experimental phenomena are all explained in terms of phase-slips: switching, hysteresis, period doubling, chaos, strong tendency to current-lock, and the broad inductive response in ac conductivity measurement.; Thirdly, superconductivity with high critical temperature (high-temperature superconductivity) is studied using a simple mean field theory of the single band Hubbard model where both superconducting and antiferromagnetic long range orders are allowed. It is shown that the phase in which both of these symmetry breakings exist is likely to have the lowest free energy.; Finally, the quantitative discrepancy found between the mean field theory of high-temperature superconductivity and experiment regarding the antiferromagnetic order is qualified. Quantum fluctuation is introduced as the next nearest neighbor antiferromagnetic coupling of spins. The derivation of the effective spin Hamiltonian and its study using the variational Monte Carlo method is presented.