| All experiments are done at non-zero temperatures ( T). Any theoretical of the properties of quantum many-body systems has to include the effects zero temperature in order to make contact with experiment, even if the phenomenon being studied (be it a phase transition driven by quantum fluctuations, or phase disordered by quantum fluctuations) is purely a T = 0 quantum effect. traditional techniques based on first formulating the problem in imaginary (the Matsubara formalism) and then analytically continuing the results for static, thermodynamic properties, they are much less successful in dealing problems involving dynamics and transport for T > 0. In this thesis, results obtained for two such problems using non-perturbative methods and working in real-time. The first part of this thesis deals with spin dynamics and transport gapped one-dimensional Heisenberg antiferromagnets, while the second par the nature of charge transport at non-zero temperatures above the quantum point in a simple model of the superfluid-insulator transition. |
