Numerous theoretical and experimental studies have investigated the dynamics of cold atoms subjected to time periodic fields. Novel effects dependent on the amplitude and frequency of the driving field, such as Coherent Destruction of Tunneling have been identified and observed. However, in the last year or so, three distinct types of experiments have demonstrated for the first time, interesting behaviour associated with the driving phase: i.e. for systems experiencing a driving field of general form $V(x)sin (omega t + phi)$, different types of large scale oscillations and directed motion were observed. We investigate and explain the phenomenon of Super-Bloch Oscillations (SBOs) in relation to the other experiments and address the role of initial phase in general. We analyse and compare the role of $phi$ in systems with homogeneous forces ($V(x)= const$), such as cold atoms in shaken or amplitude-modulated optical lattices, as well as non-homogeneous forces ($V(x) eq const$), such as the sloshing of atoms in driven traps, and clarify the physical origin of the different $phi$-dependent effects.
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