  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 ($V'(x)\neq const$), such
as the sloshing of atoms in driven traps, and clarify the physical origin of
the different $\phi$-dependent effects.
