Floquet-Bloch Dynamics in Simple Systems*

Fascinating changes in electronic properties such as topological and other phase
transitions of materials can be realized by periodically driving them using external fields.
Floquet-Bloch theory can reveal interesting signatures pertaining to above transitions.
By periodically driving the electronic states of one- and two-dimensional systems,
we obtain numerical solutions, without having to resort to a high frequency expansion.
Some of the important aspects of the above transitions will be discussed and
these ideas will be extended to small cluster-based systems with many-electron interactions.