Prof. Dr. Gian Michele Graf, Mathematical Physics Group at ITP, ETH
The Thouless theory of quantum pumps establishes quantized transport per cycle and determines the necessary conditions. When the description is shifted to a moving reference frame, as suggested by recent experiments on ultracold gases, transported and existing charges mix. That transformation is encoded in Galilean space and time, but underlying it is one of vector bundles that may be described in a number of ways, that may or may not rely on Bloch theory. In one of them, the transformation mixes strong and weak indices of a bundle on a 2-torus; in another one, a 3-torus is at center stage; in yet another one, and somewhat informal way, the transformation is related to a parodox that astonished seafarers of centuries past. (Joint work with T. Esslinger and F. Santi)