Topological transitions and robust quantization of transport in lossy – Niels Bohr Institute - University of Copenhagen

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Niels Bohr Institute > Calendar > 2011 > Topological transition...

Topological transitions and robust quantization of transport in lossy

The discovery of the quantized Hall effects opened a new chapter
in our understanding of quantum mechanics. The theoretical explanation of
these effects, which is based on the mathematical framework of topology,
revealed new mechanisms through which extremely robust quantization
phenomena could arise in large, and rather messy systems. Here we analyze
quantum transport on a one-dimensional lattice, where a particle can decay
whenever it visits sites on one of two sublattices. We find that the mean
displacement achieved by a particle initially localized on one of the
non-decaying sites is given by a winding number defined in terms of the
Bloch eigenstates in the Brillouin zone. The displacement is therefore
quantized as an integer, changing from zero to one at the critical point.
The quantization is robust against a range of time-dependent perturbations.
Implications for experiments in solid-state, quantum optical, and cold
atomic systems will be discussed.

Talk by Mark Rudner, Harvard University