# Quantum Catastrophes

**Duncan O'Dell**

Department of Physics & Astronomy, McMaster University

Tuesday, April 23, 2013

10:30 AM @ Stirling 501

## Abstract:

I will discuss the dynamics following a quench in a bosonic Josephson junction. This system can be realized using cold atoms which are so well controlled that the dynamics remains coherent for a long time. We will see that structures form in Fock space at periodic intervals of time that are equivalent to rainbows. TheseFock space rainbows can be analyzed using catastrophe theory which shows that they are both structurally stable, i.e. stable against perturbations in the initial conditions and the hamiltonian, and also in some sense generic, i.e. they are bound to appear. The mean-field approximation provided by the Gross-Pitaevskii theory predicts a singularity at the rainbows whereas the full 2nd quantized theory is well behaved. These results are therefore relevant to the question posed by Michael Berry: "Are there circumstances when it is necessary to 2nd quantize waves in order to avoid singularities?"

Reference: D.H.J. O'Dell, Phys. Rev. Lett. 109, 150406 (2012)