# Mathematics Colloquia and Seminars

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### Localization of the Ground State of Mean Field Models with Random Bernoulli Potentials

**Mathematical Physics & Probability**

Speaker: | Michael Bishop, UC Davis |

Location: | 1147 MSB |

Start time: | Wed, Nov 20 2013, 4:10PM |

In this talk, I will discuss research done with J. Wehr on the ground state of the mean-field approximation of the Bose-Hubbard model with local 'soft core' repulsive interactions and random Bernoulli potentials. This model describes a system of interacting bosons in a random potential. The interplay of interactions and random potentials is unclear: quantum particles localize in systems with random potentials, but repulsive interactions cause the wave functions to spatially spread. The main result is a general criterion for the minimal localization of a mean-field state given its per particle energy and the interaction strength. This result will be applied to the ground state in one spatial dimension in the thermodynamic limit for a low-density weak-interaction state to show a Bose glass-like state.