For more information about this meeting, contact Yuxi Zheng, Kris Jenssen.

Title: | Vortex lattice theory: A particle interaction perspective |

Seminar: | Computational and Applied Mathematics Colloquium |

Speaker: | Paul Newton, usc.edu |

Abstract: |

Recent experiments on the formation of vortex lattices in Bose-Einstein
condensates has produced the need for a mathematical theory that is capable
of predicting a broader class of lattice patterns, ones that are free of
discrete-symmetries and can form in a random environment. In this talk, I
will describe an N-particle based Hamiltonian theory which, if formulated
in terms of the interparticle distances, leads to the analysis of a
non-normal `configuration' matrix whose nullspace structure determines the
existence or non-existence of a lattice. The singular value decomposition
of this matrix leads to a method in which all lattice patterns, in principle,
can be identified and calculated by a random-walk scheme which systematically
uses the m-smallest singular values as a ratchet mechanism to home in on
lattices with many new properties, including a complete lack of discrete
symmetries and heterogeneous particle strengths. We will describe properties
of the lattice that the singular value distribution of its configuration
matrix reveals, most notably its Shannon entropy (related to robustness),
size (Frobenius norm), and distance between lattices (lattice density). |

### Room Reservation Information

Room Number: | MB106 |

Date: | 04 / 30 / 2010 |

Time: | 03:35pm - 04:25pm |