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.
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