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Lattice Effects on Interacting Bosons and their Vortex Dynamics

Lattice Effects on Interacting Bosons and their Vortex Dynamics

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The Pi operators<br />

1. reflecti<strong>on</strong> about<br />

2. charge c<strong>on</strong>jugati<strong>on</strong><br />

3. gauge transformati<strong>on</strong><br />

1. point group* symmetries<br />

2. For odd vorticity<br />

=> All states are doubly degerenate<br />

*For <strong>on</strong>e vortex, there are no translati<strong>on</strong>al symmetries <strong>on</strong> finite tori

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