MathDB2 problems
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Marzari–Vanderbilt conjecture on exponential localization of global MV minimizers
Marzari–Vanderbilt conjecture. Global minimizers of the MV functional are exponentially localized.
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Thouless's conjecture on optimal Wannier-function decay
A periodic system in two dimensions is described by a Bloch bundle, and a Wannier function is obtained from a Bloch frame by the inverse Bloch transform. For a non-trivial Bloch bu…