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#### A Variation on the Donsker-Varadhan Inequality for the Principial Eigenvalue

(2017-04-23)

The purpose of this short note is to give a variation on the classical Donsker-Varadhan
inequality, which bounds the first eigenvalue of a second-order elliptic operator
on a bounded domain $\Omega$ by the largest mean first ...

#### An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus

(2017-04-23)

We study an isoperimetric problem the energy of which contains the perimeter of a
set, Coulomb repulsion of the set with itself, and attraction of the set to a background
nucleus as a point charge with charge $Z$. For the ...

#### Wavepackets in inhomogeneous periodic media: effective particle-field dynamics and Berry curvature

(2017-04-23)

We consider a model of an electron in a crystal moving under the influence of an external
electric field: Schr\"{o}dinger's equation with a potential which is the sum of a
periodic function and a general smooth function. ...