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#### Frozen Gaussian approximation with surface hopping for mixed quantum-classical dynamics: A mathematical justification of fewest switches surface hopping algorithms

(2017-04-23)

We develop a surface hopping algorithm based on frozen Gaussian approximation for
semiclassical matrix Schr\"odinger equations, in the spirit of Tully's fewest switches
surface hopping method. The algorithm is asymptotically ...

#### Detecting localized eigenstates of linear operators

(2017-11-30)

We describe a way of detecting the location of localized eigenvectors of a linear
system $Ax = \lambda x$ for eigenvalues $\lambda$ with $|\lambda|$ comparatively large.
We define the family of functions $f_{\alpha}: \left\{1.2. ...

#### Thermodynamic Limit of Crystal Defects with Finite Temperature Tight Binding

(2017-04-23)

We consider a tight binding model for localised crystalline defects with electrons
in the canonical ensemble (finite electronic temperature) and nuclei positions relaxed
according to the Born--Oppenheimer approximation. ...