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- Quantum mechanics (1)
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In the Finite-Volume-Particle Method (FVPM), the weak formulation of a hyperbolic conservation law is discretized by restricting it to a discrete set of test functions. In contrast to the usual Finite-Volume approach, the test functions are not taken as characteristic functions of the control volumes in a spatial grid, but are chosen from a partition of unity with smooth and overlapping partition functions (the particles), which can even move along prescribed velocity fields. The information exchange between particles is based on standard numerical flux functions. Geometrical information, similar to the surface area of the cell faces in the Finite-Volume Method and the corresponding normal directions are given as integral quantities of the partition functions. After a brief derivation of the Finite-Volume-Particle Method, this work focuses on the role of the geometric coefficients in the scheme.

A simple method of calculating the Wannier-Stark resonances in 2D lattices is suggested. Using this method we calculate the complex Wannier-Stark spectrum for a non-separable 2D potential realized in optical lattices and analyze its general structure. The dependence of the lifetime of Wannier-Stark states on the direction of the static field (relative to the crystallographic axis of the lattice) is briefly discussed.