Dynamics of particles with anisotropic mass depending on time and position

T. S. Ratiu (1) , O. G. Smolyanov (2)

1 EPFL - Ecole Polytechnique Fédérale de Lausanne
2 Mechanics and Mathematics Faculty, Moscow State University, Moscow

Representations of solutions of equations describing the diffusion and quantum dynamics of particles in a Riemannian manifold are discussed under the assumption that the mass of particles is anisotropic and depends on both time and position. These equations are evolution differential equations with secondorder elliptic operators, in which the coefficients depend on time and position. The Riemannian manifold is assumed to be isometrically embedded into Euclidean space, and the solutions are represented by Feynman formulas; the representation of a solution depends on the embedding.

Domaines: Mathématiques [math]

T. S. Ratiu, O. G. Smolyanov. Dynamics of particles with anisotropic mass depending on time and position. Доклады Академии Наук / Doklady Mathematics, 2015, 92 (3), pp.723-726. ⟨10.1134/S1064562415060241⟩. ⟨hal-01398414⟩