Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
M. Gadella and O. G. Smolyanov, Dokl. Math. 77, 120–123 (2008).
O. O. Obrezkov, O. G. Smolyanov, and A. Truman, Dokl. Math. 71, 105–110 (2005).
T. Ratiu and O. G. Smolyanov, Dokl. Math. 87, 289–292 (2013).
A. S. Plyashechnik, Russ. J. Math. Phys. 19 (3), 340–359 (2012).
A. S. Plyashechnik, Russ. J. Math. Phys. 20 (3), 377–379 (2013).
N. Sidorova, Infin. Dimens. Anal. Quantum Probab. Rel. Top. 7 (3), 461–471 (2004).
O. G. Smolyanov, H. von Weizsacker, and O. Wittich, Potential Anal. 26 (1), 1–29 (2007).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © T.S. Ratiu, O.G. Smolyanov, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 4, pp. 407–410.
Rights and permissions
About this article
Cite this article
Ratiu, T.S., Smolyanov, O.G. Dynamics of particles with anisotropic mass depending on time and position. Dokl. Math. 92, 723–726 (2015). https://doi.org/10.1134/S1064562415060241
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064562415060241