• Corpus ID: 119147113

Brownian motion of free particles on curved surfaces

@article{CastaedaPriego2012BrownianMO,
  title={Brownian motion of free particles on curved surfaces},
  author={Ram{\'o}n Casta{\~n}eda-Priego and Pavel Castro-Villarreal and Sendic Estrada-Jim'enez and Jos'e Miguel M'endez-Alcaraz},
  journal={arXiv: Statistical Mechanics},
  year={2012}
}
Brownian motion of free particles on curved surfaces is studied by means of the Langevin equation written in Riemann normal coordinates. In the diffusive regime we find the same physical behavior as the one described by the diffusion equation on curved manifolds [J. Stat. Mech. (2010) P08006]. Therefore, we use the latter in order to analytically investigate the whole diffusive dynamics in compact geometries, namely, the circle and the sphere. Our findings are corroborated by means of Brownian… 

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References

SHOWING 1-10 OF 26 REFERENCES
A comprehensive introduction to differential geometry
Spivak's Comprehensive introduction takes as its theme the classical roots of contemporary differential geometry. Spivak explains his Main Premise (my term) as follows: "in order for an introduction
Quantum Field Theory and Critical Phenomena
Introduced as a quantum extension of Maxwell's classical theory, quantum electrodynamic (QED) has been the first example of a quantum field theory (QFT). Eventually, QFT has become the framework for
An introduction to dynamics of colloids
Phys
  • Rev. E 60, 302
  • 1999
Mech
  • 282 373
  • 1995
A: Math
  • Gen. 31, 7005-7009
  • 1998
Faraday Discuss
  • 1985
Phys
  • 106, 1880
  • 1997
...
...