The nonzero minimum of the diffusion parameter and the uncertainty principle for a Brownian particle
2002 (English)In: Modern physics letters B, ISSN 0217-9849, Vol. 16, no 13, 467-471 p.Article in journal (Refereed) Published
The limits of applicability of many classical (non-quantum-mechanical) theories are not sharp. These theories axe sometimes applied to the problems which axe, in their nature, not very well suited for that. Two of the most widely used classical approaches are the theory of diffusion stochastic process and Itos stochastic differential equations. It includes the Brownian-motion treatment as the basic particular case. The present work shows that, for quantum-mechanical reasons, the diffusion parameter of a Brownian paxticle cannot be arbitrarily small since it has a nonzero minimum value. This fact leads to the version of Heisenbergs uncertainty principle for a Brownian particle which is obtained in the precise mathematical form of a limit inequality. These quantitative results can help to,properly apply the theories associated with Brownian-particle modelling. The consideration also discusses a series of works of other authors.
Place, publisher, year, edition, pages
World Scientific , 2002. Vol. 16, no 13, 467-471 p.
Brownian motion, Quantum transport, Molecular dynamics, Brownian dynamics, Markov processes
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-59167DOI: 10.1142/S0217984902004020ISI: 000177568400002OAI: oai:DiVA.org:liu-59167DiVA: diva2:350174