When low-order expansions fail and all higher-order contributions matter-basic example of the mean squared displacement for Brownian motion.
Eur Phys J E Soft Matter
; 45(9): 77, 2022 Sep 19.
Article
em En
| MEDLINE
| ID: mdl-36121547
ABSTRACT
Hardly any theoretically formulated realistic problem can be solved exactly. Therefore, as a standard, we resort to approximations. In this context, expansions play a major role. We are used to relying on lowest-order expansions and confining our point of view accordingly. However, one should always bear in mind that such considerations may fail at some point. Here, we address a very common example situation, namely, the motion of a Brownian particle. We know that the associated mean-squared displacement in the long term increases linearly in time. Yet, when we take the Fokker-Planck approach in combination with a low-order expansion, the direct route towards this result fails. That is, in the expansion the term linear in time vanishes. Instead, the treatment requires consideration of all higher-order contributions. Together, they restore the linear increase in time. In this way, we stress that care is always mandatory when resorting to low-order expansions, and we present in a traceable way a route to solving the considered problem.
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Base de dados:
MEDLINE
Idioma:
En
Revista:
Eur Phys J E Soft Matter
Assunto da revista:
BIOFISICA
Ano de publicação:
2022
Tipo de documento:
Article
País de afiliação:
Alemanha