Skip to main content
SpringerLink
Log in

Trajectories of Brownian particles with space-correlated noise

  • Regular Article
  • Published:
Journal of Chemical Sciences Aims and scope Submit manuscript

Abstract

The Langevin equation used to model Brownian motion includes a stochastic process that is routinely assumed to be a Gaussian white noise. Spatial correlations of the noise are usually ruled out, and the paths traced by the random walkers are statistically independent. In this study, I consider instead noise which is white in time and has a Gaussian correlation in space, and by means of numerical simulation, I show how the spatial correlation determines the time evolution of the spatial separation of random walkers.

Spatially correlated, fluctuating random fields that drive Brownian particles produce some unexpected effects when the particles are close to one another.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5

Similar content being viewed by others

References

  1. Romero A H and Sancho J M 1998 Brownian motion in short range random potentials Phys. Rev. E 58 2833

    Article  CAS  Google Scholar 

  2. Sancho J M and Lacasta A M 2010 The rich phenomenology of brownian particles in nonlinear potential landscapes Eur. Phys. J. Spec. Top. 187 49

    Article  CAS  Google Scholar 

  3. Simon M S, Sancho J M and Lacasta A M 2012 On generating random potentials Fluctuation Noise Lett. 11 1250026

    Article  Google Scholar 

  4. Simon M S, Sancho J M and Lindberg K 2013 Transport and diffusion of overdamped Brownian particles in random potentials Phys. Rev. E 88 062105

    Article  Google Scholar 

  5. Garcia-Ojalvo J and Sancho J M 1992 Ramírez-Piscina Generation of spatiotemporal colored noise Phys. Rev. A 46 4670

    Article  CAS  Google Scholar 

  6. Yodh A G, Lin K -H, Crocker J C, Dinsmore A D, Verma R and Kaplan P D 2001 Entropically driven self-assembly and interaction in suspension Philos. Trans. R. Soc. London, Ser. A 359 921

    Article  CAS  Google Scholar 

  7. Chandrasekhar S 1943 Stochastic Problems in Physics and Astronomy Rev. Mod. Phys. 15 1

    Article  Google Scholar 

  8. Doob J L 1942 The Brownian Movement and Stochastic Equations Ann. Math. 43 351

    Article  Google Scholar 

  9. Apostol T M 1967 In Calculus Vol. 2, 2nd ed. (New York: Wiley) p. 411

    Google Scholar 

  10. Pólya G 1921 Über eine Aufgabe der Wahrscheinlichkeitrechnung betreffend die Irrfahrt im Straßennetz Math. Ann. 84 149

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, University of Trieste, Via Valerio 2, I-34127, Trieste, Italy

    EDOARDO MILOTTI

Authors
  1. EDOARDO MILOTTI
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to EDOARDO MILOTTI.

Additional information

Special Issue on THEORETICAL CHEMISTRY/CHEMICAL DYNAMICS

Dedicated to the memory of the late Professor Charusita Chakravarty.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

MILOTTI, E. Trajectories of Brownian particles with space-correlated noise. J Chem Sci 129, 983–988 (2017). https://doi.org/10.1007/s12039-017-1256-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12039-017-1256-8

Keywords

Search

Navigation