Brownian motion on a sphere: distribution of solid angles

We study the diffusion of Brownian particles on the surface of a sphere and compute the distribution of solid angles enclosed by the diffusing particles. This function describes the distribution of geometric phases in two-state quantum systems (or polarized light) undergoing random evolution. Our results are also relevant to recent experiments which observe the Brownian motion of molecules on curved surfaces such as micelles and biological membranes. Our theoretical analysis agrees well with the results of computer experiments.

• Publication year

  2000

• Venue

  Journal of Physics A

• Publication date

  2000-05-22

• Fields of study

  Physics

• Identifiers
  DOI 10.1088/0305-4470/33/34/302arXiv cond-mat/0005345
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Translational diffusion of fluorescent probes on a sphere: Monte Carlo simulations, theory, and fluorescence anisotropy experiment

  2000influential reference
• Fluorescence Dynamics of Dye Probes in Micelles

  1997cited by this paper
• Analytical Solutions and Simulations for Spin-Echo Measurements of Diffusion of Spins in a Sphere with Surface and Bulk Relaxation

  1996cited by this paper
• Dynamics of Porphyrin Molecules in Micelles. Picosecond Time-Resolved Fluorescence Anisotropy Studies

  1995cited by this paper
• Brownian motion and magnetism.

  1994cited by this paper
• Asymptotic winding angle distributions for planar Brownian motion with drift

  1993cited by this paper
• Dynamics of ionic lipophilic probes in micelles: Picosecond fluorescence depolarization measurements

  1993cited by this paper
• Algebraic areas enclosed by Brownian curves on bounded domains

  1992cited by this paper
• Magnetic fields and Brownian motion on the 2-sphere

  1991cited by this paper
• Geometric Phases in Physics

  1989cited by this paper
• Surfactant dynamics in spherical and nonspherical micelles. A nuclear magnetic resonance study

  1986cited by this paper
• Micellar dynamics and organization. A multifield 13C NMR spin-lattice relaxation and {1H}13C nuclear overhauser effect study

  1984cited by this paper
• Micellar dynamics and organization. A multifield carbon-13 NMR spin-lattice relaxation and {proton} carbon-13 nuclear Overhauser effect study

  1984cited by this paper
• THE MAGNETIC MONOPOLE FIFTY YEARS LATER

  1983cited by this paper
• Stochastic differential equations and diffusion processes: Nobuyuki Ikeda and Shinzo Watanabe North-Holland, Amsterdam, 1981, xiv + 464 pages, Dfl.175.00

  1982cited by this paper
• Stochastic differential equations and diffusion processes

  1981cited by this paper
• Techniques and Applications of Path Integration

  1981cited by this paper
• Statistical mechanics with topological constraints: I

  1967cited by this paper
• Quantum Mechanics and Path Integrals

  1965cited by this paper
• Quantum Mechanics

  1961cited by this paper
• Angular Momentum in Quantum Mechanics

  1957cited by this paper
• Quantised Singularities in the Electromagnetic Field

  1931cited by this paper
• Quantum Mechanics

  1929cited by this paper

• Inertial and confined dynamics of a constant-speed active particle in three dimensions.

  2025cites this paper
• The Shape of Markets: Machine learning modeling and Prediction Using 2-Manifold Geometries

  2025cites this paper
• Soft and Living Matter: a perspective

  2024cites this paper
• Area Formula for Spherical Polygons via Prequantization

  2023cites this paper
• Lagrangian stochastic model for the orientation of inertialess spheroidal particles in turbulent flows: An efficient numerical method for CFD approach

  2022cites this paper
• Lagrangian stochastic model for the orientation of inertialess non spherical particles in turbulent flows: an efficient numerical method for CFD approach

  2022cites this paper
• A pr 2 02 0 Brownian motion at the speed of light Maurizio Serva April

  2020cites this paper
• Brownian Motion at the Speed of Light: A New Lorentz Invariant Family of Processes

  2020cites this paper
• Random Motion of Light-Speed Particles

  2020cites this paper
• Digital Signal Processing in Coherent Optical Radio Over Fiber Systems

  2017cites this paper
• Random Molecular Transport around Biological Membranes

  2016cites this paper
• Symmetric signal and local oscillator polarization diverse coherent optical receiver.

  2016cites this paper
• Stochastic description of geometric phase for polarized waves in random media

  2012cites this paper
• Algorithm for generating a Brownian motion on a sphere

  2010cites this paper
• Ab-initio molecular dynamical study of a single transition metal atom on fullerene C60: the case of Ta

  2009cites this paper
• General framework for multiple scattering of polarized waves including anisotropies and Berry phase.

  2009cites this paper
• Molecular Dynamics of Guest Molecules in Micelles: Models Based on Fluorescence Polarization Dynamics

  2001cites this paper
• Rotational dynamics of surface probes in lipid vesicles.

  2001cites this paper
• Translational diffusion of fluorescent probes on a sphere: Monte Carlo simulations, theory, and fluorescence anisotropy experiment

  2000cites this paper