Related Experiment Video
Updated: May 14, 2026

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
Published on: February 27, 2016
Path-integral formulation for Lévy flights: evaluation of the propagator for free, linear, and harmonic potentials in
Deepika Janakiraman1, K L Sebastian
1Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India.
Abstract:
Lévy flights can be described using a Fokker-Planck equation, which involves a fractional derivative operator in the position coordinate. Such an operator has its natural expression in the Fourier domain. Starting with this, we show that the solution of the equation can be written as a Hamiltonian path integral. Though this has been realized in the literature, the method has not found applications as the path integral appears difficult to evaluate. We show that a method in which one integrates over the position coordinates first, after which integration is performed over the momentum coordinates, can be used to evaluate several path integrals that are of interest. Using this, we evaluate the propagators for (a) free particle, (b) particle subjected to a linear potential, and (c) harmonic potential. In all the three cases, we have obtained results for both overdamped and underdamped cases.
Related Concept Videos
Principle of Linear Impulse and Momentum for a System of Particles
Notably, internal forces between particles, occurring in equal and opposite collinear pairs, cancel out and are not part of the equation of motion. This exclusion simplifies the...
Velocity Potential
Plane Potential Flows
Uniform Flow
Uniform flow...
Principle of Linear Impulse and Momentum for a Single Particle
Delving into...
Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving
Properties of Definite Integral II

