Exercises in simplest dynamical random walk, or Quantum path integral approach to true diffusion law and 1/f noise of classical particle interacting with ideal gas

Abstract

Statistics of classical Hamiltonian random walk of particle colliding with atoms of ideal gas is considered from viewpoint of earlier suggested exact pseudo-quantum path integral representation of the problem, and qualitative agreement is demostrated between results of an naturally arising simple approximation of this integral and results obtained by formally different methods, thus in a new fashion showing inevitability of scaleless 1/f-type fluctuations in rates of molecular Brownian motions and other dynamical transport and evolution processes.

23 pages, no figures, LaTeX2e elsart3p

References in corpus (12)

• Fluctuation-dissipation relations: achievements and misunderstandings
• A truth about Brownian motion in gases and in general
• Virial expansion of molecular Brownian motion versus tales of "statistical independency"
• Stochastic representation of deterministic interactions and Brownian motion
• Thermodynamic restrictions on statistics of molecular random walks
• Dynamical virial relations and invalidity of the Boltzmann kinetic equation
• On statistics and 1/f noise of molecular random walk in low-density gas
• Brownian particle in ideal gas: explicit density expansions, conditional probabilities, and amusing properties of molecular chaos
• Once again on molecular Brownian motion and related fundamental 1/f noise: a logical analysis of exact equations
• Molecular random walks in a fluid and an invariance group of the Bogolyubov generating functional equation
• From shock waves to Brownian motion and 1/f-noise in gas
• On status of Boltzmann kinetic theory in the framework of statistical mechanics