On the Microscopic Conditions for Linear Macroscopic Laws

Abstract

The authors have investigated the conditions which must be imposed on the microscopic equations of motion to obtain exact linear laws for macroscopic (phase averaged) variables. The starting point in this study has been the lowest order master equation (Pauli equation) which is a linear microscopic equation in the state probabilities with a time-independent transition matrix. Discrete and continuous variable master equations as well as their multivariate generalizations have been considered. In the case of continuum state variables, the authors have used various Fokker-Planck equations and their corresponding Langevin equations as their starting microscopic equation of motion. In each case the conditions which must be imposed to obtain linear macroscopic transport equations have been derived and discussed.

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Document Details

Document Type
Technical Report
Publication Date
Mar 03, 1972
Accession Number
AD0739732

Entities

People

  • Kurt E. Shuler
  • R. I. Cukier

Organizations

  • University of California, San Diego

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boltzmann Equation
  • California
  • Differential Equations
  • Distribution Functions
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Equations Of Motion
  • Fokker Planck Equations
  • Gaussian Processes
  • Markov Processes
  • Perturbation Theory
  • Perturbations
  • Probability
  • Quantum Properties
  • Statistical Mechanics
  • Stochastic Processes

Readers

  • Approximation Theory.
  • Fluid Dynamics.
  • Quantum spin resonance or Electron Paramagnetic Resonance spectroscopy.