Melnikov's criterion for nondifferentiable weak-noise potentials
The stationary probability density of Fokker-Planck models with weak noise has an asymptotic form containing a pseudopotential theta. If theta is smooth, it satisfies a Hamilton-Jacobi equation at zero energy and can be interpreted as the action of an associated Hamiltonian system. Under this assumption, theta has the properties of a Lyapunov function, and can be used, for example, as a thermodynamic potential in nonequilibrium steady states. The author considers systems having several attractors and shows, by applying Melnikov's method to the associated Hamiltonian, that in general theta is not differentiable. A small perturbation of a model with differentiable theta leads to a nondifferentiable theta. The method is illustrated on a model used in the treatment of the unstable mode in a laser.
- Research Organization:
- Univ. de Geneve, Geneve
- OSTI ID:
- 6957454
- Journal Information:
- J. Stat. Phys.; (United States), Vol. 42:3
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
LASER RADIATION
LYAPUNOV METHOD
NOISE
OPTICAL MODES
BOUNDARY CONDITIONS
EQUATIONS OF MOTION
FLUCTUATIONS
FOKKER-PLANCK EQUATION
HAMILTONIANS
JACOBIAN FUNCTION
PROBABILITY
QUANTUM MECHANICS
STATISTICAL MECHANICS
TRANSPORT THEORY
DIFFERENTIAL EQUATIONS
ELECTROMAGNETIC RADIATION
EQUATIONS
FUNCTIONS
MATHEMATICAL OPERATORS
MECHANICS
OSCILLATION MODES
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
RADIATIONS
VARIATIONS
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics