article Open AccessTop 10% cited
Statistical Mechanics of Assemblies of Coupled Oscillators
Journal of Mathematical Physics · 1965 · Vol. 6(4) · pp. 504–515
Abstract
It is shown that a system of coupled harmonic oscillators can be made a model of a heat bath. Thus a particle coupled harmonically to the bath and by an arbitrary force to a fixed center will (in an appropriate limit) exhibit Brownian motion. Both classical and quantum mechanical treatments are given.
stochastic dynamics and bifurcationAdvanced Thermodynamics and Statistical MechanicsEcosystem dynamics and resilienceHarmonic oscillatorBrownian motionClassical mechanicsStatistical mechanicsPhysicsQuantum statistical mechanicsLimit (mathematics)QuantumHarmonicClassical limit
Funding
- National Science Foundation
Citations
942
FWCI
2.99
field-weighted impact
References
14
Percentile
91%
vs. same field & year
Citations per year
Cited by
Reaction-rate theory: fifty years after Kramers
Reviews of Modern Physics · 1990 · 6,037 citations
Nonconservative Lagrangian and Hamiltonian mechanics
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1996 · 719 citations
Path integral approach to quantum Brownian motion
Physica A Statistical Mechanics and its Applications · 1983 · 2,681 citations
Current Status of Transition-State Theory
The Journal of Physical Chemistry · 1996 · 2,225 citations
Mechanics with fractional derivatives
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1997 · 666 citations
Quantum Langevin equation
Physical review. A, General physics · 1988 · 652 citations
References
Brownian Motion of a Quantum Oscillator
Journal of Mathematical Physics · 1961 · 2,466 citations
On the Theory of the Brownian Motion
Physical Review · 1930 · 4,464 citations
Related articles
Statistical Mechanics of Assemblies of Coupled Oscillators
Journal of Mathematical Physics · 1965 · 942 citations
Citation Network
How this paper connects to the literature. Drag to explore, click any node to open that paper.