The Kramers problem in the energy-diffusion limited regime

Journal Article · Tue Dec 01 04:00:00 EST 1998 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.477657· OSTI ID:670187

Sancho, J M ^[1]; Romero, A H ^[2]; Lindenberg, K ^[3]

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1. Institute for Nonlinear Science 0402, University of California, San Diego, La Jolla, California 92093-0402 (United States)
2. Department of Chemistry and Biochemistry 0340, and Department of Physics, University of California, San Diego, La Jolla, California 92093-0340 (United States)
3. Department of Chemistry and Biochemistry 0340, and Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0340 (United States)

The Kramers problem in the energy-diffusion limited regime of very low friction is difficult to deal with analytically because of the repeated recrossings of the barrier that typically occur before an asymptotic rate constant is achieved. Thus, the transmission coefficient of particles over the potential barrier undergoes oscillatory behavior in time before settling into a steady state. Recently, Kohen and Tannor [D. Kohen and D. J. Tannor, J. Chem. Phys. {bold 103}, 6013 (1995)] developed a method based on the phase space distribution function to calculate the transmission coefficient as a function of time in the {ital high-friction} regime. Here we formulate a parallel method for the {ital low-friction} regime. We find analytic results for the full time and temperature dependence of the transmission coefficient in this regime. Our low-friction result at long times reproduces the equilibrium result of Kramers at very low friction and extends it to higher friction and lower temperatures below the turn-over region. Our results indicate that the single most important quantity in determining the entire time evolution of the transmission coefficient is the rate of energy loss of a particle that starts above the barrier. We test our results, as well as those of Kohen and Tannor for the Kramers problem, against detailed numerical simulations. {copyright} {ital 1998 American Institute of Physics.}

• OSTI ID: 670187
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 22 Vol. 109; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

40 CHEMISTRY
CHEMICAL REACTION KINETICS
DIFFUSION
DISTRIBUTION FUNCTIONS
ENERGY LOSSES
FRICTION
PARTICLES
PHASE SPACE
STATISTICAL MECHANICS