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Название: A Soluble Model for Diffusion in a Bistable Potential
Автор: van Kampen N.G.
After a general discussion of diffusion in a potential field having two minima, an explicit solution is obtained for a special form of the potential. The potential is symmetric, but the diffusing particle is initially at an arbitrary point near the potential maximum. Various suggested approximation schemes are tested, with the following conclusions, (i) In linear approximation around the maximum the probability distribution is Gaussian. A two-peaked distribution emerges only through nonlinear terms, (ii) The chances for the particle to go to the right or the left valley cannot be found from the linear approximation. Matching the linear approximation with a macroscopic description far away from the maximum is therefore wrong, (iii) Kramers' treatment of the escape across a potential barrier yields a practically exact result for this model.
The text passage describes a scientific paper about diffusion in a bistable potential, discussing various approximation schemes and their conclusions. It does not contain any explicit mathematical questions or answers.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Нашли опечатку? Выделите ее мышкой и нажмите Ctrl+Enter
Название: A Soluble Model for Diffusion in a Bistable Potential
Автор: van Kampen N.G.
After a general discussion of diffusion in a potential field having two minima, an explicit solution is obtained for a special form of the potential. The potential is symmetric, but the diffusing particle is initially at an arbitrary point near the potential maximum. Various suggested approximation schemes are tested, with the following conclusions, (i) In linear approximation around the maximum the probability distribution is Gaussian. A two-peaked distribution emerges only through nonlinear terms, (ii) The chances for the particle to go to the right or the left valley cannot be found from the linear approximation. Matching the linear approximation with a macroscopic description far away from the maximum is therefore wrong, (iii) Kramers' treatment of the escape across a potential barrier yields a practically exact result for this model.
user
The text passage describes a scientific paper about diffusion in a bistable potential, discussing various approximation schemes and their conclusions. It does not contain any explicit mathematical questions or answers.

TYPE: NO_QUESTION