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- W1991625836 abstract "Collinear collisions, with exponential repulsive potential, between a mass point and a harmonic oscillator are studied in the limit of high frequency. Multiple encounters during single collisions and an arbitrary value of the mass parameter $m$ are permitted. Methods are analytical and numerical. The main results are the following: For an initially resting oscillator the energy $E$ after the collision decays exponentially with frequency. The limiting decay constant for high frequency is independent of $m$ and identical to the golden rule prediction $2ensuremath{pi}∕ensuremath{lambda}$ where ${ensuremath{lambda}}^{ensuremath{-}1}$ is a dimensionless frequency. In the high-frequency domain the energy of the oscillator has the form $E=2{ensuremath{pi}}^{2}ensuremath{phi}{(m)}^{2}phantom{rule{0.2em}{0ex}}mathrm{exp}{ensuremath{-}2ensuremath{pi}∕ensuremath{lambda}}$ where $ensuremath{phi}(m)=2mensuremath{-}frac{2}{3}(1+mathrm{ln}phantom{rule{0.2em}{0ex}}4){m}^{2}+ensuremath{cdots}$. The first term is the golden rule result, and the second term is new. A series of polynomials ${ensuremath{phi}}_{n}$ is constructed that converges to $ensuremath{phi}(m)$. It is suggested that $ensuremath{phi}(m)$ is an entire function of the complex variable $m$ which has the form of an infinite product $ensuremath{phi}(m)=2mensuremath{prod}(1ensuremath{-}m∕{m}_{n})$ where the ${m}_{n}$ are the positive roots of $ensuremath{phi}(m)$. The first 15 roots have been determined numerically which suggests an asymptotic behavior $sqrt{{m}_{n}}ensuremath{sim}an+b$. Agreement with the numerical data is excellent." @default.
- W1991625836 created "2016-06-24" @default.
- W1991625836 creator A5044369543 @default.
- W1991625836 date "2005-10-05" @default.
- W1991625836 modified "2023-09-25" @default.
- W1991625836 title "Linear collision of a classical harmonic oscillator with a mass point in the high-frequency region" @default.
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- W1991625836 doi "https://doi.org/10.1103/physreva.72.042703" @default.
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