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arXiv quant-ph/0408169quant-ph
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经典和量子散射理论中的共振和绝热不变性

Resonances and adiabatic invariance in classical and quantum scattering theory

Sudhir R. Jain

摘要:

我们发现,在量子散射理论中,时滞的能量积分是一个绝热不变量,并且经典地对应于相空间体积。因此,发现的积分提供了一个量子化条件的共振,解释了一系列的结果,最近发现在非相对论和相对论制度。此外,量子共振宽度和经典摩擦等统计量之间的联系已经建立了一个经典的确定性的量,一个摄动周期轨道的稳定性指数。这个关系可以用来估计有限量子系统中的能量耗散率。

英文摘要:

We discover that the energy-integral of time-delay is an adiabatic invariant in quantum scattering theory and corresponds classically to the phase space volume. The integral thus found provides a quantization condition for resonances, explaining a series of results recently found in non-relativistic and relativistic regimes. Further, a connection between statistical quantities like quantal resonance-width and classical friction has been established with a classically deterministic quantity, the stability exponent of an adiabatically perturbed periodic orbit. This relation can be employed to estimate the rate of energy dissipation in finite quantum systems.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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