祖母钟和安静的激光
Grand-mother clocks and quiet lasers
摘要：
伽利略在16世纪指出，摆的振荡周期几乎与振幅无关。然而，这样的钟摆会因空气摩擦而阻尼。后者可以被看作是由于空气分子与钟摆接触而产生的。由此可见，空气摩擦不仅阻尼振荡，而且还引入随机性。在惠更斯于18世纪发现的所谓的“祖母钟”中，平均而言，阻尼是通过由下落的重物驱动的擒纵机构来补偿的。本文的目的是表明，这样的时钟，在其理想化的形式，一个安静的振荡器。我们所说的“安静”是指，尽管阻尼引入了随机性，但耗散功率（视为振荡器输出）不会缓慢波动。与1984年理论上发现的安静激光振荡器作了比较。因为输入功率在机械振荡器和安静激光振荡器中都不波动，所以输出功率在小傅立叶频率处不波动，而不管所涉及的详细机制如何。
英文摘要：
Galileo noted in the 16th century that the period of oscillation of a pendulum is almost independent of the amplitude. However, such a pendulum is damped by air friction. The latter may be viewed as resulting from air molecules getting in contact with the pendulum. It follows that air friction, not only damps the oscillation, but also introduces randomness. In the so-called ``grand-mother'' clock, discovered by Huygens in the 18th century, damping is compensated for, on the average, by an escapement mechanism driven by a falling weight. The purpose of this paper is to show that such a clock is, in its idealized form, a quiet oscillator. By ``quiet'' we mean that in spite of the randomness introduced by damping, the dissipated power (viewed as the oscillator output) does not fluctuate slowly. Comparison is made with quiet laser oscillators discovered theoretically in 1984. Because the input power does not fluctuate in both the mechanical oscillator and the quiet laser oscillator, the output power does not fluctuate at small Fourier frequencies, irrespectively of the detailed mechanisms involved.
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