有效质量和频率随时间变化的谐振子及其对影响干涉探测器的“啁啾潮汐”引力波力的可能应用
Harmonic oscillator with time-dependent effective-mass and frequency with a possible application to 'chirped tidal' gravitational waves forces affecting interferometric detectors
摘要：
含时频率和含时质量的一般理论（“有效质量”）的一般理论。本研究采用振荡器来研究干涉仪中的某些量子效应，以探测引力波，当天文双星系统接近合并点时，引力波的强度和频率都会增加，这会导致强烈的偏差本文从简单的干涉质量的谐振描述出发，指出在这种条件下，干涉质量的谐振可以用频率和有效质量随时间变化的机械谐振子来描述。在本理论模型中，有效质量随时间减小，描述了振荡器振幅随时间增加的泵浦现象。利用绝热近似分析了该系统的量子化。结果表明，在绝热近似下，随着引力波强度的增加，在一个正交方向上的量子噪声增加，而在另一个正交方向上的量子噪声减少，从而产生压缩现象.
英文摘要：
The general theory of time-dependent frequency and time-dependent mass ('effective mass') is described.The general theory for time-dependent harmonic- oscillator is applied in the present research for studying certain quantum effects in the interferometers for detecting gravitational waves.When an astronomical binary system approaches its point of coalescence the gravitational wave intensity and frequency are increasing and this can lead to strong deviations from the simple description of harmonic-oscillations for the interferometric masses on which the mirrors are placed.It is shown that under such condtions the harmonic-oscillations of these masses can be described by mechanical harmonic-oscillators with time-dependent frequency and effective-mass. In the present theoretical model the effective-mass is decreasing with time describing pumping phenomena in which the oscillator amplitude is increasing with time . The quantization of this system is analyzed by the use of the adiabatic approximation. It is found that the increase of the gravitational wave intensity, within the adiabatic approximation, leads to squeezing phenomena where the quantum noise in one quadrature is increased and in the other quadrature is decreased.
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