腔光力系统是研究从微观到介观甚至宏观系统量子力学特性的新型平台，尤其是微型腔光力系统品质因子高，体积小等，在引力波检测、量子超精密测量、量子信息处理等方面也有潜在的应用。与一般的开放量子系统一样，一个真实的光力系统一定被环境所包围，其量子动力学行为或多或少地受到环境的影响。现有的研究大都认为环境是“如此之大”以至于其噪声谱类似于具有无限展宽的白噪声谱，环境噪声的关联时间远小于系统的特征时间，因此可以采用玻恩-马尔科夫近似处理相关问题。近几年来，随着科学研究的不断深入，人们发现当量子系统与具有结构的环境耦合时玻恩-马尔科夫近似不再成立，这类环境如受限电磁环境、固态量子系统的纳米结构环境等。非马尔科夫环境的最大特点是环境噪声的关联时间接近甚至大于系统的特征时间，它所导致的时间记忆效应和环境回流效应对系统的量子动力学性质产生很大的影响。目前，已有一些关于腔光力系统与非马尔科夫环境耦合的研究报道。 本论文讨论腔光力系统的非马尔科夫量子动力学问题。该系统由可移动反射镜取代Fabry-Perot腔的一个腔镜而构成，而可移动腔镜的运动模式与具有Ohmic型密度谱的非马尔科夫环境耦合。我们采用郎之万方程方法，基于他人已有的解决相应算子积分微分方程的方法（Phys. Rev. A 2016, 93(6) 063853），给出了腔模和声子模各自的时间自相关函数以及它们的时间互相关函数，就ohmic密度谱情况，数值模拟了系统中声子、光子以及声子与光子之间的logarithmic negativity量子纠缠的动力学演化过程，详细讨论了包括谱密度的截止频率、耦合强度以及温度在内的环境因素对上述动力学的影响，同时分析了振子冷却与腔模激发以及纠缠演化之间的关系。数值模拟表明，在环境温度较低时声子数和光子数随时间演化总是减小,此时,若增加谱密度的截止频率、振子与环境的耦合强度，两种粒子数减少的速度加快，但相比于声子数的演化对上述两个环境参数变化的迅速反应,光子数演化的反应则滞后。低环境温度条件下，系统激发以被环境单向吸收为主。对于较高的环境温度，两种粒子数演化减少的速度减缓，当温度很高时，演化则向粒子数增加方向进行，即高温条件下，系统失去了对振子的冷却作用，同时环境通过振子这一媒介激发更多的腔模光子。高环境温度条件下，系统将更多地吸收来自于环境的热激发。声子与光子之间的纠缠总在演化初期达到最大，该最大值随着截止频率与耦合强度的增加而变大。环境温度的变化对最大纠缠影响最为明显，随着温度的升高纠缠急剧下降。这正如人们所预料的那样：量子效应总发生在低温情况中。

A cavity optomechanical system can be used as a platform for investigating the properties of quantum mechanical at multiple levels from microcosmic to mesoscopic even macrocosmic. Especially a micro-optomechanical system, which has many advantages compared to traditional optical cavity, such as high quality factor and smaller size, has attracted significant attention due to its potential use in the detection of gravitational waves, quantum extremely precision measurements, and quantum information processing. Like an general open quantum system，a real optomechanical system is surrounded by its environment. Thus, its quantum dynamic behavior may be more or less influenced. In the most existing studies, the environment of an open quantum system is so “large” that its spectral density has flat structure and its correlation time is much less than the characteristic time of the system. Such an environment is so called Markovian. With the development of science and technology, it was found recently that the Born-Markov approximation is no longer valid in dealing with a quantum system coupling to a nano-structured environment or a limited electromagnetic environment, etc. The most prominent characteristics of a non-Markovian environment is its correlation time is close to or even greater than the characteristic time of the system. The time memory effect and the reflux effect of the environment have a big impact on the quantum dynamics of the system. So far, there are some studies on a cavity optomechanical system coupling to a non-Markovian environment. This paper aims to study the problem of quantum dynamics of a cavity optomechanical system in a non-Markovian environment. The system is a Fabry-Perot cavity with a mirror that can vibrate freely, and the vibration mode of the mirror couples with a non-Markovian environment with Ohmic spectral density. Based on the work of literature (Phys. Rev. A 2016, 93(6) 063853), where the formula solution of the integer-differential equation for the phonon operator of the vibration mode has been obtained, we calculate the various time autocorrelation functions and time cross-correlation functions of photons and phonon. Based on them we simulate numerically the dynamic evolution of the cavity mode, the vibration mode and the logarithmic negativity entanglement between the photon and the phonon, and discuss the influence of the environment factors including the cutoff frequency of the spectrum, coupling strength and temperature on the above dynamics. The numerical results indicate that as the environment temperature is lower, both phononic and photonic numbers reduce in their evolution. At the same time, if the cutoff frequency or the coupling strength increases, two kinds of particles will lose more quickly. However, the photonic evolution in the early period of time does not sensitive against the variation of the above two factors. If the temperature is high enough, the system gets the excitations from the environment more than it loses, thus the two kinds of particles increase in their evolution. Now the cooling action for the vibration mode disappears. As to the entanglement between photon and phonon, its maximum always appears in the early period of evolution. Increasing the cutoff frequency or the coupling strength is helpful for promoting the entanglement. Relatively, lowing temperature is more effective for this purpose. The temperature-dependent property of our cavity optomechanical system provides another example to verify the statement that a quantum effect can easily be observed in the lower temperature condition.