与线性化引力相互作用的系统的主方程
Master equation for systems interacting with linearized gravity
AI总结：
该研究推导了与线性化引力波环境耦合的两质量系统的主方程，重现经典引力波能量损失，抑制态间相干性，在小涨落下简化为 Caldeira-Leggett 型方程。
AI中文摘要：
我们研究与线性化引力波环境相互作用的两质量系统的开放量子动力学。我们以两质量间的可观测固有距离展开分析，发现基于费米正则坐标的标准拉格朗日量得到的正则变量不适用于该系统的有效描述。我们通过幺正变换解决此问题，该变换提供了物理上有意义的系统-环境分解，并推导了引力常数G一阶近似下的主方程。其耗散部分重现了引力波辐射导致的经典能量损失，而噪声贡献则抑制了不同质量四极矩（或等效为不同固有间距）的态之间的相干性。在固有距离可通过平均距离l₀附近的小量子涨落描述的 regime 中，动力学简化为 Caldeira-Leggett 型方程，其退相干率取决于基线长度l₀。
英文摘要：
We investigate the open quantum dynamics of a system of two masses interacting with an environment of linearized gravitational waves. We formulate the analysis in terms of the observable proper distance between the two masses, and show that the canonical variables obtained from the standard Lagrangian, expressed in terms of the Fermi normal coordinates, are not suitable for an effective description of the system. We resolve this issue through a unitary transformation that provides a physically meaningful system--environment decomposition and derive the master equation to leading order in $G$. Its dissipative sector reproduces the classical energy loss due to gravitational-wave emission, while the noisy contributions suppress coherences between states with different mass quadrupole, or effectively, different proper separations. In the regime where the proper distance can be described by considering small quantum fluctuations around an average distance $l_0$, the dynamics reduces to a Caldeira--Leggett-type equation, with a decoherence rate dependent on the baseline length $l_0$.
