论文标题
重力脉冲中颗粒的平均非线性动力学：有效的哈密顿量，世俗加速和重力敏感性
Average nonlinear dynamics of particles in gravitational pulses: effective Hamiltonian, secular acceleration, and gravitational susceptibility
论文作者
论文摘要
与规定的准授权引力波（GW）相互作用的颗粒表现出可以用汉密尔顿方程来描述的世俗（平均）非线性动力学。我们将这种“ Ponderomotive”动力学的哈密顿量推导到GW振幅中的第二阶动力学，以实现一般背景度量。对于真空GWS的特殊情况，我们表明我们的哈密顿量等同于有效度量中的自由粒子，我们明确地计算出来。我们还表明，已经有一个线性平面GW脉冲通过有限的距离从其不受干扰的轨迹中移动，该距离独立于GW相位，与脉冲强度的积分成正比。我们通过分析计算粒子位移，并表明我们的结果与数值模拟一致。我们还展示了非线性平均动力学的哈密顿量如何自然导致具有任意相位空间分布的粒子气体的线性重力敏感性的概念。我们明确计算这种敏感性，以在后续文件中应用它，以在几何镜头近似中研究不均匀培养基中的自洽GWS。
Particles interacting with a prescribed quasimonochromatic gravitational wave (GW) exhibit secular (average) nonlinear dynamics that can be described by Hamilton's equations. We derive the Hamiltonian of this "ponderomotive" dynamics to the second order in the GW amplitude for a general background metric. For the special case of vacuum GWs, we show that our Hamiltonian is equivalent to that of a free particle in an effective metric, which we calculate explicitly. We also show that already a linear plane GW pulse displaces a particle from its unperturbed trajectory by a finite distance that is independent of the GW phase and proportional to the integral of the pulse intensity. We calculate the particle displacement analytically and show that our result is in agreement with numerical simulations. We also show how the Hamiltonian of the nonlinear averaged dynamics naturally leads to the concept of the linear gravitational susceptibility of a particle gas with an arbitrary phase-space distribution. We calculate this susceptibility explicitly to apply it, in a follow-up paper, toward studying self-consistent GWs in inhomogeneous media within the geometrical-optics approximation.
