Average nonlinear dynamics of particles in gravitational pulses: Effective Hamiltonian, secular acceleration, and gravitational susceptibility
Average nonlinear dynamics of particles in gravitational pulses: Effective Hamiltonian, secular acceleration, and gravitational susceptibility
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DOI：
10.1103/physrevd.102.064012
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发表时间：
2020-05
影响因子：
5
通讯作者：
D. Garg;I. Dodin
中科院分区：
文献类型：
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作者：
D. Garg;I. Dodin
与规定的准单色引力波 (GW) 相互作用的粒子表现出可以用汉密尔顿方程描述的长期（平均）非线性动力学。我们将这种“有质动力”动力学的哈密顿量导出为一般背景度量的引力波振幅的二阶。对于真空引力波的特殊情况，我们表明我们的哈密顿量相当于有效度量中的自由粒子的哈密顿量，我们对此进行了显式计算。我们还表明，线性平面引力波脉冲已经将粒子从其未受扰动的轨迹移出有限距离，该距离与引力波相位无关并且与脉冲强度的积分成正比。我们分析计算了粒子位移，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地导出具有任意相空间分布的粒子气体的线性引力敏感性的概念。我们明确计算了这种敏感性，以便在后续论文中应用它来研究几何光学近似中非均匀介质中的自洽引力波。
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.