应用于强激光场过程中出现的积分的渐近方法

IF 2 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL
D B Milošević, A S Jašarević, D Habibović, E Hasović, A Čerkić and W Becker
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引用次数: 0

摘要

原子和分子过程在强激光场中的量子力学转变幅度是以高度振荡函数的多维积分形式表示的。这种积分非常适合用渐近积分法进行评估。此外,利用这些方法还可以从费曼路径积分形式主义的意义上识别量子轨道的部分贡献,这些贡献与鞍点方程的特定解有关。这有助于深入了解问题的物理原理,而仅仅通过数值求解这些积分是无法做到这一点的。我们将鞍点方法应用于强场物理学和原子科学中重要的各种量子过程。凝聚或接近凝聚鞍点的特殊情况需要应用均匀近似。我们还介绍了鞍点法的两种修正方法,适用于子积分函数奇异点与鞍点完全重叠或位于其附近的情况。重点是鞍点解的分类。对于电离时间的一维积分,这个问题得到了解决,这与阈值以上电离(ATI)有关;而对于二维积分,则引入了多指数分类法,这对于高阶谐波发生(HHG)和后向散射电子(高阶 ATI)的中高能谱特别有用。对于低能结构,则采用多指数对前向散射量子轨道进行分类。除了 ATI、HHG 和高阶 ATI 等激光诱导过程之外,我们还将激光辅助散射作为激光辅助过程的一个例子进行了考虑,对于这些过程,鞍点方程的实解是存在的。我们特别关注描述这些过程的量子轨道,并将其可视化。我们还考虑了有限激光脉冲、半经典近似、库仑场的作用以及激光场强度足以导致进入相对论机制的情况。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Asymptotic methods applied to integrals occurring in strong-laser-field processes
The quantum-mechanical transition amplitudes for atomic and molecular processes in strong laser fields are expressed in the form of multidimensional integrals of highly oscillatory functions. Such integrals are ideally suited for the evaluation by asymptotic methods for integrals. Furthermore, using these methods it is possible to identify, in the sense of Feynman’s path-integral formalism, the partial contributions of quantum orbits, which are related to particular solutions of the saddle-point equations. This affords insight into the physics of the problem, which would not have been possible by only solving these integrals numerically. We apply the saddle-point method to various quantum processes that are important in strong-field physics and attoscience. The special case of coalescing or near-coalescing saddle points requires application of the uniform approximation. We also present two modifications of the saddle-point method, for the cases where a singular point of the subintegral function exactly overlaps with a saddle point or is located in its close vicinity. Particular emphasis is on the classification of the saddle-point solutions. This problem is solved for the one-dimensional integral over the ionization time, relevant for above-threshold ionization (ATI), while for two-dimensional integrals a classification by the multi-index is introduced, which is particularly useful for the medium- and high-energy spectrum of high-order harmonic generation (HHG) and backward-scattered electrons (for high-order ATI). For the low-energy structures a classification using the multi-index is introduced for the forward-scattering quantum orbits. In addition to laser-induced processes such as ATI, HHG and high-order ATI, we consider laser-assisted scattering as an example of laser-assisted processes for which real solutions of the saddle-point equation exist. Particular attention is devoted to the quantum orbits that describe and visualize these processes. We also consider finite laser pulses, the semiclassical approximation, the role of the Coulomb field and the case of laser fields intense enough to lead into the relativistic regime.
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来源期刊
CiteScore
4.10
自引率
14.30%
发文量
542
审稿时长
1.9 months
期刊介绍: Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.
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