Garnier J
Centre de Mathématiques Appliquées, Centre National de la Recherche Scientifique, Unité Mixte de Recherche 7641, Ecole Polytechnique, 91128 Palaiseau Cedex, France.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Oct;60(4 Pt A):3676-87. doi: 10.1103/physreve.60.3676.
This paper investigates the evolution of a quantum particle in a harmonic oscillator driven by time-dependent forces. The perturbations are small, but they act long enough so that we can solve the problem in the asymptotic framework corresponding to a perturbation amplitude that tends to zero and a perturbation duration that tends to infinity. We describe the effective evolution equation of the state vector, which reads as a stochastic partial differential equation. We exhibit a closed-form equation for the transition probabilities, which can be interpreted in terms of a jump process. Using standard probability tools, we are then able to compute explicitly the probabilities for observing the different energy eigenstates and give the exact statistical distribution of the energy of the particle.
本文研究了在随时间变化的力驱动下的谐振子中量子粒子的演化。扰动很小，但作用时间足够长，因此我们可以在对应于扰动幅度趋于零和扰动持续时间趋于无穷的渐近框架内解决该问题。我们描述了态矢量的有效演化方程，它表现为一个随机偏微分方程。我们给出了跃迁概率的一个封闭形式方程，它可以用跳跃过程来解释。然后，使用标准概率工具，我们能够明确计算出观测到不同能量本征态的概率，并给出粒子能量的精确统计分布。
