We consider a simple model describing the interaction of a quantum particle with a vibrational environment, which eventually acts as a friction on the particle. This equation admits soliton-like solutions, and we numerically investigate their stability when subjected to a small initial impulsion. Our findings illustrate the analogies with the behavior of classical particles and the relevance of asymptotic models.

中文翻译：

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量子耗散系统孤波稳定性的数值研究

我们考虑一个简单的模型，该模型描述了量子粒子与振动环境的相互作用，该振动环境最终充当了粒子的摩擦。该方程允许类似孤子的解决方案，我们通过数值研究了当受到较小初始冲击时的稳定性。我们的发现说明了经典粒子的行为与渐近模型的相关性。