Formation, prevalence, and stability of bouncing-ball quantum scars

Abstract

Quantum scars correspond to enhanced probability densities along unstable classical periodic orbits. In recent years, research on quantum scars has extended to various systems including the many-body regime. In this work we focus on the formation, prevalence, and stability of linear bouncing-ball (BB) scars in two-dimensional (2D) quantum wells. These scars have relevance as effective and controllable channels in quantum transport. We utilize imaginary time propagation to solve the 2D Schrödinger equation within an arbitrary external confining potential, specifically the quantum well model with external perturbations. We show how BB scars begin to emerge with a single perturbative peak, such as a repulsive bump or attractive dip that simulates the effect of a charged nanotip in the system. We then identify the optimal size of the perturbative peak to maximize the prevalence of these scars. Finally, we investigate the stability of BB scars against external noise and find that some of them are remarkably robust. This suggests promising opportunities for further applications of BB scars in quantum transport.