Stability and Control of Bouncing Ball Quantum Scars

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, stability, and control of linear "bouncing ball" scars in two-dimensional (2D) quantum dots. These scars have relevance as effective and controllable channels in quantum transport. Here, we apply imaginary time propagation to solve the 2D Schrödinger equation in an arbitrary external confining potential, that is, the quantum dot model with external perturbation. We show how the strength of a bouncing ball scar can be maximized with a single perturbative peak, i.e., a repulsive bump or an attractive dip simulating the effect of a charged nanotip in the system. Then we find the optimal size of the perturbative peak to maximize both the abundance and strength of the bouncing ball scars. Finally, we analyze the stability of bouncing ball scars against external noise in the system and show that some of the scars are remarkably robust. This provides prospects for further utilization of bouncing ball scars in quantum transport.