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

TL;DR

This paper investigates the formation, prevalence, and robustness of bouncing-ball quantum scars in 2D quantum wells, revealing how specific perturbations can enhance their occurrence and stability, with implications for quantum transport applications.

Contribution

It introduces a method to control and optimize bouncing-ball scars in quantum wells using external perturbations and analyzes their stability under noise.

Findings

Bouncing-ball scars emerge with specific perturbative peaks.

Optimal perturbation size maximizes scar prevalence.

Some scars are remarkably stable against external noise.

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 Schr\"odinger 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.