# Rogue Quantum Harmonic Oscillations

## TL;DR

This paper investigates rogue oscillations in the nonlinear quantum harmonic oscillator, developing a computational scheme and analyzing how various parameters influence the formation and dynamics of these rogue waves.

## Contribution

It introduces a split-step Fourier method for analyzing NQHO and explores the role of different parameters in rogue oscillation generation.

## Key findings

- Modulation instability triggers rogue oscillations in NQHO.
- Parameter variations significantly affect rogue wave formation probabilities.
- The developed numerical scheme effectively simulates rogue wave dynamics.

## Abstract

We show the existence and investigate the dynamics and statistics of rogue oscillations (standing waves) generated in the frame of the nonlinear quantum harmonic oscillator (NQHO). With this motivation, in this paper, we develop a split-step Fourier scheme for the computational analysis of NQHO. We show that modulation instability excites the generation of rogue oscillations in the frame of the NQHO. We also discuss the effects of various parameters such as the strength of trapping well potential, nonlinearity, dissipation, fundamental wave number and perturbation amplitude on rogue oscillation formation probabilities.