Machine learning the dynamics of quantum kicked rotor

TL;DR

This paper introduces a novel application of LSTM neural networks to analyze the dynamics of wave packets in quantum kicked rotors, enabling phase classification in higher-dimensional Anderson transitions.

Contribution

It is the first to use LSTM for analyzing wave packet dynamics in quantum systems, providing an alternative to CNN-based phase detection methods.

Findings

LSTM effectively classifies localized and delocalized phases.

The phase diagrams from LSTM align with those from CNN.

Demonstrates LSTM's potential in quantum phase analysis.

Abstract

Using the multilayer convolutional neural network (CNN), we can detect the quantum phases in random electron systems, and phase diagrams of two and higher dimensional Anderson transitions and quantum percolations as well as disordered topological systems have been obtained. Here, instead of using CNN to analyze the wave functions, we analyze the dynamics of wave packets via long short-term memory network (LSTM). We adopt the quasi-periodic quantum kicked rotors, which simulate the three and four dimensional Anderson transitions. By supervised training, we let LSTM extract the features of the time series of wave packet displacements in localized and delocalized phases. We then simulate the wave packets in unknown phases and let LSTM classify the time series to localized and delocalized phases. We compare the phase diagrams obtained by LSTM and those obtained by CNN.