Energy Transfer in Random-Matrix ensembles of Floquet Hamiltonians

TL;DR

This paper investigates energy transfer in random-matrix Floquet Hamiltonian ensembles, revealing universal statistical properties, phase transitions in energy pumping, and employing machine learning for parameter importance, advancing Hamiltonian engineering.

Contribution

It introduces a framework for analyzing energy transfer in random Floquet Hamiltonians, including a machine learning approach to identify key parameters for high efficiency.

Findings

Energy transfer distribution P(E) exhibits a non-symmetry-breaking transition.

Ensembles are shown to be nonintegrable Hamiltonian families.

Machine learning identifies parameters critical for high energy conversion efficiency.

Abstract

We explore the statistical properties of energy transfer in ensembles of doubly-driven Random- Matrix Floquet Hamiltonians, based on universal symmetry arguments. The energy pumping efficiency distribution P(E) is associated with the Hamiltonian parameter ensemble and the eigenvalue statistics of the Floquet operator. For specific Hamiltonian ensembles, P(E) undergoes a transition that cannot be associated with a symmetry breaking of the instantaneous Hamiltonian. The Floquet eigenvalue spacing distribution indicates the considered ensembles constitute generic nonintegrable Hamiltonian families. As a step towards Hamiltonian engineering, we develop a machine-learning classifier to understand the relative parameter importance in resulting high conversion efficiency. We propose Random Floquet Hamiltonians as a general framework to investigate frequency conversion effects in a new class of generic dynamical processes beyond adiabatic pumps.