Microscope for Quantum Dynamics with Planck Cell Resolution

TL;DR

This paper introduces a high-resolution out-of-time-correlation (OTOC) that acts as a microscope to explore quantum dynamics at the Planck cell scale, linking wave function spreading and quantum chaos.

Contribution

It presents a novel OTOC with Planck cell resolution that connects quantum state evolution and operator dynamics, enhancing understanding of quantum chaos.

Findings

OTOC depends on initial state, revealing fine quantum structures

Explicit relation between OTOC and wave function spreading

Clarifies exponential growth dependence on classical Lyapunov exponent

Abstract

We introduce the out-of-time-correlation(OTOC) with the Planck cell resolution. The dependence of this OTOC on the initial state makes it function like a microscope, allowing us to investigate the fine structure of quantum dynamics beyond the thermal state. We find an explicit relation of this OTOC to the spreading of the wave function in the Hilbert space, unifying two branches of the study of quantum chaos: state evolution and operator dynamics. By analyzing it in the vicinity of the classical limit, we clarify the dependence of the OTOC's exponential growth on the classical Lyapunov exponent.