Semiclassical theory of out-of-time-order correlators for low-dimensional classically chaotic systems

TL;DR

This paper develops a semiclassical framework to analyze the out-of-time-order correlator (OTOC) in low-dimensional chaotic systems, revealing exponential growth linked to classical Lyapunov exponents and temperature dependence.

Contribution

It introduces a semiclassical expansion for the OTOC in low-dimensional systems, connecting quantum growth to classical chaos indicators.

Findings

OTOC exhibits exponential growth governed by Lyapunov exponents.

Growth rate scales with the square root of temperature.

Semiclassical expansion captures leading quantum corrections.

Abstract

The out-of-time-order correlator (OTOC), recently analyzed in several physical contexts, is studied for low-dimensional chaotic systems through semiclassical expansions and numerical simulations. The semiclassical expansion for the OTOC yields a leading-order contribution in $\hbar^2$ that is exponentially increasing with time within an intermediate, temperature-dependent, time-window. The growth-rate in such a regime is governed by the Lyapunov exponent of the underlying classical system and scales with the square-root of the temperature.