Complexity Growth Following Multiple Shocks

TL;DR

This paper investigates how complexity evolves after multiple shock waves in holographic theories, showing it respects bounds, saturates at a temperature-independent value, and is affected by initial state temperature.

Contribution

It introduces a detailed analysis of complexity growth after multiple shocks using the Complexity=Action proposal, highlighting bounds and saturation behaviors.

Findings

Lloyd's bound is respected during thermalization.

Complexity growth saturates to a value proportional to the final state's energy.

Higher initial temperatures lead to lower complexity growth rates.

Abstract

In this paper by making use of the "Complexity=Action" proposal, we study the complexity growth after shock waves in holographic field theories. We consider both double black hole-Vaidya and AdS-Vaidya with multiple shocks geometries. We find that the Lloyd's bound is respected during the thermalization process in each of these geometries and at the late time, the complexity growth saturates to the value which is proportional to the energy of the final state. We conclude that the saturation value of complexity growth rate is independent of the initial temperature and in the case of thermal initial state, the rate of complexity is always less than the value for the vacuum initial state such that considering multiple shocks it gets more smaller. Our results indicate that by increasing the temperature of the initial state, the corresponding rate of complexity growth starts far from final saturation rate value.