Researchers Map $n$-Time Cumulant Function After Quantum Quenches

Riccardo Travaglino, Pasquale Calabrese of the SISSA and INFN Sezione di Trieste and Katja Klobas, Bruno Bertini of the University of Birmingham, have developed a comprehensive description of the n-time cumulant function, or n-Full Counting Statistics (n-FCS), following global quantum quenches. Their work investigates how extensive U(1) conserved charges evolve after a sudden change in a quantum system and reveals an unexpected simplification in the resulting dynamical correlation functions. The researchers show that when transport is ballistic and time correlations are sufficiently weak, the n-FCS assumes a distinctive “time-shell” structure in which the correlations depend only on the earliest time appearing in the calculation. Analytical predictions and numerical simulations demonstrate that this behavior is present in both free and interacting quantum models, suggesting that the phenomenon is broadly applicable to nonequilibrium quantum systems.

Understanding the dynamics of quantum systems driven far from equilibrium remains one of the central challenges of modern condensed matter physics. A global quantum quench, in which a system’s governing parameters are suddenly changed, generates complex many-body dynamics that are typically difficult to analyze because correlations evolve simultaneously across both space and time. Full Counting Statistics provides a powerful framework for characterizing fluctuations of conserved quantities, but extending this approach to multiple time measurements has previously resulted in increasingly complicated correlation functions.

To address this challenge, the researchers employed a space-time duality framework to study initial states that are symmetric under the action of conserved U(1) charges. Within this approach, they derived a general description of n-time Full Counting Statistics and demonstrated that, under ballistic transport conditions, the complicated multi-time correlations simplify dramatically. Rather than depending independently on every measurement time, the resulting expressions organize into a time-shell structure where the dominant contribution is determined by the smallest time in the sequence.

The researchers further show that the n-FCS factorizes into a sum of single-time Full Counting Statistics arranged according to this time-shell structure. Extensive analytical calculations, supported by numerical simulations, confirm the prediction across both exactly solvable free models and interacting many-body systems. The agreement between theory and computation indicates that the observed simplification reflects a general property of quantum dynamics rather than a feature of a particular model.

By revealing a universal structure underlying multi-time charge fluctuations after quantum quenches, the work provides a powerful new framework for studying nonequilibrium quantum dynamics. The simplified description of dynamical correlation functions could make it easier to analyze transport, conserved quantities, and fluctuation phenomena in complex quantum systems while offering new theoretical tools for exploring quantum many-body physics and future quantum technologies.