Technical University of Munich, in collaboration with Max Planck Institute for Physics (Werner Heisenberg Institute), Chinese Academy of Sciences, Germany 3 Max Planck Institute investigate how interacting quantum systems return to stability following disturbance. A detailed explanation of Zubarev’s established non-equilibrium statistical operator approach is presented, simplified for clarity, alongside an alternative method based on observing system evolution over time.

By identifying key conditions such as weak charge violation and distinct timescales for microscopic correlations versus overall relaxation, leading relaxation rates can be determined using equilibrium correlation functions. Furthermore, a link is established between this rate and the diffusion of the same charge, ultimately deriving a diffusion-relaxation equation applicable to scenarios like electroweak B+L washout and perturbative scalar models; results from these examples align with predictions made by the linearized Boltzmann equation, bridging connections between different theoretical frameworks.

Modelling active stabilisation using nonequilibrium statistical operators

Zubarev’s non-equilibrium statistical operator approach underpinned much of this development; it represents a set of mathematical rules used to describe systems that aren’t perfectly balanced, akin to employing weather models for predicting changes over time. By first defining a ‘statistical operator’, the team represented everything known about the system’s state without detailed knowledge of every particle involved, creating an averaged picture than tracking individual components.

Extending this concept to situations *away* from perfect equilibrium allowed them to chart how the system evolves towards stability after being disturbed and reveal relaxation rates, quantifying how quickly things settle down. Focusing on scenarios with approximately conserved charges, they assumed weak charge violation alongside a clear distinction between rapid microscopic changes and slower overall system relaxation.

It relies upon several key assumptions including distinct timescales for microscopic correlations versus overall charge relaxation, resulting in a loss of ‘microscopic memory’. This enabled definition of change rates based solely on properties measured when the system reaches stability, offering an alternative calculation route compared to more complex kinetic methods.

Relaxation rates derived from static properties validate quantum system dynamics

A new approach demonstrated by scientists and Max Planck Institute determines relaxation rates using properties measured during stable conditions rather than tracking dynamic shifts. Previously establishing these rates required complex kinetic calculations, but this method links the rate of change to the diffusion of that same charge, yielding a ‘diffusion-relaxation equation’ applicable to scenarios like electroweak B+L washout and scalar models. The team validated their methodology through application to both electroweak B+L washout, a process concerning baryon asymmetry, and a scalar model.

Calculating relaxation rates relies on equilibrium correlation functions of the charge-violating operator, offering an alternative simpler than previous methods. Furthermore, they established a direct link between this rate and spatial charge diffusion, providing another tool for analysing these interactions.

Validating timescales within quantum charge dynamics through convergent methodologies

The calculations offer physicists new ways to determine how quickly approximate charges dissipate within quantum systems; this is important for modelling scenarios ranging from the very early universe to high-energy particle collisions. A key reliance remains upon simplifying assumptions regarding timescale separation, specifically, assuming a clear distinction exists between rapid microscopic changes and slower overall system relaxation. While acknowledging that these calculations underpin theoretical physics necessitates consideration of potential limitations, the timescale separation distinguishing quick internal changes and slower behaviour may not always hold perfectly true in complex physical scenarios. This work establishes two independent yet equivalent methods for calculating dissipation rates of approximately conserved charges within interacting quantum systems: one utilising established non-equilibrium statistical techniques and another based on observing temporal system evolution. Consequently, physicists gain increased flexibility when modelling complex scenarios where these charges decay slowly following disturbance, such as those found in cosmology or particle physics investigations of baryon asymmetry.

The researchers demonstrated a connection between the rate of charge relaxation and equilibrium diffusion within interacting quantum systems. This provides an alternative method to calculate how quickly approximate charges dissipate, which is relevant to understanding processes like baryon asymmetry after the Big Bang. They developed two equivalent calculation methods, one based on statistical techniques and another observing system evolution over time, offering physicists greater flexibility when modelling these complex interactions.

👉 More information
🗞 On the relaxation dynamics of non-equilibrium quantum systems
✍️ Matthias Carosi, Björn Garbrecht, Silvia Pla, Nils Wagner and Edward Wang
🧠 ArXiv: https://arxiv.org/abs/2609.17447

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