Anomalous Slow Relaxation of Local Observables in Diffusive Quantum Systems

Item: Anomalous Slow Relaxation of Local Observables in Diffusive Quantum Systems
Rating: 4
Author: PostSingularity Institute

by Ewan R. McCulloch

Formal & Physical Sciences Physics PHPhysics PHSStatistical physics

🎙 Ewan R. McCulloch 👥 74K 📅 December 30, 2025 ⏱ 50 min 👁 446 📄 original study 🧭 2026-08-16

Available in: English (current) Français

Keywords

thermalizationhydrodynamic projectionrandom unitary circuitsstretched exponentialdiffusive transport

Summary

The talk addresses the relaxation of local observables in diffusive quantum systems with a conserved U(1) charge. The speaker begins by contrasting systems without conservation laws, where two-point functions decay exponentially due to operator spreading, with systems with conservation laws, where hydrodynamic modes lead to power-law decay. He introduces the concept of hydrodynamic projection to separate slow and fast operators. The main focus is on non-hydrodynamic operators, such as charge-raising operators, which are expected to decay exponentially but instead exhibit stretched exponential decay. Using random unitary circuits with U(1) symmetry, he shows that the decay exponent is 1/2, arising from rare events where the operator is shielded by a void in the background charge. He then considers translation-invariant Floquet systems, where isolated charges move ballistically, leading to a divergent diffusion constant at low densities. A toy model based on a single magnon in a void, with damping proportional to local density, yields a stretched exponential decay with exponent 2/3. The talk concludes with a schematic calculation and emphasizes the role of rare hydrodynamic events in quantum thermalization.

177 words

Critical Evaluation

Value of the Information & Strength of the Argument

The talk provides a novel and insightful explanation for the slow relaxation of non-hydrodynamic operators in diffusive quantum systems. The argumentation is logically structured, starting from known results and building up to the main findings. The use of random unitary circuits as a tractable model and the subsequent extension to more realistic Floquet systems demonstrates a systematic approach. The speaker supports his claims with numerical simulations and analytical arguments, though some steps rely on approximations and toy models. The discussion of voids and rare events is particularly compelling and provides a clear physical picture. The presentation is dense but well-organized, making it valuable for researchers in the field.

Scientific Rigor, Source Quality, Title Accuracy

The talk is scientifically rigorous, with careful attention to limits and assumptions. The speaker references relevant prior work, such as the eigenstate thermalization hypothesis, hydrodynamic projection, and studies on diffusion in low-density systems. The sources cited are appropriate and credible. The title accurately reflects the content, focusing on anomalous slow relaxation in diffusive quantum systems. The presentation is part of a specialized workshop, indicating peer recognition. The speaker does not overstate conclusions and acknowledges open questions, such as the precise definition of hydrodynamic projection. Overall, the scientific quality is high.

213 words

Title / Content Match

The title accurately reflects the content, focusing on anomalous slow relaxation in diffusive quantum systems.

Quality & Reliability

8/10

The talk presents original research with a clear theoretical framework, supported by numerical simulations and references to established concepts. The argumentation is rigorous, though some steps rely on approximations and toy models. The speaker is an expert in the field, and the presentation is part of a specialized workshop.

Key Moments

Markers derived by PSI from the transcript: the creator did not define chapters.

Cited Sources

Program: Hydrodynamics, Fluctuations, and Noise in quantum and classical systems — Workshop program page, providing context for the talk

Concurring Sources

Eigenstate thermalization hypothesis — Supports the framework of thermalization discussed in the talk.
Generalized hydrodynamics — Related to hydrodynamic projection and slow modes.

Contribution & Novelties

The talk presents original research on the relaxation of non-hydrodynamic operators in diffusive quantum systems, showing that they decay as stretched exponentials rather than simple exponentials. The key insight is the role of rare hydrodynamic events, such as voids, in shielding the operator from interactions. This provides a new understanding of thermalization in systems with conservation laws.

Pour aller plus loin :

Eigenstate thermalization hypothesis — Foundational concept for understanding thermalization in isolated quantum systems.
Generalized hydrodynamics — Framework for integrable systems, relevant to hydrodynamic projection.
Macroscopic fluctuation theory — Theory for fluctuations in diffusive systems, related to rare events.
Random unitary circuits — Reference for random circuit models and their statistical mechanics description.
Diffusion in low-density gases — Background on diffusion and divergent diffusion constants at low densities.

129 words

Radar Profile

The radar profile shows high scores in information quantity, quality, technical level, and reliability, indicating a dense and rigorous presentation. The talk is highly technical and well-supported, with a strong focus on theoretical and numerical methods.

Reliability 8/10