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Rigorous Bound on Hydrodynamic Diffusion for Chaotic Open Spin Chains
Dimitrios Ampelogiannis1, Benjamin Doyon1
1Department of Mathematics, King's College London, Strand, London, WC2R 2LS UK.
Journal of Statistical Physics
|July 23, 2026
Summary
Researchers established a lower bound for spin diffusion in chaotic quantum spin chains using Lindbladian evolution. This bound is positive only if quantum jumps transport spin, revealing a new mechanism for diffusion in many-body systems.
Area of Science:
- Quantum physics
- Condensed matter physics
- Mathematical physics
Background:
- Diffusion is a fundamental phenomenon in many-body chaotic systems.
- Rigorously proving diffusive behavior of correlation functions, like spin, is a major challenge in mathematical physics.
Purpose of the Study:
- To establish a rigorous lower bound for spin diffusion in open quantum spin chains.
- To investigate the role of quantum jumps and irreversibility in spin diffusion.
Main Methods:
- Utilizing Lindbladian evolution for a quantum spin-1/2 chain.
- Applying the Green-Kubo formula and projection techniques.
- Establishing correlation decay bounds.
Main Results:
- A strictly positive lower bound on spin diffusion is established for chaotic, translation-invariant, nearest-neighbor open quantum spin-1/2 chains.
- The bound is positive if and only if local quantum jumps transport spin.
- An additional contribution to spin diffusion strength due to irreversibility was identified and shown to vanish for reversible dynamics.
Conclusions:
- The study provides the first rigorous lower bound on spin diffusion in this class of systems.
- The findings highlight the importance of quantum jumps and macroscopic fluctuations in spin transport.
- The methods are extendable to various quantum systems, including quantum circuits.
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