Diffusion in generalized hydrodynamics and quasiparticle scattering
By J. Nardis, D. Bernard, B. Doyon. SciPost Physics, 2018
155 citations recorded by the source corpus.
We extend beyond the Euler scales the hydrodynamic theory for quantum and classical integrable models developed in recent years, accounting for diffusive dynamics and local entropy production. We review how the diffusive scale can be reached via a gradient expansion of the expectation values of the conserved fields and how the coefficients of the expansion can be computed via integrated steady-state two-point correlation functions, emphasising that {\mathcal PT}𝒫T-symmetry can fully fix the inherent ambiguity in the definition of conserved fields at the diffusive scale. We develop a form factor expansion to compute such correlation functions and we show that, while the dynamics at the Euler scale is completely determined by the density of single quasiparticle excitations on top of the local steady state, diffusion is due to scattering processes among quasiparticles, which are only present in truly interacting systems. We then show that only two-quasiparticle scattering processes contribute to the diffusive dynamics. Finally we employ the theory to compute the exact spin diffusion constant of a gapped XXZ spin-1/2−1/2 chain at finite temperature and half-filling, where we show that spin transport is purely diffusive.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/a85b77d9c45572d19c29b2dfa1d88374da378b46
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In Atomic and Molecular Physics, and Optics
- S. Gopalakrishnan
- B. Doyon
- E. Altman
- D. Parker
- Xiangyu Cao
- Austen Lamacraft
- Thomas Scaffidi
- V. Khemani
Citations in the corpus
- Unitary circuits of finite depth and infinite width from quantum channels (2019, background): “[39] Jacopo De Nardis, Denis Bernard, and Benjamin Doyon, “Diffusion in generalized hydrodynamics and quasiparticle scattering,” arXiv preprint arXiv:1812.”
- Lecture notes on Generalised Hydrodynamics (2019, methodology): “See [86].”
- A Universal Operator Growth Hypothesis (2018, background): “Even in integrable models, determining if the correct hydrodynamics is, say, diffusion or anomalous diffusion is non-trivial — let alone computing diffusion coefficients (see Refs [74–79] for recent developments).”