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branch quantum numbers", "math": [], "links": [] }, "dressing_and_entropy": { "markdown": "No thermodynamic dressing yet", "math": [], "links": [] }, "initial_state_input": { "markdown": "Boundary condition and symmetry sector", "math": [], "links": [] }, "euler_or_diffusive_observable": { "markdown": "Spectrum, energy, momentum, and form-factor input", "math": [], "links": [] }, "breaking_and_finite_size": { "markdown": "Exponential/string and algebraic $1/L$ corrections", "math": [ { "kind": "inlineMath", "tex": "1/L" } ], "links": [] }, "validation_test": { "markdown": "Exact diagonalization and state counting at several $L$", "math": [ { "kind": "inlineMath", "tex": "L" } ], "links": [] } } }, { "key": "root-density-macrostate", "row_id": "integrable-quantum-matter-generalized-hydrodynamics-claim-test-matrix--root-density-macrostate", "cells": { "description_or_claim": { "markdown": "Root-density macrostate", "math": [], "links": [] }, "quasiparticles_and_charges": { "markdown": "$\\rho_{\\mathrm p,a}$, $\\rho_{\\mathrm h,a}$ for every retained species", "math": [ { "kind": "inlineMath", "tex": "\\rho_{\\mathrm p,a}" }, { "kind": "inlineMath", "tex": "\\rho_{\\mathrm h,a}" } ], "links": [] }, "dressing_and_entropy": { "markdown": "$h^{\\mathrm{dr}}=h+Kn h^{\\mathrm{dr}}/(2\\pi)$; 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entropy production nonnegative", "math": [ { "kind": "inlineMath", "tex": "L=DC" } ], "links": [] }, "initial_state_input": { "markdown": "Smooth local macrostate and calibrated initial width", "math": [], "links": [] }, "euler_or_diffusive_observable": { "markdown": "$t^{1/2}$ broadening and Navier–Stokes currents", "math": [ { "kind": "inlineMath", "tex": "t^{1/2}" } ], "links": [] }, "breaking_and_finite_size": { "markdown": "Anomalous sector, free dispersion, finite time and resolution", "math": [], "links": [] }, "validation_test": { "markdown": "Positivity, null modes, exact limits, multi-time shared fit", "math": [], "links": [] } } }, { "key": "weakly-broken-integrability", "row_id": "integrable-quantum-matter-generalized-hydrodynamics-claim-test-matrix--weakly-broken-integrability", "cells": { "description_or_claim": { "markdown": "Weakly broken integrability", "math": [], "links": [] }, "quasiparticles_and_charges": { "markdown": "Nearly conserved charges plus exact residual charges", "math": [], "links": [] }, "dressing_and_entropy": { "markdown": "Slow-mode susceptibility and collision entropy", "math": [], "links": [] }, "initial_state_input": { "markdown": "Prepared prethermal macrostate", "math": [], "links": [] }, "euler_or_diffusive_observable": { "markdown": "Rate matrix or collision-corrected GHD", "math": [], "links": [] }, "breaking_and_finite_size": { "markdown": "Resonances, secular terms, rare processes, bath, heating", "math": [], "links": [] }, "validation_test": { "markdown": "$g$ scaling, size scaling, several modes and late times", "math": [ { "kind": "inlineMath", "tex": "g" } ], "links": [] } } }, { "key": "experimental-integrable-matter", "row_id": "integrable-quantum-matter-generalized-hydrodynamics-claim-test-matrix--experimental-integrable-matter", "cells": { "description_or_claim": { "markdown": "Experimental integrable matter", "math": [], "links": [] }, "quasiparticles_and_charges": { "markdown": "Platform-calibrated quasiparticle model and observable", "math": [], "links": [] }, "dressing_and_entropy": { "markdown": "Thermodynamic and hydrodynamic solver covariance", "math": [], "links": [] }, "initial_state_input": { "markdown": "Trap, temperature, interaction, preparation, transverse modes", "math": [], "links": [] }, "euler_or_diffusive_observable": { "markdown": "Convolved density, momentum, correlation, or current data", "math": [], "links": [] }, "breaking_and_finite_size": { "markdown": "Atom number, boundaries, loss, breaking, recurrence", "math": [], "links": [] }, "validation_test": { "markdown": "Independent calibration, held-out times, alternative model, exact cutoff", "math": [], "links": [] } } } ], "references": [ { "id": "ref-15f7aa28b90e5d94", "markdown": "Castro-Alvaredo, O. A., Doyon, B., and Yoshimura, T. (2016). “Emergent hydrodynamics in integrable quantum systems out of equilibrium.” *Physical Review X* **6**, 041065. [doi:10.1103/PhysRevX.6.041065](https://doi.org/10.1103/PhysRevX.6.041065).", "urls": [ "https://doi.org/10.1103/PhysRevX.6.041065" ] } ], "reference_scope": "The reference catalog reproduces the canonical chapter bibliography. Cell links are associated with references only when their resolved URL matches; uncited chapter references are not asserted as claim-specific support." }