Bibliography

This bibliography brings together the sources used in the open Toda sequence, the XXX spin-chain sequence, the KdV soliton sequence, finite-ring TASEP, and the singular Bethe-root case study, including their Library derivations and Reference pages. It is a focused reading list that grows with the authored material.

Sources for the learning sequences

Use each article’s claim-adjacent citation for the particular theorem, equation or convention being used. The entries below identify the editions and useful starting locations. Printed page numbers can differ from a PDF viewer’s page counter.

The on-site search finds these works by title or author. Download the complete bibliography as BibTeX, the Toda sources, the XXX course sources, the KdV sources, the TASEP sources, or the singular Bethe-root sources for a reference manager. Citation metadata and the displayed entries come from the same source records.

For Toda, use Moser for the finite open model and its spectral description, Torrielli for the distinction between Lax invariants and Hamiltonian integrability, Hairer for the numerical method, and Bloch–Karp for the QR representation. For the XXX chain, use Karbach–Müller for the coordinate Bethe construction and Faddeev for commuting transfer matrices. The lessons provide their own derivations; following a citation is not a substitute for the assigned calculations.

For finite spin correlations, Caux supplies the matrix-element and Lehmann-series framework. His stated ground-state expectation is distinguished from the site’s explicitly derived five-site excited-state example. The local calculation verifies its complete final sector and sum rules; it does not establish general Bethe completeness or a thermodynamic limit.

For KdV, use Lax for travelling waves, conservation and the operator construction; Grunert–Teschl for the precise spectral normalization; Aktosun for the Marchenko equation; and Kassam–Trefethen for the integrating-factor numerical method. The KdV pages state the field-sign and normalization conversions before using these sources.

For the singular XXX example, Nepomechie–Wang 2013 explains the regulated Bethe vector and its normalization; their 2014 paper derives the physical-solution condition with a twist. The case study uses exact PDF editions and reproduces finite examples. Its two-paper reading scope is not an exhaustive review of subsequent work on completeness.

For TASEP, Golinelli–Mallick 2004 specifies the periodic process and coordinate Bethe equations; their 2006 review explains generator conventions and the local operators. The site derives the finite stationary current and six-state example directly. Hoeffding supplies the laboratory’s bounded sampling-error inequality; Wilson is the source for score-interval attribution, with the interval formula derived on the laboratory page. These readings do not supply a general completeness proof for the selected eigenmode.

For the Hamiltonian preparation and oscillator, use Torrielli’s elementary calculations alongside Cannas da Silva’s precise symplectic formulation. Zung supplies the local action–angle proof used in the Liouville–Arnold reference. The pages explain the different symplectic signs, angle periods and action-cycle orientations before comparing formulas.

For the quartic action–angle calculation, NIST DLMF supplies the beta integral and gamma recurrence. The lesson derives the action, period and frequency from the Hamiltonian, including the energy scaling and angle branches; the special-function reference only evaluates the resulting definite integrals.

For the pendulum theorem-application lesson, DLMF Chapter 19 fixes the elliptic-integral modulus and the logarithmic limit near the separatrix. The lesson derives the period prefactors and checks the energy-level topology against Cannas da Silva’s theorem hypotheses.

For the linear algebra bridge, Preskill’s July 2015 chapter fixes the complex inner product, adjoint, tensor-product action and Pauli conventions. The bridge derives its finite matrices and sector checks directly; it does not use the chapter’s density-matrix formalism.

For differential equations and phase portraits, Teschl supplies the local existence and uniqueness theorem and the distinction between a solution’s maximal interval and all-time existence. The bridge derives and checks its elementary trajectories. Its page locators refer to the author’s preliminary PDF, whose preface is dated April 2012.