This expository review reformulates the BCS analyses of Haag, Emch--Guenin, and Thirring--Wehrl, together with subsequent operator-algebraic mean-field results of B\'ona, Raggio--Werner, and Bru--de Siqueira Pedra, in the language of quasi-local $C^{\ast}$-algebras and state decompositions. The quasi-spin model is realized on the UHF algebra of type $2^{\infty}$, with product sectors described by von Neumann's incomplete infinite tensor products. This framework distinguishes strong limits of intensive observables, domain-restricted limits of extensive observables, and sectorwise Bogoliubov--Haag limits, including their operator criterion, gap equation, and limiting dynamics. In the degenerate model, the ground-state and thermal gauge averages admit central direct-integral decompositions over the gauge circle, and the thermal decomposition converges to the ground-state decomposition at zero temperature. Adjoining the gauge phase as a central classical variable combines the phase-dependent Bogoliubov dynamics into one automorphism group on $C(\mathbb{S}^{1},\mathcal{A})$.
The para--Krawtchouk polynomials define, through their recurrence relation, a finite oscillator model that carries out fractional revival. We determine the continuum limit of this Hamiltonian, both from its recurrence relation and directly on the polynomials. The limit is the singular (isotonic) oscillator $-\partial_\...
Stéphane Z. Beaulac, Nicolas Cramp'e, Q. Labriet et al.· 2 citations
We introduce a magnetic coherent--state frame over the Landau levels of the two--dimensional Landau Hamiltonian, indexed by a discrete metric space combining spatial and energy degrees of freedom. Although overcomplete, the frame is almost--orthogonal, and we use it to endow the CAR $C^*$--algebra over the one--particl...
Using the language of q-opers, we propose an algebro-geometric description of the duality between Bethe Ansatz equations for quantum XXZ spin chains and many-body trigonometric Ruijsenaars-Schneider/Macdonald systems for classical groups. Upon this duality, the energy level sets of the classical B/C/D-type Hamiltonians...
P. Koroteev, Myungbo Shim, Rahul Singh· 0 citations
We integrate the Bondi--Sachs hierarchy of scalar--Gauss--Bonnet gravity with an arbitrary coupling function $f(\Phi)$ and a radiating massless scalar, and determine the first order in $1/r$ at which the coupling $\lambda$ becomes visible in each field equation. We obtain the asymptotic falloff of the effective Gauss--...
Maickol Muñoz-Palma, '. Restuccia, F. Tello-Ortiz· 0 citations
We prove Morita invariance of the Campbell--Lind--Malkiewich--Ponto--Zakharevich restriction-system trace after passage to perfect modules. It therefore defines an intrinsic integral restriction trace for an exact endofunctor of a small idempotent-complete stable $\infty$-category. On $\pi_0$, the $m$-th ghost is the l...
The para-Bannai--Ito polynomials are orthogonal on a Bannai--Ito bi-lattice that is \emph{two-sided} --- it extends on both sides of a central value $c_0$ --- and depend, besides the two grid parameters, on an isospectral deformation parameter. Their Jacobi matrix $J$ is invariant under the reversal of the sites at one...
Stéphane Z. Beaulac, Nicolas Cramp'e, Q. Labriet et al.· 2 citations
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