quantum spin models

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1: 32.16 Physical Applications

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Statistical Physics

►Statistical physics, especially classical and quantum spin models, has proved to be a major area for research problems in the modern theory of Painlevé transcendents. …

2: Bibliography S

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Quantum Chaos, Symmetry and Zeta Functions. Lecture I, Quantum Chaos. In Current Developments in Mathematics, 1997 (Cambridge, MA), R. Bott (Ed.), pp. 127–144.

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MathReview (Shin-ya Koyama), ZentralBlatt

Referenced by:

§25.17.

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Quantum defect theory. Rep. Prog. Phys. 46 (2), pp. 167–257.

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Document

Referenced by:

§33.14(i), §33.22(ii).

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Parabolic Cylinder Functions and their Application in Symmetric Two-centre Shell Model. In Proceedings of the Conference on Mathematical Analysis and its Applications (Inst. Engrs., Mysore, 1977), Matscience Rep., Vol. 91, Aarhus, pp. P81–P89.

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MathReview

Referenced by:

§12.17.

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Decoherent dynamics of a two-level system coupled to a sea of spins. Phys. Rev. Lett. 81 (26), pp. 5710–5713.

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Document

Referenced by:

§11.12.

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Some comments on Fourier analysis, uncertainty and modeling. SIAM Rev. 25 (3), pp. 379–393.

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ISSN 0036-1445, Document, MathReview (H. Vincent Poor), ZentralBlatt

Referenced by:

§30.15(ii), §30.15(iii), §30.15(iv), §30.15(v), §30.15(v).

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3: 31.17 Physical Applications

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§31.17(i) Addition of Three Quantum Spins

►The problem of adding three quantum spins $𝐬$, $𝐭$, and $𝐮$ can be solved by the method of separation of variables, and the solution is given in terms of a product of two Heun functions. We use vector notation $[𝐬,𝐭,𝐮]$ (respective scalar $(s,t,u)$) for any one of the three spin operators (respective spin values). … ►for the common eigenfunction $\mathrm{\Psi }(𝐱)=\mathrm{\Psi }(x_s,x_t,x_u)$, where $a$ is the coupling parameter of interacting spins. … ►For application of biconfluent Heun functions in a model of an equatorially trapped Rossby wave in a shear flow in the ocean or atmosphere see Boyd and Natarov (1998). …