Geodesic
Isolated solutions of a local polaron model
Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 3, pp. 399-404 Cet article a éte moissonné depuis la source Math-Net.Ru

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A simple local polaron model is studied. The Schrödinger equation for the model in the holomorphic representation is reduced to the system of the first order differential equations. The eigen-values are determined from the condition that the solution belongs to the class of holomorphic functions. In the general case, the eigen-values are found from a certain transcendental equation including continuous fraction. On the basis of the general theory of differential equations algebraic equations are obtained for the eigen-vectors of the simplest isolated solutions. Possibility of intersection of eigenvalues in isolated points is demonstrated. Impossibility of phase transition for the simple local polaron model is rigorously proved. 
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     author = {A. I. Volokitin},
     title = {Isolated solutions of~a~local polaron model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {399--404},
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     number = {3},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1989_80_3_a7/}
}
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A. I. Volokitin. Isolated solutions of a local polaron model. Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 3, pp. 399-404. http://geodesic.mathdoc.fr/item/TMF_1989_80_3_a7/

[1] Khomskii D. I., Sol. State Commun., 27:8 (1978), 775–779 | DOI

[2] Hewson A. C., Newns D. M., J. Phys.: Sol. State Phys., C12:9 (1979), 1665–1683 | DOI

[3] Braun O. M., Volokitin A. I., FTT, 23:12 (1981), 3530–3534 | MR

[4] Braun O. M., Volokitin A. I., FTT, 25:1 (1983), 309–311

[5] Braun O. M., Volokitin A. I., Surf. Sci., 131:1 (1983), 148–158 | DOI

[6] Kravtsov V. E., Malshukov A. G., ZhETF, 75:3 (1978), 691–704 | MR

[7] Haldane F. D. M., Phys. Rev., B15:5 (1977), 2477–2484 | DOI

[8] Schmickler W., Chem. Phys. Lett., 115:2 (1985), 216–220 | DOI

[9] Hameline A., Lipkowski J., J. Electroanal. Chem., 171:2 (1984), 317–330 | DOI

[10] Reik H. G., Nusser H., Amarante Ribeiro L. A., J. Phys.: Math. Gen., A15:11 (1982), 3491–3507 | DOI | MR

[11] Reik H. G., Kaspar F., Z. Phys.: Condensed Matter, B51:1 (1983), 77–83 | DOI