Geodesic
Impact of surface defects on a condensate of electron pairs in a quantum wire
Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 2, pp. 300-310 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the impact of surface defects on a condensate of electron pairs in a quantum wire. Based on previous results, we formulate a simple mathematical model accounting for such surface effects. For a system of noninteracting pairs, we prove the destruction of the condensate in the bulk. Finally, taking repulsive interactions between the pairs into account, we show that the condensate is recovered for pair densities greater than a critical density if the number of the surface defects is not too large.
Mots-clés : condensation
Keywords: electron pair, surface defect. 
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J. Kerner. Impact of surface defects on a condensate of electron pairs in a quantum wire. Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 2, pp. 300-310. http://geodesic.mathdoc.fr/item/TMF_2020_203_2_a9/

[1] J. Kerner, “On pairs of interacting electrons in a quantum wire”, J. Math. Phys., 59:6 (2018), 063504, 6 pp., arXiv: 1801.00696 | DOI | MR

[2] J. Kerner, “On bound electron pairs on the half-line”, Rep. Math. Phys., 83:1 (2019), 129–138 | DOI | MR

[3] P. G. de Gennes, “Boundary effects in superconductors”, Rev. Modern Phys., 36:1 (1964), 225–237 | DOI

[4] S. T. Sekula, J. H. Barrett, “Surface effects and low frequency losses in hard superconductors”, Appl. Phys. Lett., 17:5 (1970), 204–205 | DOI

[5] L. Burlachkov, A. E. Koshelev, V. M. Vinokur, “Transport properties of high-temperature superconductors: Surface vs bulk effect”, Phys. Rev. B, 54:9 (1996), 6750–6757 | DOI

[6] S. Kashiwaya, Y. Tanaka, “Tunnelling effects on surface bound states in unconventional superconductors”, Rep. Progr. Phys., 63:10 (2000), 1641–1724 | DOI

[7] L. V. Belevtsov, “Interplay between surface effects and the magnetic properties in polycrystalline superconductors”, J. Low Temperature Phys., 131:1–2 (2003), 37–49 | DOI

[8] A. V. Narlikar, The Oxford Handbook of Small Superconductors, Oxford Univ. Press, Oxford, 2017

[9] S. Alexander, “Superconductivity of networks. A percolation approach to the effects of disorder”, Phys. Rev. B, 27:3 (1983), 1541–1557 | DOI | MR

[10] F. R. K. Chung, Spectral Graph Theory, CBMS Regional Conference Series in Mathematics, 92, AMS, Providence, RI, 1997 | MR

[11] F. Schwabl, Statistical Mechanics, Springer, Berlin, 2006 | MR

[12] A. Verbeure, Many-Body Boson Systems. Half a Century Later, Theoretical and Mathematical Physics, Springer, London, 2011 | DOI | MR

[13] D. Ryuel, Statisticheskaya mekhanika. Strogie rezultaty, Mir, M., 1971 | MR

[14] P. A. Martin, F. Rothen, Many-Body Problems and Quantum Field Theory, Texts and Monographs in Physics, Springer, Berlin, 2004 | DOI | MR

[15] J. Blank, P. Exner, M. Havliček, Hilbert Space Operators in Quantum Physics, Springer, Berlin, 2008 | DOI | Zbl

[16] T. Michoel, A. Verbeure, “Non-extensive Bose–Einstein condensation model”, J. Math. Phys., 40:3 (1999), 1268–1279 | DOI | MR

[17] L. J. Landau, I. F. Wilde, “On the Bose–Einstein condensation of an ideal gas”, Commun. Math. Phys., 70:1 (1979), 43–51 | DOI | MR