Lam'e Instantons

Preprint English OPEN
Dunne, Gerald V.; Rao, Kumar;
(1999)
  • Identifiers: doi: 10.1088/1126-6708/2000/01/019
  • Subject: Condensed Matter | High Energy Physics - Phenomenology | High Energy Physics - Theory
    arxiv: High Energy Physics::Theory | High Energy Physics::Lattice

We perform a precise analytic test of the instanton approximation by comparing the exact band spectrum of the periodic Lam\'e potential to the tight-binding, instanton and WKB approximations. The instanton result gives the correct leading behavior in the semiclassical l... View more
  • References (13)
    13 references, page 1 of 2

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    [4] For a recent review see: T. Sch¨afer and E. Shuryak, “Instantons in QCD”, Rev. Mod. Phys. 70, 323 (1998).

    [5] Y. Alhassid, F. Gu¨rsey and F. Iachello, “Potential Scattering, Transfer Matrix, and Group Theory”, Phys. Rev. Lett. 50, 873 (1983).

    [6] H. Li and D. Kusnezov, “Group Theory Approach to Periodic Potentials and Transfer Matrices”, Yale preprint Nov. 1998.

    [7] E. Whittaker and G. Watson, A Course of Modern Analysis, (Cambridge, 1927); M. Abramowitz and I. Stegun (Eds.), Handbook of Mathematical Functions, (Dover, 1990).

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    [9] R. Peierls, Quantum Theory of Solids, (Oxford, 1955).

    [10] Here K′(ν) = K(1 − ν), E′(ν) = E(1 − ν), and E(ν) is the complete elliptic integral [7].

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