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The periodic Dirac operator is absolutely continuous

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Abstract

We consider the periodic Dirac operatorD inL 2(ℝd). The magnetic potentialA and the electric potentialV are periodic. Ford=2 the absolute continuity ofD is established forA,V∈L r, loc ,r>2; the proof is based on the estimates, obtained by the authors earlier [BSu2] for the periodic magnetic Schrödinger operatorM. Ford≥3 our considerations are based on the estimates forM, obtained in [So] forA∈C 2d+3. Under the same condition onA, forV∈C, the absolute continuity ofD, d≥3, is proved. ForA=0 the arguments of the paper give a new (and much simpler) proof of the main result of [D].

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References

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Authors and Affiliations

  1. Department of Physics, St. Petersburg State University, Petrodvorets, Ul'yanovskaya, 1, 198904, St. Petersburg, RUSSIA

    M. Sh. Birman & T. A. Suslina

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  1. M. Sh. Birman
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  2. T. A. Suslina
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The research was completed in the framework of the project INTAS-93-351.

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Birman, M.S., Suslina, T.A. The periodic Dirac operator is absolutely continuous. Integr equ oper theory 34, 377–395 (1999). https://doi.org/10.1007/BF01272881

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  • DOI: https://doi.org/10.1007/BF01272881

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