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Schrödinger Maps and Anti-Ferromagnetic Chains

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Abstract

We study the problem of restricting Schrödinger maps onto Lagrangian submanifolds. The restriction is imposed by an infinite constraining potential. We show that, in the limit, solutions of the Schrödinger map equations converge to solutions of generalized wave map equations. This result is applied to the anti-ferromagnetic systems where we prove rigorously that the dynamics is governed by wave map equations into .

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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY, 10012, USA

    Jalal Shatah

  2. Department of Mathematics, University of Virginia, Charlottesville, VA, 22904, USA

    Chongchun Zeng

Authors
  1. Jalal Shatah
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  2. Chongchun Zeng
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Corresponding author

Correspondence to Jalal Shatah.

Additional information

Communicated by P. Constantin

The first author is funded in part by NSF DMS 0203485.

The second author is funded in part by NSF DMS 0101969 and DMS 0239389.

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Shatah, J., Zeng, C. Schrödinger Maps and Anti-Ferromagnetic Chains. Commun. Math. Phys. 262, 299–315 (2006). https://doi.org/10.1007/s00220-005-1490-7

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  • DOI: https://doi.org/10.1007/s00220-005-1490-7

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