Convergence of spectra of mesoscopic systems collapsing onto a graph uri icon

abstract

  • Let M be a finite graph in the plane and let M be a domain that looks like the -fattened graph M (exact conditions on the domain are given). It is shown that the spectrum of the Neumann Laplacian on M converges when 0 to the spectrum of an ODE problem on M. The presence of an electromagnetic field is also allowed. Considerations of this kind arise naturally in mesoscopic physics and other areas of physics and chemistry. The results of the paper extend the ones previously obtained by J. Rubinstein and M. Schatzman. 2001 Academic Press.

published proceedings

  • JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

author list (cited authors)

  • Kuchment, P., & Zeng, H. B.

citation count

  • 97

complete list of authors

  • Kuchment, P||Zeng, HB

publication date

  • June 2001