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Ground state energy scaling laws during the onset and destruction of the intermediate state in a type I superconductor
Author(s) -
Choksi Rustum,
Conti Sergio,
Kohn Robert V.,
Otto Felix
Publication year - 2008
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20206
Subject(s) - ground state , scaling , type (biology) , superconductivity , mathematics , upper and lower bounds , state (computer science) , energy (signal processing) , bound state , nonlinear system , matching (statistics) , magnetic field , scaling law , condensed matter physics , mathematical physics , statistical physics , physics , mathematical analysis , quantum mechanics , geometry , geology , algorithm , statistics , paleontology
Abstract The intermediate state of a type I superconductor is a classical example of energy‐driven pattern formation, first studied by Landau in 1937. Three of us recently derived five different rigorous upper bounds for the ground‐state energy, corresponding to different microstructural patterns, but only one of them was complemented by a lower bound with the same scaling [Choksi, Kohn, and Otto, J. Nonlinear Sci. 14 (2004), 119–171]. This paper completes the picture by providing matching lower bounds for the remaining four regimes, thereby proving that exactly those five different regimes are traversed with an increasing magnetic field. © 2007 Wiley Periodicals, Inc.