کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9518069 | 1345518 | 2005 | 40 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Compactness in the â¯-Neumann problem, magnetic Schrödinger operators, and the Aharonov-Bohm effect
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Compactness in the â¯-Neumann problem, magnetic Schrödinger operators, and the Aharonov-Bohm effect Compactness in the â¯-Neumann problem, magnetic Schrödinger operators, and the Aharonov-Bohm effect](/preview/png/9518069.png)
چکیده انگلیسی
The analyses of compactness and condition (P) boil down to the asymptotic behavior of the lowest eigenvalues of two related sequences of Schrödinger operators, one with a magnetic field and one without, parametrized by a Fourier variable resulting from the Hartogs symmetry. The nonsmooth example is based on the Aharonov-Bohm phenomenon of quantum physics. For smooth domains not satisfying (P), we prove that there always exists an exceptional sequence of Fourier variables for which the Aharonov-Bohm effect is weak and thence that compactness fails to hold. This sequence can be very sparse, so that the lack of compactness is due to a rather subtle effect.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 197, Issue 1, 20 October 2005, Pages 1-40
Journal: Advances in Mathematics - Volume 197, Issue 1, 20 October 2005, Pages 1-40
نویسندگان
Michael Christ, Siqi Fu,