کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10136829 | 1645692 | 2018 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Quantum Hall Effect and Langlands Program
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
فیزیک و نجوم
فیزیک و نجوم (عمومی)
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چکیده انگلیسی
Recent advances in the Langlands program shed light on a vast area of modern mathematics from an unconventional viewpoint, including number theory, gauge theory, representation, knot theory and etc. By applying to physics, these novel perspectives endow with a unified account of the (integer/ fractional) quantum Hall effect. The plateaus of the Hall conductance are described by Hecke eigensheaves of the geometric Langlands correspondence. Especially, the particle-vortex duality, which is explained by S-duality of Chern-Simons theory, corresponds to the Langlands duality in Wilson and Hecke operators. Moreover the Langlands duality in the quantum group associated with the Hamiltonian describes fractal energy spectrum structure, know as Hofstadter's butterfly. These results suggest that the Langlands program has many physically realistic meanings.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Physics - Volume 397, October 2018, Pages 136-150
Journal: Annals of Physics - Volume 397, October 2018, Pages 136-150
نویسندگان
Kazuki Ikeda,