کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5772177 | 1413350 | 2017 | 84 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Quantum ergodicity and symmetry reduction
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We study the spectral and ergodic properties of Schrödinger operators on a compact connected Riemannian manifold M without boundary in case that the examined system possesses certain symmetries. More precisely, if M carries an isometric and effective action of a compact connected Lie group G, we prove a generalized equivariant version of the semiclassical Weyl law with an estimate for the remainder, using a semiclassical functional calculus for h-dependent functions and relying on recent results on singular equivariant asymptotics. We then deduce an equivariant quantum ergodicity theorem under the assumption that the symmetry-reduced Hamiltonian flow on the principal stratum of the singular symplectic reduction of M is ergodic. In particular, we obtain an equivariant version of the Shnirelman-Zelditch-Colin-de-Verdière theorem, as well as a representation theoretic equidistribution theorem. If M/G is an orbifold, similar results were recently obtained by Kordyukov. When G is trivial, one recovers the classical results.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 273, Issue 1, 1 July 2017, Pages 41-124
Journal: Journal of Functional Analysis - Volume 273, Issue 1, 1 July 2017, Pages 41-124
نویسندگان
Benjamin Küster, Pablo Ramacher,