کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8896579 | 1630586 | 2018 | 39 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the derivation of the Hartree equation from the N-body Schrödinger equation: Uniformity in the Planck constant
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In this paper the Hartree equation is derived from the N-body Schrödinger equation in the mean-field limit, with convergence rate estimates that are uniform in the Planck constant ħ. Specifically, we consider the two following cases: (a) Töplitz initial data and Lipschitz interaction forces, and (b) analytic initial data and interaction potential, over short time intervals independent of ħ. The convergence rates in these two cases are 1/logâ¡logâ¡N and 1/N respectively. The treatment of the second case is entirely self-contained and all the constants appearing in the final estimate are explicit. It provides a derivation of the Vlasov equation from the N-body classical dynamics using BBGKY hierarchies instead of empirical measures.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 275, Issue 7, 1 October 2018, Pages 1603-1649
Journal: Journal of Functional Analysis - Volume 275, Issue 7, 1 October 2018, Pages 1603-1649
نویسندگان
François Golse, Thierry Paul, Mario Pulvirenti,