کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5495973 | 1529830 | 2017 | 23 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Quadratic time dependent Hamiltonians and separation of variables
ترجمه فارسی عنوان
همدلیان وابسته به زمان کوبه ای و جداسازی متغیرها
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
فیزیک و نجوم
فیزیک و نجوم (عمومی)
چکیده انگلیسی
Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Physics - Volume 381, June 2017, Pages 90-106
Journal: Annals of Physics - Volume 381, June 2017, Pages 90-106
نویسندگان
A. Anzaldo-Meneses,