کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1901186 | 1045623 | 2008 | 26 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Self-adjoint time operators and invariant subspaces
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
The question of existence of self-adjoint time operators for unitary evolutions in classical and quantum mechanics is revisited on the basis of Halmos-Helson theory of invariant subspaces, Sz.-Nagy-FoiaÅ dilation theory and Misra-Prigogine-Courbage theory of irreversibility. It is shown that the existence of self-adjoint time operators is equivalent to the intertwining property of the evolution plus the existence of simply invariant subspaces or rigid operator-valued functions for its Sz.-Nagy-FoiaÅ functional model. Similar equivalent conditions are given in terms of intrinsic randomness in the context of statistical mechanics. The rest of the contents are mainly a unifying review of the subject scattered throughout an unconnected literature. A well-known extensive set of equivalent conditions is derived from the above results; such conditions are written in terms of Schrrdinger couples, the Weyl commutation relation, incoming and outgoing subspaces, innovation processes, Lax-Phillips scattering, translation and spectral representations, and spectral properties. Also the natural procedure dealing with symmetric time operators in standard quantum mechanics involving their self-adjoint extensions is illustrated by considering the quantum Aharonov-Bohm time-of-arrival operator.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Reports on Mathematical Physics - Volume 61, Issue 1, February 2008, Pages 123-148
Journal: Reports on Mathematical Physics - Volume 61, Issue 1, February 2008, Pages 123-148
نویسندگان
Fernando Gómez,