منابع مشابه
Bounding the Bogoliubov coefficients
While over the last century or more considerable effort has been put into the problem of finding approximate solutions for wave equations in general, and quantum mechanical problems in particular, it appears that as yet relatively little work seems to have been put into the complementary problem of establishing rigourous bounds on the exact solutions. We have in mind either bounds on parametric...
متن کاملOn vacuum-vacuum amplitude and Bogoliubov coefficients
Even if the electromagnetic field does not create pairs, virtual pairs lead to the appearance of a phase in vacuum-vacuum amplitude. This makes it necessary to distinguish the inand out-solutions even when it is commonly assumed that there is only one complete set of solutions as, for example, in the case of a constant magnetic field. Then inand out-solutions differ only by a phase factor which...
متن کاملar X iv : 0 80 1 . 06 10 v 1 [ qu an t - ph ] 3 J an 2 00 8 Bounding the Bogoliubov coefficients
While over the last century or more considerable effort has been put into the problem of finding approximate solutions for wave equations in general, and quantum mechanical problems in particular, it appears that as yet relatively little work seems to have been put into the complementary problem of establishing rigourous bounds on the exact solutions. We have in mind either bounds on parametric...
متن کاملBounding the coefficients of the characteristic polynomials of simple binary matroids
We give an upper bound and a class of lower bounds on the coefficients of the characteristic polynomial of a simple binary matroid. This generalizes the corresponding bounds for graphic matroids of Li and Tian (1978) [3], as well as a matroid lower bound of Björner (1980) [1] for simple binary matroids. As the flow polynomial of a graph G is the characteristic polynomial of the dual matroid M(G...
متن کاملOn the significance of reflection coefficients produced by active surfaces bounding one-dimensional sound fields.
Active boundary surfaces intended to control reverberation or other characteristics of enclosed sound fields have often been investigated using plane wave tubes. This paper presents an analysis of actively terminated semi-infinite and finite-length plane wave tubes to provide needed clarification of the effects of these surfaces. By considering relationships between complex pressure-amplitude r...
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ژورنال
عنوان ژورنال: Annals of Physics
سال: 2008
ISSN: 0003-4916
DOI: 10.1016/j.aop.2008.02.002