期刊
ANNALS OF PHYSICS
卷 323, 期 11, 页码 2779-2798出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2008.02.002
关键词
Bogoliubov coefficients; Transmission coefficient; Reflection coefficient; Rigorous bounds
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 amplification and the related quantum phenomenon of particle production (as encoded in the Bogoliubov coefficients), or bounds on transmission and reflection coefficients. Modifying and streamlining an approach developed by one of the present authors [M. Visser, Phys. Rev. A 59 (1999) 427-438, arXiv:quant-ph/9901030], we investigate this question by developing a formal but excat solution for the appropriate second-order linear ODE in terms of a time-ordered exponential of 2 x 2 matrices, then relating the Bogoliubov coefficients to certain invariants of this matrix. By bounding the matrix in an appropriate manner, we can thereby bound the Bogoliubov coefficients. (C) 2008 Elsevier Inc. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据