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arXiv quant-ph/9906022quant-phcond-mat.stat-mechhep-th
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量子退相干与大时间指数行为的高阶修正

Quantum Decoherence and Higher Order Corrections to the Large Time Exponential Behaviour

I. Ya. Aref'eva, I. V. Volovich

摘要:

在量子理论中,存在着描述演化算符矩阵元大时间行为的著名近似表达式:<U(t)>=exp(at)+.这个表达式在考虑量子退相干、辐射、衰变、散射理论、随机极限、主方程和动力学方程的推导等问题中起着至关重要的作用。这个表达式是在Weisskopf-Wigner近似和van Hove(随机)极限下得到的。我们导出了包含对上述近似表达式的高阶修正的精确通式:<U(t)>=exp(At+B+C(t))。常数A和B以及振荡函数C(t)是用微扰理论计算的。采用谱和重整化波算符的微扰方法。该公式对统计物理和量子场论中使用的一般类哈密顿量都是有效的。

英文摘要:

There exists the well known approximate expression describing the large time behaviour of matrix elements of the evolution operator in quantum theory: <U(t)>=exp(at)+... This expression plays the crucial role in considerations of problems of quantum decoherence, radiation, decay, scattering theory, stochastic limit, derivation of master and kinetic equations etc. This expression was obtained in the Weisskopf-Wigner approximation and in the van Hove (stochastic) limit. We derive the exact general formula which includes the higher order corrections to the above approximate expression: <U(t)>=exp(At+B+C(t)). The constants A and B and the oscillating function C(t) are computed in perturbation theory. The method of perturbation of spectra and renormalized wave operators is used. The formula is valid for a general class of Hamiltonians used in statistical physics and quantum field theory.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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