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arXiv 0705.1649quant-ph
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作为与宏观外系统的终态相互作用的量子测量

Quantum Measurement as a Final-State Interaction with a Macroscopic External System

K. -E. Eriksson

摘要:

研究了一个小的量子散射系统(微系统)与一个由未知随机变量描述的大系统(宏系统)的相互作用。两个系统之间的相互作用是对角的微系统在一定的正交基,和相互作用给一个印记的宏观系统。此外,相互作用被认为只涉及两个系统之间的能量和动量的小转移(与微系统内的典型能量/动量相比)。在散射理论内进行分析。在传统的方法计算,整个系统的过渡振幅因式分解。发生在宏观系统内的相互作用被假定为依赖于随机变量,在这样的方式,平均而言,没有特定的基向量状态的微观系统是有利的。密度矩阵的形式化研究,其中包括产生的进入状态和吸收的最终状态。那么微系统的最终状态对常规散射振幅的依赖性是高度非线性的。在宏观系统的热力学极限中,系综(微观系统加宏观系统)的密度矩阵发展成一个最终状态,该最终状态涉及一组宏观上可区分的状态,每个状态中的微观系统处于基矢量状态之一,而宏观系统处于纠缠状态。对于集合的元素,即,对于单次测量,结果是随机游走,其中微系统以基矢量状态之一结束(波包的减小)。

英文摘要:

A small quantum scattering system (the microsystem) is studied in interaction with a large system (the macrosystem) described by unknown stochastic variables. The interaction between the two systems is diagonal for the microsystem in a certain orthonormal basis, and the interaction gives an imprint on the macrosystem. Moreover, the interaction is assumed to involve only small transfers of energy and momentum between the two systems (as compared to typical energies/momenta within the microsystem). The analysis is carried out within scattering theory. Calculated in the conventional way, the transition amplitude for the whole system factorizes. The interaction taking place within the macrosystem is assumed to depend on the stochastic variables in such a way that, on the average, no particular basis vector state of the microsystem is favoured. The density matrix is studied in a formalism which includes generation of the ingoing state and absorption of the final state. Then the dependence of the final state on the conventional scattering amplitude for the microsystem is highly non-linear. In the thermodynamic limit of the macrosystem, the density matrix of the ensemble (of microsystem plus macrosystem) develops into a final state which involves a set of macroscopically distinguishable states, each with the microsystem in one of the basis vector states and the macrosystem in an entangled state. For an element of the ensemble, i.e., for a single measurement, the result is instead a random walk, where the microsystem ends up in one of the basis vector states (reduction of the wave packet).

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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