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arXiv quant-ph/0303121quant-ph
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量子测量和量子概率的热力学方法

A thermodynamic approach to quantum measurement and quantum probability

Blagowest Nikolov

摘要:

本文提出了一个简单的量子粒子模型,其中粒子在{ \it宏观}静止坐标系中用{ \it微观d}维振子表示,{ \it s=(d-1)/2}是粒子的自旋.状态向量简单地由坐标和动量的复杂组合来定义。证明了系统的观测量是厄米特形式(唯一对应于厄米矩阵)。量子测量将制备后获得的平衡态转换为一族平衡态,这些平衡态对应于所测量的可观测值的临界值,这些临界值表现为与可观测值相关联的随机量的值。我们的主要假设是:i)在测量过程中,被测的可观测量趋于最小,ii)与某个状态下的可观测量相关的每个随机量的平均值与同一状态下对应的可观测量的值成比例。这使得可以以非常简单的方式获得玻恩规则。

英文摘要:

A simple model of quantum particle is proposed in which the particle in a {\it macroscopic} rest frame is represented by a {\it microscopic d}-dimensional oscillator, {\it s=(d-1)/2} being the spin of the particle. The state vectors are defined simply by complex combinations of coordinates and momenta. It is argued that the observables of the system are Hermitian forms (corresponding uniquely to Hermitian matrices). Quantum measurements transforms the equilibrium state obtained after preparation into a family of equilibrium states corresponding to the critical values of the measured observable appearing as values of a random quantity associated with the observable. Our main assumptions state that: i) in the process of measurement the measured observable tends to minimum, and ii) the mean value of every random quantity associated with an observable in some state is proportional to the value of the corresponding observable at the same state. This allows to obtain in a very simple manner the Born rule.

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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