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arXiv quant-ph/0512198quant-ph
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耗散原子系统中的Bohm-Aharonov型效应

Bohm-Aharonov type effects in dissipative atomic systems

Allan I. Solomon, Sonia G. Schirmer

摘要:

量子力学中的一个态被定义为范数为1的正算符。对于有限系统,这可以被认为是迹1的正矩阵。这种积极性的约束对这种状态的允许演化施加了严格的限制。从数学的角度来看,我们描述了两种形式的标准动力学方程-全球(克劳斯)和本地(Lindblad)-并显示如何每个这些引起了一个半组描述的演变。然后,我们看看原子系统的具体例子,为简单起见,涉及3能级系统,并显示这些数学约束如何引起非直观的物理现象,让人想起Bohm-Aharonov效应。特别是,我们表明,对于一个多能级原子系统,它通常是不可能的隔离的水平,这将导致可观察到的效果的人口弛豫和退相干。

英文摘要:

A state in quantum mechanics is defined as a positive operator of norm 1. For finite systems, this may be thought of as a positive matrix of trace 1. This constraint of positivity imposes severe restrictions on the allowed evolution of such a state. From the mathematical viewpoint, we describe the two forms of standard dynamical equations - global (Kraus) and local (Lindblad) - and show how each of these gives rise to a semi-group description of the evolution. We then look at specific examples from atomic systems, involving 3-level systems for simplicity, and show how these mathematical constraints give rise to non-intuitive physical phenomena, reminiscent of Bohm-Aharonov effects. In particular, we show that for a multi-level atomic system it is generally impossible to isolate the levels, and this leads to observable effects on the population relaxation and decoherence.

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