Bohm-Aharonov type effects in dissipative atomic systems
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.
引用
@article{arxiv.quant-ph/0512198,
title = {Bohm-Aharonov type effects in dissipative atomic systems},
author = {Allan I. Solomon and Sonia G. Schirmer},
journal= {arXiv preprint arXiv:quant-ph/0512198},
year = {2007}
}
备注
9 pages, 4 references. Presented at the 23rd International Conference on Differential Geometric Methods in Theoretical Physics,August 20-26, Nankai Institute of Mathematics, Tianjin, China