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arXiv:quant-ph/9912050 · Nuclear Physics B - Proceedings Supplements

Quantization and time

A.A. Abrikosov, Ennio Gozzi

Published Jun 1, 2000• 8 citations
arXivHTMLPDF
DOI
10.1016/s0920-5632(00)00804-5

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Time of arrival (TOA) operators for anharmonic oscillator potential are obtained using Weyl, simple-symmetric, Born-Jordan quantization and supraquantization. The quantized TOA operators are compared to determine which is closest to the supraquantized TOA operator. The Wigner transform of the simple symmetric and Born-Jordan quantized diverge while the Weyl-quantized and the supraquantized vanish as the initial point, q, approaches the arrival point, implying that Weyl out of the three is the quantization that gives a TOA operator closest to the supraquantized TOA operator.
Measurements can be used to monitor the evolution of quantum systems and may lead to a universally quantized time statistics. It is known that the mean return time is quantized for strong and indirect monitoring through the winding number of the return amplitude in a one-dimensional space. Here we discuss that under multi-channel strong or indirect monitoring, where the latter is achieved through ancilla coupling, the mean return time of a quantum walk in the projected subspace is also quantized. This reflects a universal time quantization for a higher dimensional evolution.