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Quantum Simulation

Quantum localisation on the circle

arXiv
Authors: Rodrigo Fresneda, Jean Pierre Gazeau, Diego Noguera

Year

2017

Paper ID

44077

Status

Preprint

Abstract Read

~2 min

Abstract Words

106

Citations

N/A

Abstract

Covariant integral quantisation using coherent states for semidirect product groups is studied and applied to the motion of a particle on the circle. In the present case the group is the Euclidean group E(2). We implement the quantisation of the basic classical observables, particularly the 2π-periodic discontinuous angle function and the angular momentum, and compute their corresponding lower symbols. An important part of our study is devoted to the angle operator given by our procedure, its spectrum and lower symbol, its commutator with the quantum angular momentum, and the resulting Heisenberg inequality. Comparison with other approaches to the long-standing question of the quantum angle is discussed.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • Covariant integral quantisation using coherent states for semidirect product groups is studied and applied to the motion of a particle on the circle.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1708.03693 [2] arXiv https://arxiv.org/abs/1708.03693 [3] Publisher https://arxiv.org/abs/1708.03693

Local Citation Graph (Related-Paper Links)

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