Commutation Relations in Mesoscopic Electric Circuits

Details Commutation Relations in Mesoscopic Electric Circuits Commutation Relations in Mesoscopic Electric Circuits

2000-09-22

arxiv.org/abs/cond-mat/0009352v1

AIP Conf.Proc. 545 (2001) 85

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

7 pages, talk at ``Spin-Statistics Connection and Commutation Relations'' Capri 2000

Scientific paper

10.1063/1.1337717

In the talk, I briefly demonstrate the quantum theory for mesoscopic electric circuits and its applications. In the theory, the importance of the charge discreteness in a mesoscopic electric circuit is addressed. As a result, a new kind of commutation relation for electric charge and current occurred inevitably. The charge representation, canonical current representation and pseudo-current representation are discussed extensively. It not only provides a concrete realization of mathematical models which discuss the space quantization in high energy physics and quantum gravity but also presents a sequence of applications in condensed matter physics from a different point of view. A possible generalization to coupled circuits is also proposed.

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