Quantum knots and knotted zeros

Louis H. Kauffman, Samuel J. Lomonaco

Результат исследования: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучнаярецензирование

Аннотация

In 2001, Michael Berry4 published the paper "Knotted Zeros in the Quantum States of Hydrogen" in Foundations of Physics. In this paper we show how to place Berry's discovery in the context of general knot theory and in the context of our formulations for quantum knots. Berry gave a time independent wave function for hydrogen, as a map from three space R3 to the complex plane and such that the inverse image of 0 in the complex plane contains a knotted curve in R3. We show that for knots in R3 this is a generic situation in that every smooth knot K in R3 has a smooth classifying map f: R3-→ C (the complex plane) such that f-1(0) = K. This leaves open the question of characterizing just when such f are wave-functions for quantum systems. One can compare this result with the work of Mark Dennis and his collaborators and with the work of Lee Rudolph. Our approach provides great generality to the structure of knotted zeros of a wavefunction and opens up many new avenues for research in the relationships of quantum theory and knot theory. We show how this classifying construction can be related our previous work on two dimensional and three dimensional mosaic and lattice quantum knots.

Язык оригиналаанглийский
Название основной публикацииQuantum Information Science, Sensing, and Computation XI
РедакторыEric Donkor, Michael Hayduk, Michael R. Frey, Samuel J. Lomonaco, John M. Myers
ИздательSPIE
Число страниц9
ISBN (электронное издание)9781510626331
DOI
СостояниеОпубликовано - 1 янв 2019
СобытиеQuantum Information Science, Sensing, and Computation XI 2019 - Baltimore, Соединенные Штаты Америки
Продолжительность: 18 апр 2019 → …

Серия публикаций

НазваниеProceedings of SPIE - The International Society for Optical Engineering
Том10984
ISSN (печатное издание)0277-786X
ISSN (электронное издание)1996-756X

Конференция

КонференцияQuantum Information Science, Sensing, and Computation XI 2019
СтранаСоединенные Штаты Америки
ГородBaltimore
Период18.04.2019 → …

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  • Цитировать

    Kauffman, L. H., & Lomonaco, S. J. (2019). Quantum knots and knotted zeros. В E. Donkor, M. Hayduk, M. R. Frey, S. J. Lomonaco, & J. M. Myers (Ред.), Quantum Information Science, Sensing, and Computation XI [109840A] (Proceedings of SPIE - The International Society for Optical Engineering; Том 10984). SPIE. https://doi.org/10.1117/12.2518685