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Article has an altmetric score of 1

Grant support

O P S is grateful to the Universidad Autonoma and to the ICMAT in Madrid, where this work was performed, by their hospitality. The present work is supported by CONICET, Argentina and by the Grant PICT 2020-02181. This project has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 777822. F Ch is partially supported by the PID2020-113350GB-I00 grant of the MICINN (Spain) and by Severo Ochoa Programme for Centres of Excellence in R & D' (CEX2019-000904-S).

Analysis of institutional authors

Chamizo, FernandoAuthor

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June 19, 2023
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Article
Hybrid Gold

About the quantum Talbot effect on the sphere

Publicated to:Journal of Physics A-Mathematical and Theoretical. 56 (25): 020501- - 2023-06-23 56(25), DOI: 10.1088/1751-8121/acd489

Authors: Chamizo, F.; Santillán, O.P.

Affiliations

UBA, Inst Matemat Luis Santalo IMAS, CONICET, Buenos Aires, Argentina - Author
Univ Autonoma Madrid, Dept Matemat, Madrid 28049, Spain - Author
Univ Autonoma Madrid, ICMAT, Madrid 28049, Spain - Author

Abstract

The Schrodinger equation on a circle with an initially localized profile of the wave function is known to give rise to revivals or replications, where the probability density of the particle is partially reproduced at rational times. As a consequence of the convolutional form of the general solution it is deduced that a piecewise constant initial wave function remains piecewise constant at rational times as well. For a sphere instead, it is known that this piecewise revival does not necessarily occur, indeed the wave function becomes singular at some specific locations at rational times. It may be desirable to study the same problem, but with an initial condition being a localized Dirac delta instead of a piecewise constant function, and this is the purpose of the present work. By use of certain summation formulas for the Legendre polynomials together with properties of Gaussian sums, it is found that revivals on the sphere occur at rational times for some specific locations, and the structure of singularities of the resulting wave function is characterized in detail. In addition, a partial study of the regions where the density vanishes, named before valley of shadows in the context of the circle, is initiated here. It is suggested that, differently from the circle case, these regions are not lines but instead some specific set of points along the sphere. A conjecture about the precise form of this set is stated and the intuition behind it is clarified.

Keywords

EquationGaussian sumsQuantum revivalsTalbot effect

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Journal of Physics A-Mathematical and Theoretical due to its progression and the good impact it has achieved in recent years, according to the agency Scopus (SJR), it has become a reference in its field. In the year of publication of the work, 2023, it was in position , thus managing to position itself as a Q1 (Primer Cuartil), in the category Modeling and Simulation.

From a relative perspective, and based on the normalized impact indicator calculated from the Field Citation Ratio (FCR) of the Dimensions source, it yields a value of: 3.16, which indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: Dimensions Aug 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-08-07, the following number of citations:

  • Scopus: 5

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-08-07:

  • The use, from an academic perspective evidenced by the Altmetric agency indicator referring to aggregations made by the personal bibliographic manager Mendeley, gives us a total of: 2.
  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 2 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

  • The Total Score from Altmetric: 0.75.
  • The number of mentions on the social network X (formerly Twitter): 2 (Altmetric).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Argentina.

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (CHAMIZO LORENTE, FERNANDO) .