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Marie Curie fellow

  • Nombre:   DI COSMO, FABIO
  • Doctorado en:   Física
  • Departamento UC3M:  Matemáticas E-mail (uc3m): fcosmo@math.uc3m.es

Proyecto:

In a series of recent works, it has been proposed a relationship between Schwinger’s formulation of Quantum Mechanics and groupoids: the basic ingredient to describe a physical system is the notion of transition and from a dual point of view of probability amplitude. Starting from this analysis, in this project the possibility of defining an action principle for abstract groupoids will be investigated, extending the principle that Schwinger introduced. Furthermore, the geometrical and algebraic properties of the space of states in this formulation will be studied. Two main goals will be pursued after developing these methods:

designing quantum algorithms by suitably choosing an action functional;

defining sampling procedures for quantum signals.

Concerning the first goal, the departure point is the possibility of describing quantum algorithms as quantum random walks on suitable graphs. With regards to the second point, techniques from noncommutative harmonic analysis will be employed to sample paths on groupoids.

CV:

My career as researcher starts in the city of Naples, where I got my degree in Physics in 2013 and my Ph.D. in Physics in October 2017 with a thesis on the Hamilton-Jacobi theory. After that, my research activity has been always characterized by a deep interaction between mathematics, especially differential geometry and algebraic structures, and theoretical physics. My first collaboration in a project as Post-Doc started in february 2018 at the M&MOCS Center, where I worked on the applications of techniques from field theories to the design of mechanical metamaterials. After one year, in March 2019, I got a Post-Doc position in Madrid at the Department of Mathematics of the University Carlos III to collaborate to the development of the groupoid picture of Quantum Mechanics. Eventually, in May 2021, I was awarded with the CONEX-Plus fellowship to develop at the same department a project aimed at the application of this groupoid approach to Quantum Information.

Perfiles públicos del investigador:

Producción Científica

Resume of the activities of the researcher Fabio Di Cosmo in the period 01/05/2021 – 09/09/2022

Scientific publications 

F.M. Ciaglia, F. Di Cosmo, A. Ibort, G. Marmo. Quantum tomography and Schwinger’s picture of Quantum Mechanics. J. Phys. A: Math. Theor. 55 274008 (2022)  doi:10.1088/1751-8121/ac7591

F.M. Ciaglia, F. Di Cosmo, A. Ibort, G. Marmo, L. Schiavone, A. Zampini. Symmetries and Covariant Poisson Brackets on Presymplectic Manifolds. Symmetry, 14, 70 (2022).  doi:10.3390/sym14010070

F.M. Ciaglia, F. Di Cosmo, A. Ibort, G. Marmo, L. Schiavone, A. Zampini. Causality in Schwinger’s Picture of Quantum Mechanics. Entropy, 24, 75 (2022). doi:10.3390/e24010075

F. M. Ciaglia, F. Di Cosmo, A. Ibort, G. Marmo. Dynamical Maps and Symmetroids. Open Syst. Inf. Dyn. 28(4) 2150019 (2021). doi:10.1142/S1230161221500190 

F.M. Ciaglia, F. Di Cosmo, A. Ibort, G. Marmo, L. Schiavone, A. Zampini. Feynman’s propagator in Schwinger’s picture of Quantum Mechanics. Mod. Phys. Lett. A, 36(26) 2150187 (2021).  doi:10.1142/S021773232150187X

Communication and dissemination activities

Member of the Reviewer Board of the journals Mathematics, Symmetry and Entropy.

Reviewer for the journals European Physical Journal Plus and International Journal of Geometric Methods in Modern Physics.

Guest Editor of the Research Topic (Frontiers in Physics) on Advances in Information Geometry: Beyond the Conventional Approach.

Contributions to workshops:

The space of solutions of the Jacobi sigma-model, Mini-Workshop on New Trends in Quantum Physics, Zaragoza, 06/05/2022
Quantum tomography and Schwinger’s picture of Quantum Mechanics, Quantum Theory and Applications 2022, Policeta-San Rufo, 21/06/2022
Talk:
The space of solutions of the Jacobi sigma model, Differential Geometry and its Applications, Hradec Kralove, 19/07/2022     
Research presentation:
Schwinger’s picture of Quantum Mechanics, ICMAT PostDoc Presentation Day, ICMAT, 05/11/2022


Other outreach activities
Participation in the XI Feria Madrid es Ciencia 2022 with the activity “Juegos en Grupos”, Madrid, 02/03/2022
Director of Master Thesis “Entropy and Discrete Probability Spaces” presented by the student Vito Flavio Bellino, 13/07/2022.


Participation in Research Projects

Member of the Work Team of the Project “Classical and Quantum Information Theory and Functional Analysis: Foundations and applications”
Member of the Work Team of the Project “Grupoides, Álgebras de Von Neumann y los fundamentos matemáticos de la mecánica cuántica: teoría y aplicaciones”