Research
Research
A detailed description of my research activity can be found here
Publications
Preprint
[19] M. Gallone, B. Langella, Prethermalization and conservation laws in quasi-periodically driven quantum systems, arXiv:2306.14022
[18] F. Boni, M. Gallone, Two dimensional NLS ground states with attractive Coulomb potential and point interaction, arXiv:2304.13629
Accepted
[17] M. Gallone, V. Mastropietro, Universality in the 2D Ising Model and Harris-Luck Irrelevance, accepted in Comm. Math. Phys.; doi: 10.1007/s00220-024-05092-6
[16] M. Gallone, S. Lucente, Singularity: A Seventh Memo?, accepted in INdAM-Springer; arXiv:2403.18487
Published
[15] M. Gallone, A. Ponno, Hamiltonian field theory close to wave equation: from Fermi-Pasta-Ulam to water waves, in: Georgiev, V., Michelangeli, A., Scandone, R. (eds) Qualitative Properties of Dispersive PDEs. INdAM 2021. Springer INdAM Series, vol 52. Springer, Singapore. doi: 10.1007/978-981-19-6434-3_10
[14] M. Gallone, A. Michelangeli, E. Pozzoli, Heat equation with inverse-square potential of bridging-type across two half-lines, in: Georgiev, V., Michelangeli, A., Scandone, R. (eds) Qualitative Properties of Dispersive PDEs. INdAM 2021. Springer INdAM Series, vol 52. Springer, Singapore doi: 10.1007/978-981-19-6434-3_7
[13] M. Gallone, M. Marian, A. Ponno, S. Ruffo, Burgers turbulence in the Fermi-Pasta-Ulam-Tsingou chain, Phys. Rev. Lett. 129 114101 (2022) doi: 10.1103/PhysRevLett.129.114101
(press release on LeScienze.it - in Italian)
[12] B. Cassano, M. Gallone, F. Pizzichillo, Dirac-Coulomb operators with Infinite Mass Boundary Conditions in Sector, J. Math. Phys. 63, 071503 (2022) doi: 10.1063/5.0089526
[11] M. Gallone, A. Michelangeli, E. Pozzoli, Quantum Geometric Confinement and Dynamical Transmission in Grushin Cylinder, Reviews in Mathematical Physics 3 Vol. 34 no. 7 (2022) 2250018 doi: 10.1142/S0129055X22500180
[10] M. Gallone, A. Ponno, B. Rink, Korteweg-de Vries and Fermi-Pasta-Ulam-Tsingou: asymptotic integrability of quasi unidirectional waves, J. Phys. A: Math. Theor. 54 305701 (2021) doi: 10.1088/1751-8121/ac0a2
[9] M. Gallone, S. Pasquali, Metastability phenomena in two-dimensional rectangular lattices with nearest-neighbour interaction, Nonlinearity 34 4983 (2021) doi: 10.1088/1361-6544/ac0483
[8] M. Gallone, A. Michelangeli, Quantum particle across Grushin singularity, J. Phys. A: Math. Theor. 54, 215201 (2021) doi: 10.1088/1751-8121/abeb81
[7] M. Gallone, A. Michelangeli, A. Ottolini, Krein-Višik-Birman self-adjoint extension theory revisited, in "Mathematical Challenges of Zero-Range Physics", INdAM-Springer series, vol. 42, 219-304 (2020) doi: 10.1007/978-3-030-60453-0_12
[6] M. Gallone, A. Michelangeli, Self-adjoint extensions with Friedrichs lower bound, Complex Anal. Oper. Theory 14, 73 (2020) doi: 10.1007/s11785-020-01032-z
[5] M. Gallone, A. Michelangeli, Hydrogenoid spectra with central perturbations, in Reports on Mathematical Physics Volume 84, Issue 2, October 2019, Pages 215-243 , DOI https://doi.org/10.1016/S0034-4877(19)30084-9
[4] M. Gallone, A. Michelangeli, E. Pozzoli, On geometric quantum confinement in Grushin-type manifolds, Z. Angew. Math. Phys. (2019) 70: 158 https://doi.org/10.1007/s00033-019-1203-2
[3] M. Gallone, A. Michelangeli, Discrete spectra for critical Dirac-Coulomb Hamiltonians, Journal of Mathematical Physics 59, 062108 (2018); https://doi.org/10.1063/1.5011305
[2] M. Gallone, A. Michelangeli, Self-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei, Anal.Math.Phys. (2019) 9: 585-616. https://doi.org/10.1007/s13324-018-0219-7
[1] M. Gallone, Self-adjoint extensions of Dirac operator with Coulomb potential, in Advances in Quantum Mechanics, G. Dell' Antonio and A. Michelangeli, eds., vol. 18 of INdAM-Springer series, Springer International Publishing. pp. 169-185 (2017), doi 10.1007/978-3-319-58904-6_10
Book
M. Gallone, A. Michelangeli, Self-Adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians, Springer Monographs in Mathematics, Springer International Publishing, 2023 (doi: 10.1007/978-3-031-10885-3)
Errata: (link)
Ph.D. Thesis
M. Gallone, Self-adjointness of Quantum Hamiltonians with Symmetry, (SISSA Digital Library)
Scientific Communications
Self-adjoint extensions of the Aharonov-Bohm Hamiltonian: non-relativistic and δ-like limit, 15 July 2024, First Workshop on Singular Interactions and Effective Models in Mathematical Physics, Rome (Italy)
Ground States of NLS with Point Interaction and Coulomb Potential, 9 July 2024, Future Perspectives on Linear and Nonlinear Modelling of Contact-Type Perturbations, Rome (Italy)
Time quasi-periodically driven quantum systems: prethermalization and conservation laws, 2-7 June 2024, SPQT2024, S. Margherita di Pula (Italy)
Prethermalization and conservation laws in quasi-periodically driven quantum systems, 20 April 2023, Math Physics Seminar, Georgiatech, online
Universality in 2D quasi-periodic Ising modeland Harris-Luck irrelevance, 23 March 2023, Mathematics of Many Body Systems, SISSA, Trieste (Italy)
Integrable and Turbulent dynamics in the FPUT chain, 8 March 2023, Integrable Systems Seminars, SISSA, Trieste (Italy)
Self-Adjoint Extensions of the Dirac Coulomb Operators, 21 February 2023, Two Dirac Days, Università di Padova, Padova (Italy)
Two dimensional Ising model with weak quasi-periodic disorder, 9 January 2023, Mathematical Quantum Matter, Università degli Studi di Milano, Milan (Italy)
Prethermalization in Classical and Quantum Physics, 14 December 2022, La Sapienza (Roma)
Burgers Turbulence in the Fermi-Pasta-Ulam-Tsingou chain, 23 November 2022, GSSI-TNT-Sapienza Statistical Mechanics Webinars
The Laplace-Beltrami Operator on the Grushin Cylinder, 4 October 2022, Mini-Workshop: Zero-Range and Point-Like Singular Perturbations, MFO (Germany)
Two-dimensional Quasi-periodic Ising model, 23 August 2022, Quantissima in the Serenissima IV
Perturbation of classical Hamiltonian field theories and application to the FPUT problem, 16 February 2022, SISSA (Trieste)
2D Ising model with quasi-periodic disorder, 22 December 2021, Università di Milano (Milano), Quantum before Christmas
Self-adjoint Laplacians on the Grushin cylinder, 5 October 2021, Politecnico di Torino (Torino)
Geometric Quantum Confinement and Transmission on Grushin-type Manifolds, August 2021, Geneva (Switzerland), International Congress on Mathematical Physics (poster)
Slow thermalisation in 1D and 2D lattices 2 March 2021, Lund (Sweden)*, Seminar on Analysis, Geometry and PDEs
On Geometric Quantum Confinement in Grushin-type Manifolds 20 August 2019, Venice, Quantissima in the Serenissima III
Self-adjoint realisation(s) of quantum Hamiltonians with symmetry 24-26 July 2019, ICTP (Trieste), Trieste Junior Quantum Days (poster)
On Geometric Quantum Confinement in Grushin-type Manifolds 22 March 2019, SISSA (Trieste), AJS Seminar
What is the ergodic problem? 14 March 2019, Geometry and Mathematical Physics Student Seminars (SISSA, Trieste)
Darwin-Like perturbations of the Hydrogen Spectra, 11 July 2018, Mathematical Challenges of Zero-Range Physics: Rigorous Results and Open Problems (Rome)
Fermi-Pasta-Ulam-Tsingou: When Paradox Turns into Discovery 22 June 2018, Geo & Math Phys Student Seminars (SISSA, Trieste)
Dirac operators with Coulomb Interaction 18 June 2018, International Workshop on PDEs: Analysis and Modelling (Zagreb)
The Touchy Business of Formal Computations 18 May 2018, Trieste Junior Quantum Days (Universita' di Trieste)
FPU and KdV Hierarchy 13 April 2018, Il problema di Fermi-Pasta-Ulam: Stato dell'arte e prospettive (Scuola Galileiana, Padova)
Self-adjoint realisations of the Dirac-Coulomb Operator 19 February 2018, Mathematical Challenges in Quantum Mechanics (La Sapienza, Rome)
Discrete Spectra and Self-Adjointness for Critical Dirac-Coulomb 12 December 2017, Università Milano Bicocca (Milano)
Self-adjoint realisations of Dirac-Coulomb operators 24 November 2017, SISSA (Trieste), AJS Seminar
Self-adjoint realisations of the Dirac operator with Coulomb interaction 24 May 2017, SISSA (Trieste), AMPQ Seminar
Self-adjoint realisations of the Dirac-Coulomb Hamiltonian 12 May 2017, ICTP (Trieste), Junior Trieste Quantum Days
A brief journey in Mathematical Physics 25 April 2017, Università di Padova
* = online due to COVID-19 pandemic
Collaborators
Filippo Boni (Scuola Superiore Meridionale)
Biagio Cassano (Università della Campania)
Marko Erceg (University of Zagreb)
Beatrice Langella (SISSA)
Vieri Mastropietro (Università di Milano)
Alessandro Michelangeli (HCM-IAM Bonn)
Diego Noja (Università Milano Bicocca)
Andrea Ottolini (University of Washington)
Stefano Pasquali (Université Paris-Saclay)
Antonio Ponno (Università di Padova)
Eugenio Pozzoli (Institut de Recherche Mathématique de Rennes)
Fabio Pizzichillo (Universidad Politecnica de Madrid)
Bob Rink (Vrije Universiteit Amsterdam)
Stefano Ruffo (SISSA (Trieste) )
Attended Conferences/Workshops/Schools
Invited at conferences
First Workshop on Singular Interactions and Effective Models in Mathematical Physics, Rome (Italy), 15-17 July 2024
Future Perspectives on Linear and Nonlinear Modelling of Contact-Type Perturbations, Rome (Italy), 8 - 12 July 2024
Two Dirac Days, Padova (Italy), 20-21 February 2023
Mathematical Quantum Matter, Milan (Italy), 9-11 January 2023
Mini-Workshop: Zero-Range and Point-Like Singular Perturbations, Oberwolfach (Germany), 3 - 7 October 2022
Quantissima in the Serenissima IV, Venice (Italy), 15-26 August 2022
Quantum before Christmas, Milan (Italy), 20-22 December 2021
Mathematical Challenges of zero range physics: rigorous results and open problems, Rome (Italy), 9 - 13 July 2018
International Workshop on PDEs: Analysis and Modelling, Zagreb (Croatia), 17 - 20 June 2018
Il problema di Fermi-Pasta-Ulam: stato dell’arte e prospettive, Padova (Italy), 12 - 14 April 2018
Participation to conferences/workshops/schools
SPQT2024-Symmetries and Perturbation in Quantum Theory, S. Margherita di Pula, 2-7 June 2024
Quantum and Dynamical Christmas, Università di Milano (Milano), 19-22 December 2023
50 years of Mountain Pass Theorem, SISSA (Trieste), 23-25 November 2023
School/Workshop on Wave Dynamics: Turbulent vs Integrable Effects, ICTP (Trieste), 28 August-1 September 2023
Conference (Puglia Summer Trimester 2023-Singularities, Asymptotics and Limiting Models), Università di Bari "A. Moro", 26-30 June 2023
Analysis and PDEs: remembering Thomas Kappeler, University of Zurich (Zurich, Switzerland), 5-9 June 2023
Summer School (Puglia Summer Trimester 2023-Singularities, Asymptotics and Limiting Models), Università di Bari "A. Moro", 9-12 May 2023
Opening Workshop (Puglia Summer Trimester 2023 -Singularities, Asymptotics and Limiting Models), Università di Bari "A. Moro", 17 April 2023
Trails in Quantum Mechanics and Surroundings, SISSA (Trieste), 8-10 February 2023
Universality in Condensed Matter and Statistical Mechanics, Università Roma 3 (Roma), 6-8 February 2023
Workshop on Singular Perturbations and Geometric Structures, SISSA (Trieste), 21-23 November 2022
The many facets of Statistical Field Theory, SISSA, Trieste (Italy), 17-19 October 2022
Trials in Wave Turbulence : from random waves to kinetic equations, GSSI, L'Aquila (Italy), 5-10 September 2022
Wave turbulence and beyond, Università di Torino, Torino (Italy), 18-21 July 2022
Mathematical Challenges in Quantum Mechanics, Insubria University, como (Italy), 13-18 June 2022
Advances in Classical, Quantum and Statistical Mechanics, Università Roma 3 (Roma), 11-13 May 2022
Exact Quantisation and Applications to Condensed Matter Systems, SISSA (Trieste), 27-30 September 2021
Statistical and Quantum Mechanics: reconsidering their foundations in the light of new cutting edge experiments and theoretical models, GSSI (L'Aquila), 20-23 September 2021 (online)
Qualitative properties of dispersive PDEs, Globus Hotel, Roma (Italy), 2-4 September 2021 (online)
International Congress on Mathematical Physics, International Conference Centre Geneva, Geneva (Switzerland), 2-7 August 2021
Young Researchers Symposium, University of Geneva, Geneva (Switzerland), 29-31 July 2021
Quantissima in the Serenissima III, Venice (Italy), 19 - 23 July 2019
Trieste Junior Quantum Days, Trieste (Italy), 24 - 26 July 2019
Matematica a Misura della Natura, Padova (Italy), 13 - 14 September 2018
International Congress on Mathematical Physics, McGill University, Montreal (Canada), 23 - 27 July 2018
Young Researchers Symposium, McGill University, Montreal (Canada), 20 - 21 July 2018
Junior Trieste Quantum Days, Trieste (Italy), 11, 18 May 2018
Junior Math Days, Trieste (Italy), 6 - 10 May 2018
Mathematical Challenges in Quantum Mechanics, Rome (Italy), 19 - 24 February 2018
Trails in Quantum Mechanics and Surroundings, Trieste (Italy), 29 - 30 January 2018
Insubria Summer School in Mathematical Physics. Spectral and scattering theory: from selfadjoint operators to boundary value problems, Como (Italy), 18 - 22 September 2017;
Junior Trieste Quantum Days 2017, Trieste (Italy), 12, 19 May 2017;
Spectral Days 2017, Stuttgart (Germany), 3 - 7 April 2017;
Workshop on Macroscopic Limits of Quantum Systems, München (Germany), 30 March - 1 April 2017;
Trieste Quantum Days 2017, Trieste (Italy), 20 - 24 February 2017;
Linear and Nonlinear Dirac Equation: advances and open problems, Como (Italy), 8 - 10 February 2017;
OTIND - Operator Theory and Indefinite Inner Product Spaces, Wien (Austria), 17 - 20 December 2016;
Mathematical Challenges of Zero-range physics: rigorous results and open problems, Trieste (Italy), 7 - 10 November 2016
Summer School: Universality, Scaling Limits and Effective Theories, Rome (Italy), 11 - 15 July 2016;
Contemporary Trends in the Mathematics of Quantum Mechanics, Rome (Italy), 4 - 8 July 2016;
Trieste Quantum Days, Trieste (Italy), 21 - 23 June 2016;
Mathematical Challenges in Quantum Mechanics, Bressanone (Italy), 8 - 13 February 2016.