Sigillo personale — R. Carlone
SIGIL
PLACEHOLDER
ID◆RC-2025◆NPL
// ALIAS FILE // MATH-03/A

RaffaeleCarlone

Professore Associato di Analisi Matematica
CLANNEAPOLIS // FED-II DISCIPLINEMATH ANALYSIS SECTOR40°50'N 14°15'E
DATI VITALI LIVE
Status ATTIVO
Grado PROF · L.240/10
In servizio 12.2022
Trasmissioni 30+
Apprendisti 3
Anni di servizio 18
01

Profilo

// DOSSIER · ENCRYPTED · CLR-04
ACCESS GRANTED

Sono Professore Associato di Analisi Matematica presso il Dipartimento di Matematica e Applicazioni "Renato Caccioppoli" dell'Università degli Studi di Napoli Federico II.

Mi occupo da oltre vent'anni di interazioni puntuali e modelli risolubili in meccanica quantistica.

Mi sono laureato in Fisica (Federico II, 2004, 110/110 cum laude) sotto la supervisione di Rodolfo Figari.

Parole chiave
  • Interazioni puntuali
  • Equazioni NLS e Dirac
  • Ibridi quantistici
  • Teoria spettrale
  • Modelli di decoerenza
  • Grafi metrici
Email raffaele.carlone@unina.it
Sede Dip. di Matematica e Applicazioni "R. Caccioppoli" — Napoli
arXiv arxiv.org/a/carlone_r_1
02

Percorso Accademico

// CHRONOLOGY · MISSION LOG
RECORDS: 08
12/2022 — oggi
Professore Associato
MATH-03/A, Federico II Napoli — Dip. Matematica e Applicazioni "R. Caccioppoli".
2019 — 2022
Ricercatore RTD-B
SSD MAT/05, Università Federico II, Napoli.
2014 — 2019
Ricercatore RTD-A
SSD MAT/07, Federico II Napoli (due contratti consecutivi).
2011 — 2013
Post-Doc
Università Federico II, Napoli — coordinatore: R. Figari.
2009 — 2011
Post-Doc Insubria
Progetto Point interactions in QM — coord. A. Posilicano.
2008 — 2009
Post-Doc Praga
Doppler Institute for Mathematical Physics & Applied Math — coord. P. Exner.
2007
PhD Fisica Fondamentale
Federico II — tesi Models of few (and many) body quantum systems with point interactions.
2004
Laurea in Fisica · 110/110 cum laude
Federico II — relatore R. Figari, tesi su decoerenza indotta dall'ambiente.
03

Dottorandi · Supervisione

// APPRENTICES · CLASS XXXVII–XXXVIII
ACTIVE: 03
α
Ciclo XXXVII
Ilenia
Di Giorgio
Ground states normalizzati per l'NLS su sistemi quantistici ibridi (modello a doppio piano).
β
Ciclo XXXVIII
Salvatore
Niro
Equazione di Dirac non lineare con interazioni puntuali e ground states dell'NLS su domini planari limitati e ibridi.
γ
Ciclo XXXVIII
Giuseppe
Rizzello
Beyond the Winter Model: estensioni del modello di Winter — dimensione 2, gusci deformati, sistemi ibridi semiretta–disco, regime non lineare.
04

Progetti Finanziati

// CONTRACTS · GRANT REGISTRY
ENTRIES: 06
Responsabile
Progetto Giovani GNFM 2017
Dinamica quasi-classica per il modello di polarone.
2017 — 2018
Resp. locale
PRIN 2022
Nonlinear dispersive equations in presence of singularities. PI: S. Dovetta.
2022 — 2025
Resp. locale
FIR Cond-Math
Condensed Matter in Mathematical Physics. PI: M. Correggi.
2014 — 2017
Partecipante
PRIN 2022 PNRR
Linear and Nonlinear PDE's: New directions and Applications. PI: C. Trombetti.
2022 — 2025
Partecipante
COST CA18232
Mathematical models for interacting dynamics on networks.
2019
Partecipante
GNAMPA-INdAM 2019
Aspetti geometrici, analitici e dinamici di problemi differenziali singolari e degeneri. Coord. L. Tentarelli.
2019
05

Pubblicazioni

// TRANSMISSIONS · ARXIV.NET · DOI
ENTRIES: 33
Selezione di lavori su riviste internazionali, in ordine cronologico inverso.
↗ All preprints on arXiv
2025
Normalized NLS ground states on a double-plane hybrid
F. Boni, R. Carlone, I. Di Giorgio
Zeitschrift für Angewandte Mathematik und Physik (ZAMP) 76, 179
▶ arXiv:2407.19810 DOI
2025
The search for NLS ground states on a hybrid domain: motivations, methods, and results
R. Adami, F. Boni, R. Carlone, L. Tentarelli
In: Singularities, Asymptotics and Limiting Models — Springer INdAM Series 64, 287–311
▶ arXiv:2404.07843
2024
NLS ground states on a hybrid plane PREPRINT
R. Adami, F. Boni, R. Carlone, L. Tentarelli
Preprint arXiv
▶ arXiv:2401.09888
2023
NLS ground states on the half-line with point interactions
F. Boni, R. Carlone
NoDEA — Nonlinear Differential Equations and Applications 30:51
arXiv n/a
2023
Spectral stability and instability of solitary waves of the Dirac equation with concentrated nonlinearity
N. Boussaid, C. Cacciapuoti, R. Carlone, A. Comech, D. Noja, A. Posilicano
AIMS Communications on Pure and Applied Analysis 22(10)
arXiv n/a
2022
Ground states for the planar NLSE with a point defect as minimizers of the constrained energy
R. Adami, F. Boni, R. Carlone, L. Tentarelli
Calculus of Variations and Partial Differential Equations 61(5), 195
arXiv n/a
2022
Complete ionization for a non-autonomous point interaction model in d = 2
W. Borrelli, R. Carlone, L. Tentarelli
Communications in Mathematical Physics 395(2), 963–1005
arXiv n/a
2022
Existence, structure, and robustness of ground states of a NLSE in 3D with a point defect
R. Adami, F. Boni, R. Carlone, L. Tentarelli
Journal of Mathematical Physics 63(7), 071501
arXiv n/a
2021
Bifurcating standing waves for effective equations in gapped honeycomb structures
W. Borrelli, R. Carlone
Nanosystems: Physics, Chemistry, Mathematics 12(1), 5–14
▶ arXiv:2012.14680
2021
Emergence of Time-Dependent Point Interactions in Polaron Models
R. Carlone, M. Correggi, M. Falconi, M. Olivieri
SIAM Journal on Mathematical Analysis 53(4), 4657–4691
arXiv n/a
2021
A Note on the Dirac Operator with Kirchhoff-Type Vertex Conditions on Metric Graphs
W. Borrelli, R. Carlone, L. Tentarelli
In "Mathematical Challenges of Zero-Range Physics", Springer, 81–104
arXiv n/a
2021
On the nonlinear Dirac equation on noncompact metric graphs
W. Borrelli, R. Carlone, L. Tentarelli
Journal of Differential Equations 278 (25 March 2021), 326–357
▶ arXiv:1912.11459
2021
Stability of the standing waves of the concentrated NLSE in dimension two
R. Adami, R. Carlone, M. Correggi, L. Tentarelli
Mathematics in Engineering 3(2), 1–15
▶ arXiv:2001.03969 DOI
2020
Blow-up for the pointwise NLS in dimension two: absence of critical power
R. Adami, R. Carlone, M. Correggi, L. Tentarelli
Journal of Differential Equations 269(1), 1–37
▶ arXiv:1808.10343
2019
Nonlinear singular perturbations of the fractional Schrödinger equation in dimension one
R. Carlone, D. Finco, L. Tentarelli
Nonlinearity 32(8), 3112–3143
▶ arXiv:1805.06952 DOI
2019
A model for Feshbach resonances
R. Carlone, M. Correggi, D. Finco, A. Teta
Annales Henri Poincaré 20(9), 2899–2935
▶ arXiv:1901.08282 DOI
2019
Nonlinear Dirac Equation on Graphs with Localized Nonlinearities: Bound States and Non-Relativistic Limit
W. Borrelli, R. Carlone, L. Tentarelli
SIAM Journal on Mathematical Analysis 51(2), 1046–1081
▶ arXiv:1807.06937
2019
An overview on the standing waves of nonlinear Schrödinger and Dirac equations on metric graphs with localized nonlinearity
W. Borrelli, R. Carlone, L. Tentarelli
Symmetry 11(2), 169
▶ arXiv:1901.02696 DOI
2018
Expansion of the resolvent in a Feshbach model
R. Carlone, D. Finco
Rendiconti di Matematica e delle sue Applicazioni 39(7), 241–255
▶ arXiv:1902.03626
2018
An introduction to the two-dimensional Schrödinger equation with nonlinear point interactions
R. Carlone, M. Correggi, L. Tentarelli
Nanosystems 9, 187–195
DOI
2018
Solvable models of quantum beating
R. Carlone, R. Figari, C. Negulescu, L. Tentarelli
Nanosystems 9, 162–170
DOI
2018
Well-posedness of the two-dimensional nonlinear Schrödinger equation with concentrated nonlinearity
R. Carlone, M. Correggi, L. Tentarelli
Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire
DOI
2017
The quantum beating and its numerical simulation
R. Carlone, R. Figari, C. Negulescu
Journal of Mathematical Analysis and Applications 450(2), 1294–1316
▶ arXiv:1610.00379 DOI
2017
A quantum hybrid with a thin antenna at the vertex of a wedge
R. Carlone, A. Posilicano
Physics Letters A 381(12), 1076–1080
▶ arXiv:1612.03025 DOI
2017
The 1-D Dirac equation with concentrated nonlinearity
C. Cacciapuoti, R. Carlone, D. Noja, A. Posilicano
SIAM Journal on Mathematical Analysis 49(3), 2246–2268
▶ arXiv:1607.00665 DOI
2017
The action of Volterra integral operators with highly singular kernels on Hölder continuous, Lebesgue and Sobolev functions
R. Carlone, A. Fiorenza, L. Tentarelli
Journal of Functional Analysis 273(3), 1258–1294
▶ arXiv:1611.08503 DOI
2016
Two-dimensional time-dependent point interactions
R. Carlone, M. Correggi, R. Figari
In "Functional Analysis and Operator Theory for Quantum Physics", EMS Publishing House
▶ arXiv:1601.02390 DOI
2015
A Model of a Quantum Particle in a Quantum Environment: A Numerical Study
R. Carlone, R. Figari, C. Negulescu
Communications in Computational Physics 18(1), 247–262
DOI
2013
On the spectral theory of Gesztesy-Šeba realizations of 1-D Dirac operators with point interactions on a discrete set
R. Carlone, M. Malamud, A. Posilicano
Journal of Differential Equations 254(9), 3835–3902
DOI
2011
Perturbations of eigenvalues embedded at threshold: two-dimensional solvable models
C. Cacciapuoti, R. Carlone, R. Figari
Journal of Mathematical Physics 52
DOI
2010
Dynamics of an electron confined to a hybrid plane and interacting with a magnetic field
R. Carlone, P. Exner
Reports on Mathematical Physics 67(2), 211–227
DOI
2010
Perturbations of eigenvalues embedded at threshold: one and three dimensional solvable models
C. Cacciapuoti, R. Carlone, R. Figari
Journal of Physics A: Mathematical and Theoretical 43(47), 474009
DOI
2009
Resonances in models of spin-dependent point interactions
C. Cacciapuoti, R. Carlone, R. Figari
Journal of Physics A: Mathematical and Theoretical 42(3), 035202
arXiv n/a
2007
A solvable model of a tracking chamber
C. Cacciapuoti, R. Carlone, R. Figari
Reports on Mathematical Physics 59(3), 337–349
arXiv n/a
2007
Spin-dependent point potentials in one and three dimensions
C. Cacciapuoti, R. Carlone, R. Figari
Journal of Physics A: Mathematical and Theoretical 40(2), 249
arXiv n/a
2005
Decoherence induced by scattering: a three-dimensional model
C. Cacciapuoti, R. Carlone, R. Figari
Journal of Physics A: Mathematical and Theoretical 38(22), 4933
arXiv n/a
2004
The Joos-Zeh formula and the environment-induced decoherence
R. Carlone, R. Figari, A. Teta
International Journal of Modern Physics B 18(4/5), 667–674
arXiv n/a
06

Didattica

// TUTELAGE · TRAINING LOG
ONGOING

Corsi di Dottorato

2025
Basic Quantum Mechanics (20h) — PhD Scienze Matematiche e Informatiche, Federico II.
2024
The mathematics of superconductivity (10h) — PhD Scienze Matematiche e Informatiche.
2024
Basic Quantum Mechanics (20h) — PhD Scienze Matematiche e Informatiche.
2017
An introduction to some equations of Quantum Mechanics — PhD Federico II.
2016
Organizzatore di Strichartz estimates and applications to dispersive PDEs (Prof. Boussaid).

Insegnamenti universitari · Titolare

2024/25
Istituzioni di Matematica (9 CFU, 2 ed.); Meccanica Analitica (6 CFU, Fisica); Mathematical Methods for Quantum Information (3 CFU).
2023/24
Istituzioni di Matematica (9 CFU); Meccanica Analitica (6 CFU, Fisica).
2022/23
Analisi I — Ing. Chimica e Automazione; Meccanica Analitica (Fisica).
2020/21
Analisi I & Analisi II — Ingegneria Gestionale (18 CFU complessivi).
2019/20
Analisi II — Ingegneria Meccanica e Aerospaziale.
2016 – 2019
Meccanica Razionale — Ingegneria Edile-Architettura.
2014 – 2018
Matematica — Tecnologia della Produzione Animale.
07

Talks · Selezione

// BROADCASTS · COMM-LINK
SELECT: 14
'25
InvitedRecent advances in operator theory — Politecnico di Milano.
'25
SeminarQuantum hybrids — Politecnico di Bari, 10/01/2025.
'24
InvitedFirst Workshop on Singular Interactions and Effective Models in Mathematical Physics — Sapienza, Roma.
'24
InvitedMathematical aspects in non-equilibrium systems: from micro to macro — Erice, Centro E. Majorana.
'24
SeminarQuantum hybrids — Università "L. Vanvitelli", Caserta.
'22
INdAM Quantum Meetings 2022 — Politecnico di Milano.
'22
Modern Trends in Quantum Theory — Charles Technical University, Praga.
'20
Quantum Mechanics of Artificial Material Structure — Sirius Mathematical Center, Sochi.
'20
Pierre Duclos Workshop — San Pietroburgo.
'19
InvitedHamiltonian PDEs: KAM, Reducibility & Normal Forms — Casa Matemática Oaxaca, Messico.
'18
InvitedDirac-90: Waves, Particles, Spectra — St. Petersburg.
'18
InvitedMathematical Challenges of Zero-Range Physics — INdAM, Roma.
'17
InvitedRencontres autour de l'équation de Dirac avec des interactions singulières — Besançon.
'14
InvitedMathematical challenges of zero-range physics — LMU München.
08

Editoriale · Associazioni · Incarichi

// CODICES · CLAN AFFILIATIONS
SERVICE

Referee

  • Communications in Mathematical Physics
  • Annales Henri Poincaré
  • Calculus of Variations and PDE
  • J. Differential Equations
  • J. Functional Analysis
  • J. Math. Phys. · J. Phys. A
  • Letters in Mathematical Physics
  • MathSciNet (2007 — 2025)

Associazioni

  • ICMP — dal 2008
  • UMI — dal 2016
  • GNAMPA — 2019 / 2022
  • GNFM — dal 2023 (e periodi precedenti)
  • INFN — 2005–2008, 2012, 2013

Incarichi

  • Membro Giunta DMA 2025 — 2028
  • Giunta DMA · 2020 — 2022
  • Consiglio SPSB · 2020 — 2022
  • Collegio Dottorato Matematica e Applicazioni · cicli 38 — 41
  • Comm. selezione CNR (15 Primi Ricercatori) · 2024
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