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Symmetry (Basel), ISSN 2073-8994, 2019, Volume 11, Issue 3, p. 359
We consider a compact metric graph of size ε and attach to it several edges (leads) of length of order one (or of infinite length). As ε goes to zero, the... 
point interactions | MULTIDISCIPLINARY SCIENCES | scaling limit | CONVERGENCE | Krein formula | VERTEX COUPLINGS | FORMULA | SPECTRA | metric graphs | SELF-ADJOINT EXTENSIONS | Kreĭn formula
Journal Article
JOURNAL D ANALYSE MATHEMATIQUE, ISSN 0021-7670, 10/2019, Volume 139, Issue 1, pp. 155 - 177
Let Omega(-) and Omega(+) be two bounded smooth domains in R-n, n >= 2, separated by a hypersurface Sigma. For mu > 0, consider the function h(mu) = 1(Omega-)... 
MATHEMATICS | EXTENSIONS | INTERFACE | REPRESENTATION THEOREMS | QUADRATIC-FORMS | SPECTRAL-ANALYSIS | OPERATORS | EQUATION | Operators (mathematics) | Domains | Boundary conditions | Dirichlet problem | Hyperspaces
Journal Article
Probability Theory and Related Fields, ISSN 0178-8051, 10/2015, Volume 163, Issue 1-2, pp. 1 - 59
...=10.1007/s00440-014-0586-4&domain=pdf Web End = Bounds for the Stieltjes transform and the density of states of Wigner matrices Claudio Cacciapuoti Anna Maltsev... 
Random matrices | Rate of convergence | Wigner matrices | Rigidity of the eigenvalues | DELOCALIZATION | SEMICIRCLE LAW | STATISTICS & PROBABILITY | BULK UNIVERSALITY | SPECTRAL STATISTICS | EIGENVALUES | LOCAL STATISTICS | FLUCTUATIONS | DIFFUSION | EDGE | Studies | Probability distribution | Mathematical models | Eigen values | Convergence | Mathematical analysis | Transforms | Eigenvalues | Texts | Counting | Optimization | Symmetry
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 11/2014, Volume 257, Issue 10, pp. 3738 - 3777
We study standing waves for a nonlinear Schrödinger equation on a star graph G, i.e. N halflines joined at a vertex. At the vertex an interaction occurs... 
Non-linear Schrödinger equation | Solitary waves | Quantum graphs | MATHEMATICS | SYMMETRY | NONLINEAR SCHRODINGER-EQUATION | Non-linear Schrodinger equation | GROUND-STATES | CONSTRAINED ENERGY MINIMIZATION
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 2019, Volume 473, Issue 1, pp. 215 - 257
We study scattering for the couple (AF,A0) of Schrödinger operators in L2(R3) formally defined as A0=−Δ+αδπ0 and AF=−Δ+αδπF, α>0, where δπF is the Dirac... 
Point interactions supported by unbounded hypersurfaces | Kreĭn's resolvent formulae | Scattering theory | MATHEMATICS | MATHEMATICS, APPLIED | Krein's resolvent formulae | BOUND-STATES | LIMITING ABSORPTION PRINCIPLE | OPERATORS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 05/2016, Volume 260, Issue 10, pp. 7397 - 7415
On a star graph made of N≥3 halflines (edges) we consider a Schrödinger equation with a subcritical power-type nonlinearity and an attractive delta interaction... 
MATHEMATICS | STATES | MINIMIZATION | NONLINEAR SCHRODINGER-EQUATION | ORBITAL STABILITY
Journal Article
Nonlinearity, ISSN 0951-7715, 07/2017, Volume 30, Issue 8, pp. 3271 - 3303
We consider a nonlinear Schrodinger equation (NLS) posed on a graph (or network) composed of a generic compact part to which a finite number of half-lines are... 
non-linear Schrodinger equation | concentrationcompactness techniques | quantum graphs | MATHEMATICS, APPLIED | TADPOLE GRAPH | STANDING WAVES | concentration-compactness techniques | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | CONSTRAINED ENERGY MINIMIZATION
Journal Article
Journal of mathematical physics, ISSN 1089-7658, 2018, Volume 59, Issue 7, p. 072104
We consider a Hamiltonian describing three quantum particles in dimension one interacting through two-body short-range potentials. We prove that, as a suitable... 
PHYSICS, MATHEMATICAL
Journal Article
Archivum Immunologiae et Therapiae Experimentalis, ISSN 1661-4917, 2018, Volume 67, Issue 1, pp. 1 - 18
... in Inflammatory Skin Diseases Anna Balato 1 · Sara Cacciapuoti 2 · Roberta Di Caprio 2 · Claudio Marasca 2 · Anna Masarà 2 · Annunziata Raimondo 2 · Gabriella Fabbrocini 2... 
Biomedicine | Immunology | Inflammatory skin diseases | Bacteria | Skin | Pharmacology/Toxicology | Microbiome | CLOSTRIDIUM-DIFFICILE INFECTION | INTESTINAL MICROBIOTA | OROPHARYNGEAL FLORA | FECAL MICROBIOTA | IMMUNOLOGY | HUMAN GUT MICROBIOME | ATOPIC-DERMATITIS | CHRONIC PLAQUE PSORIASIS | STAPHYLOCOCCUS-AUREUS | ACNE-VULGARIS | HIDRADENITIS SUPPURATIVA | Skin - microbiology | Age Factors | Acne Vulgaris - immunology | Humans | Middle Aged | Bacteria - drug effects | Hidradenitis Suppurativa - drug therapy | Child, Preschool | Infant | Dermatitis, Atopic - microbiology | Dermatologic Agents - therapeutic use | Dysbiosis | Hidradenitis Suppurativa - microbiology | Young Adult | Anti-Bacterial Agents - therapeutic use | Bacteria - immunology | Dermatitis, Atopic - immunology | Aged, 80 and over | Anti-Inflammatory Agents - therapeutic use | Bacteria - classification | Adult | Child | Infant, Newborn | Skin - immunology | Psoriasis - immunology | Psoriasis - drug therapy | Acne Vulgaris - drug therapy | Psoriasis - microbiology | Host-Pathogen Interactions | Dermatitis, Atopic - drug therapy | Gastrointestinal Microbiome - drug effects | Adolescent | Aged | Bacteria - pathogenicity | Hidradenitis Suppurativa - immunology | Skin - drug effects | Acne Vulgaris - microbiology | Psoriasis | Atopic dermatitis | Health aspects | Disease prevention | Immune response | Acne | Microbiomes | Skin diseases | Gastrointestinal tract | Dermatitis | Niches
Journal Article
Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 11/2014, Volume 31, Issue 6, pp. 1289 - 1310
On a star graph G, we consider a nonlinear Schrödinger equation with focusing nonlinearity of power type and an attractive Dirac's delta potential located at... 
MATHEMATICS, APPLIED | STANDING WAVES | NONLINEAR SCHRODINGER-EQUATIONS | SOLITONS | GROUND-STATES | QUANTUM GRAPHS | Orbits
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 09/2017, Volume 273, Issue 5, pp. 1762 - 1809
We consider a scaling limit of a nonlinear Schrödinger equation (NLS) with a nonlocal nonlinearity showing that it reproduces in the limit of cutoff removal a... 
Zero-range limit of concentrated nonlinearities | Nonlinear delta interactions | Nonlinear Schrödinger equation | MATHEMATICS | Nonlinear Schrodinger equation | nonlinearities | SCHRODINGER-EQUATION | Zero-range limit of concentrated | GLOBAL WELL-POSEDNESS
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2017, Volume 49, Issue 3, pp. 2246 - 2268
We define and study the Cauchy problem for a one-dimensional (1-D) nonlinear Dirac equation with nonlinearities concentrated at one point. Global... 
Nonlinear Dirac equation | Point interactions | Well-posedness | MATHEMATICS, APPLIED | nonlinear Dirac equation | WAVES | NLS EQUATION | well-posedness | point interactions | FIELD | SCHRODINGER-EQUATION | CAUCHY-PROBLEM | GLOBAL WELL-POSEDNESS
Journal Article
Reviews in Mathematical Physics, ISSN 0129-055X, 05/2011, Volume 23, Issue 4, pp. 409 - 451
We define the Schrödinger equation with focusing, cubic nonlinearity on one-vertex graphs. We prove global well-posedness in the energy domain and conservation... 
solitary waves | nonlinear Schrödinger equation | Quantum graphs | nonlinear Schrodinger equation | PHYSICS, MATHEMATICAL | SCATTERING
Journal Article
Milan Journal of Mathematics, ISSN 1424-9286, 12/2018, Volume 86, Issue 2, pp. 305 - 327
We consider the nonlinear Schrodinger equation with pure power nonlinearity on a general compact metric graph, and in particular its stationary solutions with... 
stationary solutions | critical growth | Nonlinear Schrödinger equation | stability | metric graphs | MATHEMATICS, APPLIED | Nonlinear Schrodinger equation | STANDING WAVES | NONLINEAR SCHRODINGER-EQUATION | ORBITAL STABILITY | MATHEMATICS | BOUND-STATES | DYNAMICS | GROUND-STATES | QUANTUM GRAPHS
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 12/2014, Volume 104, Issue 12, pp. 1557 - 1570
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 06/2007, Volume 40, Issue 26, pp. F511 - F523
... waveguide Claudio Cacciapuoti 1 and Pavel Exner 2,3 1 Institut f¨ ur Angewandte Mathematik, Universit¨ at Bonn, Wegelerstr. 6, 53115 Bonn, Germany 2 Nuclear Physics... 
LAPLACIAN | BOUND-STATES | PHYSICS, MULTIDISCIPLINARY | DELTA | CONVERGENCE | SPECTRUM | PHYSICS, MATHEMATICAL | GRAPHS
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 04/2013, Volume 54, Issue 4, p. 43302
...JOURNAL OF MATHEMATICAL PHYSICS 54, 043302 (2013) Local Marchenko-Pastur law at the hard edge of sample covariance matrices Claudio Cacciapuoti, a) Anna... 
DELOCALIZATION | WIGNER RANDOM MATRICES | SEMICIRCLE LAW | BULK UNIVERSALITY | PHYSICS, MATHEMATICAL | EIGENVALUE STATISTICS | Intervals | Law | Asymptotic properties | Mathematical analysis | Eigenvalues | Spectra | Density | Optimization
Journal Article
03/2019
We consider a compact metric graph of size $\varepsilon$, and attach to it several edges (leads) of length of order one (or of infinite length). As... 
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 2020, Volume 482, Issue 1, p. 123554
We correct a minor mistake in the final formula for the scattering matrix. 
Point interactions supported by unbounded hypersurfaces | Kreĭn's resolvent formulae | Scattering theory
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 03/2007, Volume 48, Issue 3, pp. 032103 - 032103-21
We analyze the problem of approximating a smooth quantum waveguide with a quantum graph. We consider a planar curve with compactly supported curvature and a... 
CONVERGENCE | BOUND-STATES | SPECTRA | PHYSICS, MATHEMATICAL | LAPLACIAN | WAVEGUIDES | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | BOUNDARY-VALUE PROBLEMS | PERTURBATION THEORY | DECOUPLING | QUANTUM MECHANICS | BOUNDARY CONDITIONS | GRAPH THEORY
Journal Article