References
- F. Dalfovo, S. Giorgini, L. Pitaevskii, and S. Stringari, Theory of Bose-Einstein condensation in trapped gases, Reviews of Modern Physics, vol. 71, pp. 463–512, 1999.
- B. Malomed, Nonlinear Schrödinger Equations, in Encyclopedia of Nonlinear Science (A. Scott, ed.), pp. 639–643, Routledge, 2005.
- E. Fermi, Sul moto dei neutroni nelle sostanze idrogenate, Ricerca Scientifica, vol. 7, 1936.
- O. Bulashenko, V. Kochelap, and L. Bonilla, Coherent patterns and self-induced diffraction of electrons on a thin nonlinear layer, Physical Review B, vol. 54, pp. 1537–1540, 1996.
- G. J. Lasinio, C. Presilla, and J. Sjostrand, On Schrödinger equations with concentrated nonlinearities, Annals of Physics, vol. 240, pp. 1–21, 1995.
- B. Malomed and M. Azbel, Modulational instability of a wave scattered by a nonlinear center, Physical Review B, vol. 47, pp. 10402–10406, 1993.
- M. Molina and C. Bustamante, The attractive nonlinear delta-function potential, American Journal of Physics, vol. 70, pp. 67–70, 2002.
- F.Nier, The dynamics of some quantum open systems with short-range nonlinearities, Nonlinearity, vol. 11, pp. 1127–1172, 1998.
- C. Presilla, G. Jona-Lasinio, and F. Capasso, Nonlinear feedback oscillations in resonant tunneling through double barriers, Physical Review B, vol. 43, pp. 5200–5203, 1991.
- A. Sukhorukov, Y. Kivshar, and O. Bang, Two-color nonlinear localized photonic modes, Physical Review E, vol. 60, pp. R41–R44, 1999.
- A. Sukhorukov, Y. Kivshar, O. Bang, J. Rasmussen, and P. Christiansen, Nonlinearity and disorder: Classification and stability of nonlinear impurity modes, Physical Review E, vol. 63, pp. 366011–3660118, 2001.
- P. Yeh, Optical Waves in Layered Media. Wiley, 2005.
- N. Dror and B. Malomed, Solitons supported by localized nonlinearities in periodic media, Physical Review A, vol. 83, Paper No. 033828, 2011.
- K. Li, P. Kevrekidis, B. Malomed, and D. Frantzeskakis, Transfer and scattering of wave packets by a nonlinear trap, Physical Review E, vol. 84, Paper No. 056609, pp. 1103–1128, 2011.
- H. Sakaguchi and B. Malomed, Singular solitons, Physical Review E, vol. 101, Paper No. 012211, 2020.
- E. Shamriz, Z. Chen, B. Malomed, and H. Sakaguchi, Singular mean-field states: A brief review of recent results, Condensed Matter, vol. 5, Paper No. 20, 2020.
- R. Adami and D. Noja, Existence of dynamics for a 1D NLS equation perturbed with a generalized point defect, Journal of Physics. A. Mathematical and Theoretical, vol. 42, Paper No. 495302, 2009.
- R. Adami and D. Noja, Stability and symmetry-breaking bifurcation for the ground states of a NLS with a δ1 interaction, Communications in Mathematical Physics, vol. 318, pp. 247–289, 2013.
- R. Adami, D. Noja, and N. Visciglia, Constrained energy minimization and ground states for NLS with point defects, Discrete and Continuous Dynamical Systems - Series B, vol. 18, pp. 1155–1188, 2013.
- K. Datchev and H. J, Fast soliton scattering by attractive delta impurities, Communications in Partial Differential Equations, vol. 34, pp. 1074–1113, 2009.
- R. Fukuizumi and L. Jeanjean, Stability of standing waves for a nonlinear Schrödinger equation with a repulsive Dirac delta potential, Discrete and Continuous Dynamical Systems, vol. 21, pp. 121–136, 2008.
- R. Fukuizumi, M. Otha, and T. Ozawa, Nonlinear Schrödinger equation with a point defect, Annales de l’Institut Henri Poincaré C, Analyse non linéaire, vol. 25, pp. 837–845, 2008.
- R. Goodman, P. Holmes, and M. Weinstein, Strong NLS soliton-defect interactions, Physica D: Nonlinear Phenomena, vol. 192, pp. 215–248, 2004.
- J.Holmer, J. Marzuola, and M. Zworski, Fast soliton scattering by delta impurities, Communications in Mathematical Physics, vol. 274, pp. 187–216, 2007.
- S. L. Coz, R. Fukuizumi, G. Fibich, B. Ksherim, and Y. Sivan, Instability of bound states of a nonlinear Schrödinger equation with a Dirac potential, Physica D: Nonlinear Phenomena, vol. 237, pp. 1103–1128, 2008.
- J. Murphy and K. Nakanishi, Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations, Discrete and Continuous Dynamical Systems, vol. 41, pp. 1507–1517, 2021.
- R. Adami, F. Boni, R. Carlone, and L. Tentarelli, Ground states for the planar NLSE with a point defect as minimizers of the constrained energy, Calculus of Variations and Partial Differential Equations, vol. 61, Paper No. 195, 2022.
- R. Adami, F. Boni, R. Carlone, and L. Tentarelli, Existence, structure, and robustness of ground states of a NLSE in 3D with a point defect, Journal of Mathematical Physics, vol. 63, Paper No. 071501, 2022.
- C. Cacciapuoti, D. Finco, and D. Noja, Well posedness of the nonlinear Schrödinger equation with isolated singularities, Journal of Differential Equations, vol. 305, pp. 288–318, 2021.
- C. Cacciapuoti, D. Finco, and D. Noja, Failure of scattering for the NLSE with a point interaction in dimension two and three, arXiv:2212.14216 [math-ph], 2023.
- N. Fukaya, V. Georgiev, and M. Ikeda, On stability and instability of standing waves for 2d-nonlinear Schrödinger equations with point interaction, Journal of Differential Equations, vol. 321, pp. 258–295, 2022.
- D. Finco and D. Noja, Blow-up and instability of standing waves for the NLS with a point interaction in dimension two, Zeitschrift für angewandte Mathematik und Physik, vol. 74, Paper No. 162, 2023.
- T. Fülöp and I. Tsutsui, A free particle on a circle with point interaction, Physics Letters A, vol. 264, pp. 366–374, 2000.
- F. Boni and R. Carlone, NLS ground states on the half-line with point interactions, Nonlinear Differential Equations and Applications NoDEA, vol. 30, Paper No. 51, 2023.
- R. Adami, F. Boni, and S. Dovetta, Competing nonlinearities in NLS equations as source of threshold phenomena on star graphs, Journal of Functional Analysis, vol. 283, Paper No. 109483, 2022.
- F. Boni and S. Dovetta, Prescribed mass ground states for a doubly nonlinear Schrödinger equation in dimension one, Journal of Mathematical Analysis and Applications, vol. 496, Paper No. 124797, 2021.
- F. Boni and S. Dovetta, Doubly nonlinear Schrödinger ground states on metric graphs, Nonlinearity, vol. 35, pp. 3283–3323, 2022.
- S. Albeverio, F. Gesztesy, R. Høegh-Krohn, and H. Holden, Solvable Models in Quantum Mechanics. Springer-Verlag, 1988.
- R. Adami, A Class of Schrödinger Equations with Concentrated Nonlinearity. PhD thesis, Department of Mathematics “Guido Castelnuovo”, 2000.
- M. Abramovitz and I. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables. Dover, 1965.
- M. Reed and B. Simon, Methods of modern mathematical physics. II. Fourier analysis, self-adjointness. Academic Press, 1975.
- S. Albeverio, Z. Brzežniak, and L. Dabrowski, Time-dependent propagator with point interaction, Journal of Physics. A. Mathematical and General, vol. 27, pp. 4933–4943, 1994.
- R. Adami and A. Teta, A class of nonlinear Schrödinger equations with concentrated nonlinearity, Journal of Functional Analysis, vol. 180, pp. 148–175, 2001.
- C. Carlone, M. Correggi, and L. Tentarelli, Well-posedness of the two-dimensional nonlinear Schrödinger equation with concentrated nonlinearity, Annales de l’Institut Henri Poincaré C, Analyse non linéaire, vol. 36, pp. 257–294, 2019.
- R. Adami, G. Dell’Antonio, R. Figari, and A. Teta, The Cauchy problem for the Schrödinger equation in dimension three with concentrated nonlinearity, Annales de l’Institut Henri Poincaré C, Analyse non linéaire, vol. 20, pp. 477–500, 2003.
- C. Carlone, A. Fiorenza, and L. Tentarelli, The action of Volterra integral operators with highly singular kernels on Hölder continuous, Lebesgue and Sobolev functions, Journal of Functional Analysis, vol. 273, pp. 1258–1294, 2017.
- C. Carlone, D. Finco, and L. Tentarelli, Nonlinear singular perturbations of the fractional Schrödinger equation in dimension one, Nonlinearity, vol. 32, pp. 3112–3143, 2019.
- C. Cacciapuoti, D. Finco, D. Noja, and A. Teta, The point-like limit for a NLS equation with concentrated nonlinearity in dimension three, Journal of Functional Analysis, vol. 273, pp. 1762–1809, 2017.
- R. Adami, R. Carlone, M. Correggi, and L. Tentarelli, Stability of the standing waves of the concentrated NLSE in dimension two, Mathematics in Engineering, vol. 3, pp. 1–15, 2021.
- R. Adami, D. Noja, and C. Ortoleva, Orbital and asymptotic stability for standing waves of a nonlinear Schrödinger equation with concentrated nonlinearity in dimension three, Journal of Mathematical Physics, vol. 54, Paper No. 013501, 2013.
- M. Grillakis, J. Shatah, and W. Strauss, Stability theory of solitary waves in the presence of symmetry. I, Journal of Functional Analysis, vol. 74, pp. 160–197, 1987.
- V. Buslaev, A. Komech, E. Kopylova, and D. Stuart, On asymptotic stability of solitary waves in Schrödinger equation coupled to nonlinear oscillator, Communications in Partial Differential Equations, vol. 33, pp. 669–705, 2008.
- A. Komech, E. Kopylova, and D. Stuart, On asymptotic stability of solitons in a nonlinear Schrödinger equation, Communications on Pure and Applied Analysis, vol. 11, pp. 1063–1079, 2012.
- R. Adami, D. Noja, and C. Ortoleva, Asymptotic stability for standing waves of a NLS equation with subcritical concentrated nonlinearity in dimension three: neutral modes, Discrete and Continuous Dynamical Systems - Series B, vol. 36, pp. 5837–5879, 2016.
- R. Glassey, On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations, Journal of Mathematical Physics, vol. 18, pp. 1794–179, 1977.
- R. Adami, R. Carlone, M. Correggi, and L. Tentarelli, Blow-up for the pointwise NLS in dimension two: absence of critical power, Journal of Differential Equations, vol. 269, pp. 1–37, 2020.
- R. Adami, G. Dell’Antonio, R. Figari, and A. Teta, Blow-up solutions for the Schrödinger equation in dimension three with a concentrated nonlinearity, Annales de l’Institut Henri Poincaré C, Analyse non linéaire, vol. 21, pp. 121–137, 2004.
- R. Adami and A. Teta, A simple model of concentrated nonlinearity, Operator Theory: Advances and Applications, vol. 108, pp. 183–189, 1999.
- J.Holmer and C.Liu, Blow-up for the 1d nonlinear Schrödinger equation with point nonlinearity I: Basic theory, Journal of Mathematical Analysis and Applications, vol. 483, Paper No. 123522, 2020.
- J.Holmer and C.Liu, Blow-up for the 1d nonlinear Schrödinger equation with point nonlinearity II: supercritical blow-up profiles, Communications on Pure and Applied Analysis, vol. 20, pp. 215–242, 2021.
- R. Adami, R. Fukuizumi, and J. Holmer, Scattering for the L2-supercritical point NLS, Transactions of the American Mathematical Society, vol. 374, pp. 35–60, 2021.
- T. Cazenave, Semilinear Schrödinger equations. American Mathematical Society, 2003.
- T. Tao, Nonlinear dispersive equations. Local and global analysis. American Mathematical Society, 2006.
- C. Cacciapuoti, D. Finco, D. Noja, and A. Teta, The NLS equation in dimension one with spatially concentrated nonlinearities: the pointlike limit, Letters in Mathematical Physics, vol. 104, pp. 1557–1570, 2014.
- A. Michelangeli, A. Ottolini, and R. Scandone, Fractional powers and singular perturbations of quantum differential Hamiltonians, Journal of Mathematical Physics, vol. 59, Paper No. 072106, 2018.
- J. Antoine, F. Gesztesy, and J. Shabani, Exactly solvable models of sphere interactions in quantum mechanics, Journal of Physics. A. Mathematical and General, vol. 20, pp. 3687–3712, 1987.
- J. Behrndt, P. Exner, and V. Lotoreichik, Schrödinger operators with δ-interactions supported on conical surfaces, Journal of Physics. A. Mathematical and Theoretical, vol. 47, Paper No. 355202, 2014.
- J. Behrndt, P. Exner, M. Holzmann, and V. Lotoreichik, Approximation of Schrödinger operators with δ-interactions supported on hypersurfaces, Mathematische Nachrichten, vol. 290, pp. 1215–1248, 2017.
- J. Behrndt, M. Langer, and V. Lotoreichik, Schrödinger operators with δ and δ1-potentials supported on hypersurfaces, Annales Henri Poincaré, vol. 14, pp. 385–423, 2013.
- D. Finco, L. Tentarelli, and A. Teta, Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity, arXiv:2209.13504 [math.AP], 2022.
- C. Carlone, M. Correggi, M. Falconi, and M. Olivieri, Emergence of time-dependent point interactions in polaron models, SIAM Journal on Mathematical Analysis, vol. 53, pp. 4657–4691, 2021.
- M. Correggi, M. Falconi, and M. Olivieri, Quasi-classical dynamics, Journal fo the European Mathematical Society, vol. 25, pp. 731–783, 2023.
- C. Kittel, Introduction to Solid State Physics - 8th edn. Wiley, 2004.
- T. Hmidi, A. Mantine, and F. Nier, Time-dependent delta-interactions for 1d Schrödinger Hamiltonians, Mathematical Physics, Analysis and Geometry, vol. 13, pp. 83–103, 2010.
- W. Borrelli, R. Carlone, and L. Tentarelli, Complete ionization for a non-autonomous point interaction model in d “ 2, Communications in Mathematical Physics, vol. 395, pp. 963–1005, 2022.
- M. Sayapova and D. Yafaev, The evolution operator for time-dependent potentials of zero radius, Akademiya Nauk SSSR. Trudy Matematicheskogo Instituta imeni V. A. Steklova, vol. 159, pp. 167–174, 1983.
- O. Costin, R. Costin, J. Lebowitz, and A. Rokhlenko, Evolution of a model quantum system under time periodic forcing: conditions for complete ionization, Communications in Mathematical Physics, vol. 221, pp. 1–26, 2001.
- O. Costin, R. Costin, and J. Lebowitz, Nonperturbative time dependent solution of a simple ionization model, Communications in Mathematical Physics, vol. 361, pp. 217–238, 2018.
- M. Correggi, G. Dell’Antonio, R. Figari, and A. Mantile, Ionization for three dimensional time-dependent point interactions, Communications in Mathematical Physics, vol. 257, pp. 169–192, 2005.
- G. Dell’Antonio, R. Figati, and A. Teta, The Schrödinger equation with moving point interactions in three dimensions, in Stochastic processes, physics and geometry: new interplays, I (F. Gesztesy, H. Holden, J. Jost, S. Paycha, M. Röckner, and S. Scarlatti, eds.), pp. 99–113, American Mathematical Society, 2000.