LEADER 03688oam 2200457 450 001 996466551303316 005 20210629165655.0 010 $a3-030-60453-5 024 7 $a10.1007/978-3-030-60453-0 035 $a(CKB)4100000011746999 035 $a(DE-He213)978-3-030-60453-0 035 $a(MiAaPQ)EBC6469878 035 $a(PPN)253860121 035 $a(EXLCZ)994100000011746999 100 $a20210629d2021 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aMathematical challenges of zero-range physics $emodels, methods, rigorous results, open problems /$fAlessandro Michelangeli, editor 205 $a1st ed. 2021. 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (VIII, 329 p. 16 illus., 9 illus. in color.) 225 1 $aSpringer INdAM Series ;$vVolume 42 311 $a3-030-60452-7 327 $a1. Iori, M. et al., Thermodynamic properties of ultracold Fermi gases across the BCS?BEC crossover and the Bertsch problem -- 2. Cacciapuoti, C., et al., Scattering theory for delta-potentials supported by locally deformed planes -- 3. Schmidt, J., The Massless Nelson Hamiltonian and its Domain -- 4. Borrelli, W. et al., A note on the Dirac operator with Kirchoff-type vertex conditions on metric graphs -- 5. Ourmières-Bonafos, T., Dirac operators and shell interactions: a survey -- 6. Lampart, J., Ultraviolet properties of a polaron model with point interactions and a number cutoff -- 7. Scandone, R., Zero modes and low-energy resolvent expansion for three dimensional Schrödinger operators with point interactions -- 8. Ottolini, A., Spectral properties of point interactions with fermionic symmetries -- 9. Akbas, H. and Teoman Turgut, O., Oppenheimer Type Approximation for a Simple Renormalizable System -- 10. Lotoreichik, V., Spectral isoperimetric inequality for the ??-interaction on a contour -- 11. Pozzoli, E., Quantum confinement in Grushin-type manifolds -- 12. Gallone, M. et al., Kre?n-Vi?ik-Birman self-adjoint extension theory revisited -- 13. Khotyakov, M. and Michelangeli, A., Translation and adaptation from Russian of M. Sh. Birman On the theory of selfadjoint extensions of positive definite operators Math. Sb. 28 (1956), 431-450 (1956). 330 $aSince long over the decades there has been a large transversal community of mathematicians grappling with the sophisticated challenges of the rigorous modelling and the spectral and scattering analysis of quantum systems of particles subject to an interaction so much localised to be considered with zero range. Such a community is experiencing fruitful and inspiring exchanges with experimental and theoretical physicists. This volume reflects such spirit, with a diverse range of original contributions by experts, presenting an up-to-date collection of most relevant results and challenging open problems. It has been conceived with the deliberate two-fold purpose of serving as an updated reference for recent results, mathematical tools, and the vast related literature on the one hand, and as a bridge towards several key open problems that will surely form the forthcoming research agenda in this field. 410 0$aSpringer INdAM series ;$vVolume 42. 606 $aMathematical physics 615 0$aMathematical physics. 676 $a530.15 702 $aMichelangeli$b Alessandro 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bUtOrBLW 906 $aBOOK 912 $a996466551303316 996 $aMathematical challenges of zero-range physics$92831543 997 $aUNISA