LEADER 04731nam 22006855 450 001 9910254299503321 005 20210628225659.0 010 $a3-319-58904-0 024 7 $a10.1007/978-3-319-58904-6 035 $a(CKB)3710000001631058 035 $a(MiAaPQ)EBC4935642 035 $a(DE-He213)978-3-319-58904-6 035 $a(PPN)203851927 035 $a(EXLCZ)993710000001631058 100 $a20170802d2017 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aAdvances in Quantum Mechanics $eContemporary Trends and Open Problems /$fedited by Alessandro Michelangeli, Gianfausto Dell'Antonio 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (292 pages) 225 1 $aSpringer INdAM Series,$x2281-518X ;$v18 311 $a3-319-58903-2 320 $aIncludes bibliographical references at the end of each chapters. 327 $a1 Shell interactions for Dirac operators -- 2 Correlation inequalities for classical and quantum XY models -- 3 Dissipatively generated entanglement -- 4 Abelian gauge potentials on cubic lattices -- 5 Relative-Zeta and Casimir energy for a semitransparent hyperplane selecting transverse modes -- 6 Analysis of fluctuations around non-linear effective dynamics -- 7 Logarithmic Sobolev inequalities for an ideal Bose gas -- 8 Spherical Schrödinger Hamiltonians: spectral analysis and time decay -- 9 On the Ground state for the NLS equation on a general graph -- 10 Self-adjoint extensions of the Dirac operator with Coulomb potential -- 11 Dispersive estimates for Schrödinger operators with point interactions in R3 -- 12 Chern and Fu?Kane?Mele invariants as topological obstructions -- 13 Norm approximation for many-body quantum dynamics and Bogoliubov theory -- 14 Effective non-linear dynamics of binary condensates and open problems -- 15 Remarks on the derivation of the Gross-Pitaevskii equation with magnetic Laplacian -- 16 On the inverse spectral problems for quantum graphs -- 17 Double-barrier resonances and time decay of the survival probability: a toy model. 330 $aThis volume collects recent contributions on the contemporary trends in the mathematics of quantum mechanics, and more specifically in mathematical problems arising in quantum many-body dynamics, quantum graph theory, cold atoms, unitary gases, with particular emphasis on the developments of the specific mathematical tools needed, including: linear and non-linear Schrödinger equations, topological invariants, non-commutative geometry, resonances and operator extension theory, among others. Most of contributors are international leading experts or respected young researchers in mathematical physics, PDE, and operator theory. All their material is the fruit of recent studies that have already become a reference in the community. Offering a unified perspective of the mathematics of quantum mechanics, it is a valuable resource for researchers in the field. 410 0$aSpringer INdAM Series,$x2281-518X ;$v18 606 $aFunctional analysis 606 $aMathematical physics 606 $aOperator theory 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005 606 $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003 615 0$aFunctional analysis. 615 0$aMathematical physics. 615 0$aOperator theory. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 14$aFunctional Analysis. 615 24$aMathematical Physics. 615 24$aOperator Theory. 615 24$aTheoretical, Mathematical and Computational Physics. 615 24$aApplications of Mathematics. 676 $a530.12 702 $aMichelangeli$b Alessandro$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aDell'Antonio$b G. F.$f1933-.$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254299503321 996 $aAdvances in Quantum Mechanics$91562264 997 $aUNINA