LEADER 04910nam 2200661Ia 450 001 9910452287103321 005 20200520144314.0 010 $a981-4460-15-X 035 $a(CKB)2550000001096036 035 $a(EBL)1275548 035 $a(OCoLC)854975164 035 $a(SSID)ssj0001076010 035 $a(PQKBManifestationID)11573704 035 $a(PQKBTitleCode)TC0001076010 035 $a(PQKBWorkID)11251297 035 $a(PQKB)10084384 035 $a(MiAaPQ)EBC1275548 035 $a(WSP)00008753 035 $a(PPN)189428430 035 $a(Au-PeEL)EBL1275548 035 $a(CaPaEBR)ebr10731522 035 $a(CaONFJC)MIL502611 035 $a(EXLCZ)992550000001096036 100 $a20130718d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aComplex quantum systems$b[electronic resource] $eanalysis of large Coulomb systems /$feditor: Heinz Siedentop 210 $a[Hackensack], NJ $cWorld Scientific$dc2013 215 $a1 online resource (303 p.) 225 1 $aLecture notes series,$x1793-0758 ;$vv. 24 300 $aDescription based upon print version of record. 311 $a981-4460-14-1 311 $a1-299-71360-2 320 $aIncludes bibliographical references. 327 $aCONTENTS; Foreword; Preface; Stability of Matter Rafael D. Benguria and Benjam?n A. Loewe; 1. Introduction: The stability of quantum systems: A historical overview; 2. Stability of Matter: The classical proof of Lieb and Thirring; 2.1. Stability of the hydrogen atom in non-relativistic quantum mechanics; 2.2. Stability of a system of N electrons in non-relativistic quantum mechanics; 2.3. Stability of a many particle system via Thomas-Fermi theory; 2.4. Bibliographical remarks; 3. Lieb-Thirring Inequalities 327 $a3.1. Use of commutation methods to prove the Lieb-Thirring inequality for = 3/2 in dimension 13.2. The Eden-Foias bound ([46]); 3.3. Bibliographical remarks; 4. Electrostatic Inequalities; 5. The Maximum Number of Electrons an Atom Can Bind; 5.1. The maximum number of electrons for a one center case in the Thomas-Fermi model; 5.2. Bound on Nc(Z) for the TFW model in the atomic case; 6. The Stability of Matter for a Relativistic Toy Model; 6.1. Bibliographical remarks; 7. A New Lieb-Oxford Bound with Gradient Corrections; Acknowledgments; Appendix: A Short History of the Atom; References 327 $aMathematical Density and Density Matrix Functional Theory (DFT and DMFT) Volker Bach1. Introduction; 2. Exchange Correlation and LDA; 3. Kinetic Energy and Lieb-Thirring Inequality; 4. Thomas-Fermi Theory and Stability of Matter; 5. Hartree-Fock Theory; 6. Correlation Estimate Improving the Lieb-Oxford Inequality; 7. Accuracy of the Hartree-Fock Approximation for Large Neutral Atoms; 8. N-Representability; Acknowledgments; References; On the Dynamics of a Fermi Gas in a Random Medium with Dynamical Hartree-Fock Interactions Thomas Chen; 1. Introduction; Acknowledgment 327 $aReferencesOn the Minimization of Hamiltonians over Pure Gaussian States Jan Derezinski, Marcin Napiorkowski, and Jan Philip Solovej; 1. Introduction; Acknowledgments; 2. Preliminaries; 2.1. 2nd quantization; 2.2. Wick quantization; 2.3. Bogoliubov transformations; 2.4. Pure Gaussian states; 3. Main Result; References; Variational Approach to Electronic Structure Calculations on Second-Order Reduced Density Matrices and the N-Representability Problem Maho Nakata, Mituhiro Fukuda, and Katsuki Fujisawa; 1. Introduction; 2. The Reduced-Density-Matrix Method; 2.1. Pure states and ensemble states 327 $a2.2. The first-order and second-order reduced density matrices 330 $aThis volume is based on lectures given during the program Complex Quantum Systems held at the National University of Singapore's Institute for Mathematical Sciences from 17 February to 27 March 2010. It guides the reader through two introductory expositions on large Coulomb systems to five of the most important developments in the field: derivation of mean field equations, derivation of effective Hamiltonians, alternative high precision methods in quantum chemistry, modern many body methods originating from quantum information, and - the most complex - semirelativistic quantum electrodynamics. 410 0$aLecture notes series (National University of Singapore. Institute for Mathematical Sciences) ;$vv. 24. 606 $aQuantum statistics 606 $aQuantum electrodynamics$xMathematics 608 $aElectronic books. 615 0$aQuantum statistics. 615 0$aQuantum electrodynamics$xMathematics. 676 $a530.12 701 $aSiedentop$b Heinz$0296334 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910452287103321 996 $aComplex quantum systems$91914324 997 $aUNINA