Advances in quantum mechanics : contemporary trends and open problems

✍ Scribed by Dell'Antonio, Gianfausto; Michelangeli, Alessandro

• Year: 2017
• Tongue: English
• Leaves: 292
• Series: Springer INdAM series volume 18
• Category: Library

✦ Synopsis

This 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.

✦ Table of Contents

Front Matter ....Pages i-ix
Shell Interactions for Dirac Operators (Naiara Arrizabalaga)....Pages 1-14
Correlation Inequalities for Classical and Quantum XY Models (Costanza Benassi, Benjamin Lees, Daniel Ueltschi)....Pages 15-31
Dissipatively Generated Entanglement (Fabio Benatti)....Pages 33-45
Abelian Gauge Potentials on Cubic Lattices (M. Burrello, L. Lepori, S. Paganelli, A. Trombettoni)....Pages 47-70
Relative-Zeta and Casimir Energy for a Semitransparent Hyperplane Selecting Transverse Modes (Claudio Cacciapuoti, Davide Fermi, Andrea Posilicano)....Pages 71-97
Analysis of Fluctuations Around Non-linear Effective Dynamics (Serena Cenatiempo)....Pages 99-119
Logarithmic Sobolev Inequalities for an Ideal Bose Gas (Fabio Cipriani)....Pages 121-133
Spherical Schrödinger Hamiltonians: Spectral Analysis and Time Decay (Luca Fanelli)....Pages 135-151
On the Ground State for the NLS Equation on a General Graph (Domenico Finco)....Pages 153-167
Self-Adjoint Extensions of Dirac Operator with Coulomb Potential (Matteo Gallone)....Pages 169-185
Dispersive Estimates for Schrödinger Operators with Point Interactions in ℝ3 (Felice Iandoli, Raffaele Scandone)....Pages 187-199
Chern and Fu–Kane–Mele Invariants as Topological Obstructions (Domenico Monaco)....Pages 201-222
Norm Approximation for Many-Body Quantum Dynamics and Bogoliubov Theory (Phan Thành Nam, Marcin Napiórkowski)....Pages 223-238
Effective Non-linear Dynamics of Binary Condensates and Open Problems (Alessandro Olgiati)....Pages 239-256
Remarks on the Derivation of Gross-Pitaevskii Equation with Magnetic Laplacian (Alessandro Olgiati)....Pages 257-266
On the Inverse Spectral Problems for Quantum Graphs (M. Olivieri, D. Finco)....Pages 267-281
Double-Barrier Resonances and Time Decay of the Survival Probability: A Toy Model (Andrea Sacchetti)....Pages 283-293

✦ Subjects

Quantum theory;QUANTENTHEORIE;WISSENSCHAFTLICHE FORSCHUNG;AUFSATZSAMMLUNGEN (DOKUMENTENTYP);QUANTUM THEORY;THÉORIE QUANTIQUE;RECHERCHE SCIENTIFIQUE;SCIENTIFIC RESEARCH;COLLECTIONS OF ESSAYS (TYPE OF DOCUMENT);COLLECTIONS D'ARTICLES ET D'ESSAIS (TYPE DE DOCUMENT)