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Michelangeli A., Dell'Antonio G. (Eds.) Advances in Quantum Mechanics: Contemporary Trends and Open Problems

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Michelangeli A., Dell'Antonio G. (Eds.) Advances in Quantum Mechanics: Contemporary Trends and Open Problems
Springer International Publishing AG, 2017. — 292 p. — (Springer INdAM Series 18) — ISBN 3319589032.
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.
Table of contents
Shell Interactions for Dirac Operators
Correlation Inequalities for Classical and Quantum XY Models
Dissipatively Generated Entanglement
Abelian Gauge Potentials on Cubic Lattices
Relative-Zeta and Casimir Energy for a Semitransparent Hyperplane Selecting Transverse Modes
Analysis of Fluctuations Around Non-linear Effective Dynamics
Logarithmic Sobolev Inequalities for an Ideal Bose Gas
Spherical Schrödinger Hamiltonians: Spectral Analysis and Time Decay
On the Ground State for the NLS Equation on a General Graph
Self-Adjoint Extensions of Dirac Operator with Coulomb Potential
Dispersive Estimates for Schrödinger Operators with Point Interactions in ℝ3
Chern and Fu–Kane–Mele Invariants as Topological Obstructions
Norm Approximation for Many-Body Quantum Dynamics and Bogoliubov Theory
Effective Non-linear Dynamics of Binary Condensates and Open Problems
Remarks on the Derivation of Gross-Pitaevskii Equation with Magnetic Laplacian
On the Inverse Spectral Problems for Quantum Graphs
Double-Barrier Resonances and Time Decay of the Survival Probability: A Toy Model
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