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Table of Contents
Preface; Contents; About the Editors; Shell Interactions for Dirac Operators; 1 Introduction and Main Results; 1.1 Self-Adjointness for H+V; 1.2 Point Spectrum for H+V; 1.2.1 Applications to Electrostatic Shell Potentials; 1.3 Isoperimetric-Type Inequality; 2 On the Proof of the Main Results; 2.1 Monotonicity; 2.2 Quadratic Forms; 2.3 The Isoperimetric-Type Inequality; References; Correlation Inequalities for Classical and Quantum XY Models; 1 Setting and Results; 2 Comparison Between Ising and XY Models; 3 Proofs for the Classical XY Model
3.1 Griffiths and FKG Inequalities, and Proof of Theorem 1.13.2 Proof of Theorem 1.3; 3.3 Proof of Theorem 2.1; 4 Proof for the Quantum XY Model; References; Dissipatively Generated Entanglement; 1 Introduction; 2 Dissipative Entanglement Generation; 2.1 Checking Entanglement Generation; 2.2 Case 1: Z Does Not Generate Entanglement; 2.3 Case 2: Z Generates Entanglement; 3 Conclusions; References; Abelian Gauge Potentials on Cubic Lattices; 1 Introduction; 2 Realization of Artificial Magnetic Fluxes in Optical Lattice Systems; 2.1 An Effective Description for Periodically Driven Systems
2.2 Artificial Gauge Potentials from Lattice Shaking2.3 Artificial Gauge Potential from Laser-Assisted Tunneling; 3 Cubic Lattice Tight-Binding Models with Commensurate Flux; 3.1 Isotropic Flux; 3.2 Generalization: Anisotropic Abelian Lattice Fluxes; 4 Two Applications of Synthetic Gauge Potentials in 1D Rings; 4.1 Quantum State Transfer in a Ring Pierced by a Magnetic Flux; 4.2 Violation of the Area-Law in Long-Range Systems; References; Relative-Zeta and Casimir Energy for a Semitransparent Hyperplane Selecting Transverse Modes; 1 Introduction; 2 The General Framework
2.2 Choice of the Class of Initial States in the Gross-Pitaevskii Regime3 Norm Approximation Result and Ideas of the Proof; 4 Conclusions and Open Problems; References; Logarithmic Sobolev Inequalities for an Ideal Bose Gas; 1 Introduction; 2 Logarithmic Sobolev Inequalities for Ideal Bosons Gas in Finite Volume; References; Spherical Schrödinger Hamiltonians: Spectral Analysisand Time Decay; 1 Introduction; 2 A Stationary Viewpoint: Hardy's Inequality; 3 Decay Estimates: Main Results; References; On the Ground State for the NLS Equation on a General Graph; 1 Introduction; 2 Main Result
3.1 Griffiths and FKG Inequalities, and Proof of Theorem 1.13.2 Proof of Theorem 1.3; 3.3 Proof of Theorem 2.1; 4 Proof for the Quantum XY Model; References; Dissipatively Generated Entanglement; 1 Introduction; 2 Dissipative Entanglement Generation; 2.1 Checking Entanglement Generation; 2.2 Case 1: Z Does Not Generate Entanglement; 2.3 Case 2: Z Generates Entanglement; 3 Conclusions; References; Abelian Gauge Potentials on Cubic Lattices; 1 Introduction; 2 Realization of Artificial Magnetic Fluxes in Optical Lattice Systems; 2.1 An Effective Description for Periodically Driven Systems
2.2 Artificial Gauge Potentials from Lattice Shaking2.3 Artificial Gauge Potential from Laser-Assisted Tunneling; 3 Cubic Lattice Tight-Binding Models with Commensurate Flux; 3.1 Isotropic Flux; 3.2 Generalization: Anisotropic Abelian Lattice Fluxes; 4 Two Applications of Synthetic Gauge Potentials in 1D Rings; 4.1 Quantum State Transfer in a Ring Pierced by a Magnetic Flux; 4.2 Violation of the Area-Law in Long-Range Systems; References; Relative-Zeta and Casimir Energy for a Semitransparent Hyperplane Selecting Transverse Modes; 1 Introduction; 2 The General Framework
2.2 Choice of the Class of Initial States in the Gross-Pitaevskii Regime3 Norm Approximation Result and Ideas of the Proof; 4 Conclusions and Open Problems; References; Logarithmic Sobolev Inequalities for an Ideal Bose Gas; 1 Introduction; 2 Logarithmic Sobolev Inequalities for Ideal Bosons Gas in Finite Volume; References; Spherical Schrödinger Hamiltonians: Spectral Analysisand Time Decay; 1 Introduction; 2 A Stationary Viewpoint: Hardy's Inequality; 3 Decay Estimates: Main Results; References; On the Ground State for the NLS Equation on a General Graph; 1 Introduction; 2 Main Result