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1. Iori, M. et al., Thermodynamic properties of ultracold Fermi gases across the BCS-BEC crossover and the Bertsch problem
2. Cacciapuoti, C., et al., Scattering theory for delta-potentials supported by locally deformed planes
3. Schmidt, J., The Massless Nelson Hamiltonian and its Domain
4. Borrelli, W. et al., A note on the Dirac operator with Kirchoff-type vertex conditions on metric graphs
5. Ourmières-Bonafos, T., Dirac operators and shell interactions: a survey
6. Lampart, J., Ultraviolet properties of a polaron model with point interactions and a number cutoff
7. Scandone, R., Zero modes and low-energy resolvent expansion for three dimensional Schrödinger operators with point interactions
8. Ottolini, A., Spectral properties of point interactions with fermionic symmetries
9. Akbas, H. and Teoman Turgut, O., Oppenheimer Type Approximation for a Simple Renormalizable System
10. Lotoreichik, V., Spectral isoperimetric inequality for the '-interaction on a contour
11. Pozzoli, E., Quantum confinement in Grushin-type manifolds
12. Gallone, M. et al., Kreın-Višik-Birman self-adjoint extension theory revisited
13. Khotyakov, M. and Michelangeli, A., Translation and adaptation from Russian of M. Sh. Birman On the theory of selfadjoint extensions of positive definite operators Math. Sb. 28 (1956), 431-450 (1956).
Intro
Preface
Contents
Thermodynamic Properties of Ultracold Fermi Gases Across the BCS-BEC Crossover and the Bertsch Problem
1 Introduction
2 BCS-BEC Crossover in the Mean Field Approximation
2.1 Mean Field Results at T = 0
3 BCS-BEC Crossover at Finite Temperature
3.1 Effective Action
3.2 Saddle Point Approximation
4 Gaussian Fluctuations
4.1 Equations for the Energy Gap and for the Number of Particles
4.2 Results for the Critical Temperature and the Bertsch Parameter
5 Conclusions
Appendix
References
4.3 Self-adjointness: Proof of Theorem 3.3
5 Concluding Remarks
References
A Note on the Dirac Operator with Kirchoff-Type Vertex Conditions on Metric Graphs
1 Introduction
2 Functional Setting
3 Self-adjointness and Spectrum
3.1 Self-adjointness
3.2 Essential Spectrum
3.3 Absence of Eigenvalues in the Spectral Gap
3.4 Graphs with Eigenvalues at the Thresholds
3.5 Graphs with Embedded Eigenvalues
4 A Model Case: The Triple Junction
5 The Form-Domain
References
Dirac Operators and Shell Interactions: A Survey
1 Introduction
3.3 Remarks and Open Problems
4 Structure of the Spectrum
4.1 A Resolvent Formula and Its Consequences
4.2 Spectral Asymptotics
References
Ultraviolet Properties of a Polaron Model with Point Interactions and a Number Cutoff
1 Introduction
2 Extension of the Free Operator and Boundary Conditions
2.1 Boundary Values
2.2 The Hamiltonian for Nmax=1
2.3 The Hamiltonians for Nmax>1
References
Zero Modes and Low-Energy Resolvent Expansion for Three Dimensional Schrödinger Operators with Point Interactions
1 Introduction and Main Results
2. Cacciapuoti, C., et al., Scattering theory for delta-potentials supported by locally deformed planes
3. Schmidt, J., The Massless Nelson Hamiltonian and its Domain
4. Borrelli, W. et al., A note on the Dirac operator with Kirchoff-type vertex conditions on metric graphs
5. Ourmières-Bonafos, T., Dirac operators and shell interactions: a survey
6. Lampart, J., Ultraviolet properties of a polaron model with point interactions and a number cutoff
7. Scandone, R., Zero modes and low-energy resolvent expansion for three dimensional Schrödinger operators with point interactions
8. Ottolini, A., Spectral properties of point interactions with fermionic symmetries
9. Akbas, H. and Teoman Turgut, O., Oppenheimer Type Approximation for a Simple Renormalizable System
10. Lotoreichik, V., Spectral isoperimetric inequality for the '-interaction on a contour
11. Pozzoli, E., Quantum confinement in Grushin-type manifolds
12. Gallone, M. et al., Kreın-Višik-Birman self-adjoint extension theory revisited
13. Khotyakov, M. and Michelangeli, A., Translation and adaptation from Russian of M. Sh. Birman On the theory of selfadjoint extensions of positive definite operators Math. Sb. 28 (1956), 431-450 (1956).
Intro
Preface
Contents
Thermodynamic Properties of Ultracold Fermi Gases Across the BCS-BEC Crossover and the Bertsch Problem
1 Introduction
2 BCS-BEC Crossover in the Mean Field Approximation
2.1 Mean Field Results at T = 0
3 BCS-BEC Crossover at Finite Temperature
3.1 Effective Action
3.2 Saddle Point Approximation
4 Gaussian Fluctuations
4.1 Equations for the Energy Gap and for the Number of Particles
4.2 Results for the Critical Temperature and the Bertsch Parameter
5 Conclusions
Appendix
References
4.3 Self-adjointness: Proof of Theorem 3.3
5 Concluding Remarks
References
A Note on the Dirac Operator with Kirchoff-Type Vertex Conditions on Metric Graphs
1 Introduction
2 Functional Setting
3 Self-adjointness and Spectrum
3.1 Self-adjointness
3.2 Essential Spectrum
3.3 Absence of Eigenvalues in the Spectral Gap
3.4 Graphs with Eigenvalues at the Thresholds
3.5 Graphs with Embedded Eigenvalues
4 A Model Case: The Triple Junction
5 The Form-Domain
References
Dirac Operators and Shell Interactions: A Survey
1 Introduction
3.3 Remarks and Open Problems
4 Structure of the Spectrum
4.1 A Resolvent Formula and Its Consequences
4.2 Spectral Asymptotics
References
Ultraviolet Properties of a Polaron Model with Point Interactions and a Number Cutoff
1 Introduction
2 Extension of the Free Operator and Boundary Conditions
2.1 Boundary Values
2.2 The Hamiltonian for Nmax=1
2.3 The Hamiltonians for Nmax>1
References
Zero Modes and Low-Energy Resolvent Expansion for Three Dimensional Schrödinger Operators with Point Interactions
1 Introduction and Main Results