One-boson scattering processes in the massless Spin-Boson model – A non-perturbative formula

Ballesteros, Miguel; Deckert, Dirk-André; Hänle, Felix

doi:10.1016/j.aim.2020.107248

Cited by 6 publications

(3 citation statements)

References 28 publications

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“…Remark 2.8. We note that a relation similar to (2.15) has been shown in [5] for the spin boson model. In contrast to the spin boson model there is in non-relativistic qed an additional term in the T -matrix, which comes from the quadratic expressions of the field operators in the Hamiltonian.…”

Section: Hypothesis Bsupporting

confidence: 82%

“…The relation which we obtain, can be used to calculate expansions of the one photon scattering matrix using well established results about the ground state, resonance states, and boundary values of the resolvent [3,4,1,25,18,13,16,17]. We note that an analogous relation has been obtained for the spin boson model, where the leading order expansion has been studied in connection with resonances [6,5]. For the hydrogen atom with a spinless electron expansions of the scattering matrix have been studied in [2] using the LSZ formalism combined with iterated perturbation theory.…”

Section: Introductionsupporting

confidence: 56%

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On one photon scattering in non-relativistic qed

Hasler¹

2021

Preprint

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Section: Hypothesis Bsupporting

confidence: 82%

Section: Introductionsupporting

confidence: 56%

On one photon scattering in non-relativistic qed

Hasler¹

2021

Preprint

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“…Ideas and techniques from the NR QED were extended to the Nelson and spinboson models of the condensed matter physics 19 in [40,43,44,42,240,242,87,184,186,234,275,278,280].…”

mentioning

confidence: 99%

Differential Equations of Quantum Mechanics

Sigal

2022

Preprint

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We review very briefly the main mathematical structures and results in some important areas of Quantum Mechanics involving PDEs and formulate open problems. Contents 1. Preface 1 Acknowledgments 2 2. Schrödinger equation 2 3. Including photons (Nonrelativistic QED) 4 4. Effective Equations 6 5. Hartree-Fock-Bogolubov system 8 6. Bogolubov-de Gennes system 9 7. Ginzburg-Landau equations 12 8. Summary 14 9. Remarks on literature 15 Appendix A. The NR QED Hamiltonian 17 Appendix B. Hartree-Fock-Bogolubov equations 18 Appendix C. Bogolubov-de Gennes Equations: Discussion 19 References 20 1 ONEPAS and MCQM stand for Online Northeast PDE and Analysis Seminar and Mathematical Challenges in Quantum Mechanics.

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Infraparticle States in the Massless Nelson Model: Revisited

Beaud

Dybalski

Graf

2023

Ann. Henri Poincaré

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We provide a new construction of infraparticle states in the massless Nelson model. The approximating sequence of our infraparticle state does not involve any infrared cut-offs. Its derivative w.r.t. the time parameter t is given by a simple explicit formula. The convergence of this sequence as $$t\rightarrow \infty $$ t → ∞ to a nonzero limit is then obtained by the Cook method combined with stationary phase estimates. To apply the latter technique, we exploit recent results on regularity of ground states in the massless Nelson model, which hold in the low coupling regime.

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One-boson scattering processes in the massless Spin-Boson model – A non-perturbative formula

Cited by 6 publications

References 28 publications

On one photon scattering in non-relativistic qed

On one photon scattering in non-relativistic qed

Differential Equations of Quantum Mechanics

Infraparticle States in the Massless Nelson Model: Revisited

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