C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians

Amrein, Werner O.; Monvel, Anne Boutet de; Georgescu, Vladimir

doi:10.1007/978-3-0348-0733-3

Cited by 260 publications

(692 citation statements)

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“…In this section we describe the conjugate operator method in the version of Amrein, Boutet de Monvel, Georgescu, and Sahbani [1,23]. In the paper of Sahbani the theory of Amrein et al is generalized in a way that is crucial for our paper.…”

Section: B Conjugate Operator Methodsmentioning

confidence: 99%

Spectral Theory for the Standard Model of Non-Relativistic QED

Fröhlich

Griesemer

Sigal

2008

Commun. Math. Phys.

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For a model of atoms and molecules made from static nuclei and non-relativistic electrons coupled to the quantized radiation field (the standard model of non-relativistic QED), we prove a Mourre estimate and a limiting absorption principle in a neighborhood of the ground state energy. As corollaries we derive local decay estimates for the photon dynamics, and we prove absence of (excited) eigenvalues and absolute continuity of the energy spectrum near the ground state energy, a region of the spectrum not understood in previous investigations.The conjugate operator in our Mourre estimate is the second quantized generator of dilatations on Fock space.

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Section: B Conjugate Operator Methodsmentioning

confidence: 99%

Spectral Theory for the Standard Model of Non-Relativistic QED

Fröhlich

Griesemer

Sigal

2008

Commun. Math. Phys.

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“…Therefore, M 1 (0) is the sum of the unitary and self-adjoint operator u, the self-adjoint and compact operator n∈Z k (λ) ⊥ v Pnv β k,n (λ) 2 , and the compact operator with non-negative imaginary part i n∈Z k (λ) − v Pnv β k,n (λ) 2 . So, since S 0 is an orthogonal projection with finite-dimensional kernel, the operator I 1 (0) = S 0 M 1 (0)S 0 acting in the Hilbert space S 0 L 2 (T) can also be written as the sum of a unitary and self-adjoint operator, a self-adjoint and compact operator, and a compact operator with non-negative imaginary part.…”

Section: Resolvent Expansions For H V Kmentioning

confidence: 99%

Spectral and scattering properties at thresholds for the Laplacian in a half-space with a periodic boundary condition

Richard

Aldecoa

2017

Journal of Mathematical Analysis and Applications

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“…Using the stationary formalism of [Kur73] and the commutator methods of [ABG96], we show in Section 3.1 some results concerning short-range scattering theory in waveguides. In Theorem 3.4, we obtain limiting absorption principles (which lead to the existence of the wave operators) and state spectral properties of the total Hamiltonian.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Time Delay and Short-Range Scattering in Quantum Waveguides

Aldecoa

2006

Ann. Henri Poincaré

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Although many physical arguments account for using a modified definition of time delay in multichannel-type scattering processes, one can hardly find rigorous results on that issue in the literature. We try to fill in this gap by showing, both in an abstract setting and in a short-range case, the identity of the modified time delay and the Eisenbud-Wigner time delay in waveguides. In the short-range case we also obtain limiting absorption principles, state spectral properties of the total Hamiltonian, prove the existence of the wave operators and show an explicit formula for the S-matrix. The proofs rely on stationary and commutator methods.

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C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians

Cited by 260 publications

References 0 publications

Spectral Theory for the Standard Model of Non-Relativistic QED

Spectral Theory for the Standard Model of Non-Relativistic QED

Spectral and scattering properties at thresholds for the Laplacian in a half-space with a periodic boundary condition

Time Delay and Short-Range Scattering in Quantum Waveguides

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