Existence of a ground state for the Nelson model with a singular perturbation

Hidaka, Takeru

doi:10.1063/1.3548076

Cited by 5 publications

(8 citation statements)

References 27 publications

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“…Models with higher order perturbations are treated in [9], [11], [13] and [21]. Spin-boson type models are treated in [11], [13] and [21], but the authors assume either that the field is massive or that the coupling is weak.…”

Section: Introductionmentioning

confidence: 99%

“…Spin-boson type models are treated in [11], [13] and [21], but the authors assume either that the field is massive or that the coupling is weak. The results in [9] does not assume weak coupling or a massive field, but the model treated in that paper is not the spin-boson model and rather strong infrared conditions are assumed. Furthermore, the author of [9] only proves selfadjointness of the Hamiltonian and existence of ground states, while we treat several other questions as well.…”

Section: Introductionmentioning

confidence: 99%

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Spin-Boson type models analysed using symmetries

Dam,

Møller

2018

Preprint

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In this paper, we analyse a family of models for a qubit interacting with a bosonic field. This family of models is very large and contains models where higher order perturbations of field operators are added to the Hamiltonian. The Hamiltonian has a special symmetry, called spin-parity symmetry, which plays a central role in our analysis. Using this symmetry, we find the domain of selfadjointness and decompose the Hamiltonian into two fiber operators each defined on Fock space. We then prove an HVZ theorem for the fiber operators and single out a particular fiber operator which has a ground state if and only if the full Hamiltonian has a ground state. From these results we deduce a simple criterion for the existence of an exited state.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spin-Boson type models analysed using symmetries

Dam,

Møller

2018

Preprint

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“…We give our strategy comparing with some related works. Self-adjointness: To show the self-adjointness of H, we apply the method in [15]. A key lemma is that the interaction term is H-bounded.…”

Section: Introductionmentioning

confidence: 99%

“…After that, we consider the mass zero limit of the massive ground state. In the massive case, we apply methods used in [7,8,15] and references therein. In these methods the so-called Number-Energy Estimate is an important lemma to show the existence of a ground state of the massive Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

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Spectral analysis of a massless charged scalar field with cutoffs

Wada¹

2017

Hokkaido Math. J.

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The quantum system of a massless charged scalar field with a self-interaction is investigated. By introducing a spacial cut-off function, the Hamiltonian of the system is realized as a linear operator on a boson Fock space. It is proven that the Hamiltonian strongly commutes with the total charge operator. This fact implies that the state space of the charged scalar field is decomposed into the infinite direct sum of fixed total charge spaces. Moreover, under certain conditions, the Hamiltonian is bounded below, self-adjoint and has a ground ground state for an arbitrarily coupling constant. A relation between the total charge of the ground state and a number operator bound is also revealed.

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Ground states of quantum electrodynamics with cutoffs

Takaesu

2018

Journal of Mathematical Physics

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In this paper, we investigate a system of quantum electrodynamics with cutoffs. The total Hamiltonian is defined on a tensor product of a fermion Fock space and a boson Fock. It is shown that, under spatially localized conditions and momentum regularity conditions, the total Hamiltonian has a ground state for all values of coupling constants. In particular, its multiplicity is finite. MSC 2010 : 47A10, 81Q10. key words : Fock spaces, Spectral analysis, Quantum Electrodynamics. [T, J 0 ]h [T, J ∞ ]h , h ∈ D([T, J 0 ]) ∩ D([T, J ∞ ]).(ii) Fermion Fock Space on X ⊕ X Let X be a complex Hilbert space. Let J f = J 0 f J ∞ f , J 0 f , J ∞ f ∈ L(X) and B f = B 0 f B ∞ f , B 0 f , B ∞ f ∈

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Existence of a ground state for the Nelson model with a singular perturbation

Abstract: The existence of a ground state of the Nelson Hamiltonian with perturbations of the form 4 j=1 c j φ j with c 4 > 0 is considered. The self-adjointness of the Hamiltonian and the existence of a ground state are proven for arbitrary values of coupling constants.

Cited by 5 publications

References 27 publications

Spin-Boson type models analysed using symmetries

Spin-Boson type models analysed using symmetries

Spectral analysis of a massless charged scalar field with cutoffs

Ground states of quantum electrodynamics with cutoffs

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