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Thomas Norman Dam

Publications and source records attributed to Thomas Norman Dam.

4 recordsLinked to original sources
arXiv2022

Absence of Ground States in the Renormalized Massless Translation-Invariant Nelson Model

We consider a model for a massive uncharged non-relativistic particle interacting with a massless bosonic field, widely referred to as the Nelson model. It is well known, that an ultraviolet renormalized Hamilton operator exists in this case. Further, due to translation-invariance, it decomposes into fiber operators. In this paper, we treat the renormalized fiber operators. We give a description of the operator and form domains and prove that the fiber operators do not have a ground state. Our results hold for any non-zero coupling constant and arbitrary total momentum. Our proof for the absence of ground states is a new generalization of methods recently applied to related models. A major enhancement we provide, is that the method can be applied to models with degenerate ground state eigenspaces.

math-ph↗
arXiv2018

Asymptotics in Spin-Boson type models

In this paper we investigate a family of models for a qubit interacting with a bosonic field. More precisely, we find asymptotic limits of the Hamiltonian as the strength of the interaction tends to infinity. The main result has two applications. First of all, we show that self-energy renormalisation schemes similar to that of the Nelson model will never give a physically interesting result. This is because any limit obtained through such a scheme would be independent of the qubit. Secondly, we find that exited states exist in the massive Spin-Boson models for sufficiently large interaction strengths. We are also able to compute the asymptotic limit of many physical quantities.

math-ph↗
arXiv2018

Spin-Boson type models analysed using symmetries

In this paper we analyse a family of models for a qubit interacting with a bosonic field. These models have a parity symmetry, which enables them to have a ground state even in some infrared irregular cases. In this paper we investigate this symmetry and consider higher order perturbations of field operators to any even order. 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 each operator under minimal conditions, and show that the ground state is always associated with the same fiber operator, while eigenvalues of the other fiber operator corresponds to exited states. Thus the problem of analysing the ground state and exited states is reduced to a simpler problem on Fock space.

math-ph↗