# Asymptotics in Spin-Boson Type Models

@article{Dam2018AsymptoticsIS, title={Asymptotics in Spin-Boson Type Models}, author={Thomas Norman Dam and Jacob Schach M{\o}ller}, journal={Communications in Mathematical Physics}, year={2018}, volume={374}, pages={1389-1415} }

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 interaction strength tends to infinity. The main result has two applications. First of all, we show that any self-energy renormalisation scheme similar to that of the Nelson model does not converge for the three-dimensional Spin-Boson model. Secondly, we show that excited states exist in the massive Spin-Boson model for sufficiently…

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## References

SHOWING 1-10 OF 38 REFERENCES

### Spin-boson type models analyzed using symmetries

- Mathematics
- 2018

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…

### Ground States in the Spin Boson Model

- Physics, Mathematics
- 2011

We prove that the Hamiltonian of the model describing a spin which is linearly coupled to a field of relativistic and massless bosons, also known as the spin-boson model, admits a ground state for…

### Ground state(s) of the spin-boson hamiltonian

- Physics
- 1989

We establish that the finite temperature KMS states of the spin-boson hamiltonian have a limit as the temperature drops to zero. Using recent advances on the one-dimensional Ising model with long…

### Spin-boson model through a Poisson-driven stochastic process

- Mathematics
- 2012

We give a functional integral representation of the semigroup generated by the spin-boson Hamiltonian by making use of a Poisson point process and a Euclidean field. We present a method of…

### Quantum tunneling with dissipation and the Ising model over ℝ

- Physics
- 1985

We consider a quantum particle in a double-well potential, for simplicity in the two-level approximation, coupled to a phonon field. We show that static and dynamical ground state correlations of the…

### Quantum tunneling with dissipation and the Ising model over ℝ

- Physics
- 1985

We consider a quantum particle in a double-well potential, for simplicity in the two-level approximation, coupled to a phonon field. We show that static and dynamical ground state correlations of the…

### QUANTUM ELECTRODYNAMICS OF CONFINED NONRELATIVISTIC PARTICLES

- Physics
- 1998

Abstract We consider a system of finitely many nonrelativistic, quantum mechanical electrons bound to static nuclei. The electrons are minimally coupled to the quantized electromagnetic field; but we…

### Ergodicity of the Spin-Boson Model for Arbitrary Coupling Strength

- Physics
- 2014

We prove that the spin-boson system is ergodic for arbitrary strengths of the coupling between the spin and the boson bath, provided the spin tunneling matrix element is small enough.