On generalized spin-boson models with singular perturbations

Abstract

In this paper we consider generalized spin-boson models with singular perturbations. It is proven that under the infrared regularity condition Hamiltonians have the unique ground state for sufficiently small values of coupling constants. In addition it is shown that the asymptotic creation and annihilation operators of massless boson field exist.

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

“…Miyao and Sasaki [20] show the existence of the ground state for a generalized spinboson model with φ 2 -perturbation, and it is not supposed that the particle Hamiltonian has a compact resolvent. Takaesu [24] shows the existence of a ground state for a generalized spin-boson model with a singular perturbation of the form (1.3) but for sufficiently small coupling constants.…”

Quantum regression beyond the Born-Markov approximation for generalized spin-boson models

“…For this reason, apart from their fundamental interest, they also find applications in quantum optics [1,4,[6][7][8], quantum information and simulation [12], and quantum phase transitions [13], to name a few. The interest in such models has also led to an extensive study of their mathematical properties [14][15][16][17][18][19][20][21]; the wider class of generalized spin-boson (GSB) models, which accommodates multilevel atoms, has also been investigated [22][23][24][25][26].…”

Spectral analysis of a massless charged scalar field with cutoffs

“…Hence from Lebesgue's dominated convergence theorem, we see that S 2 (k)Φ m is strongly differentiable and its strong derivative is −iS 2,l (k)Φ m . By using the Leibniz rule for (24), we obtain the desired results.…”

“…Recently, some singular perturbed models are studied. Takaesu [24] considered the generalized spin-boson model with φ 4 -perturbation. He showed the existence of a ground state and the existence of asymptotic fields for a sufficiently small coupling constant.…”