Positive commutators, Fermi golden rule and the spectrum of zero temperature Pauli-Fierz Hamiltonians

On the self-adjointness and domain of Pauli-Fierz type Hamiltonians

We prove a general theorem about the self-adjointness and domain of Pauli-Fierz type Hamiltonians. Our proof is based on commutator arguments which allow us to treat fields with non-commuting components. As a corollary it follows that the domain of the Hamiltonian of non-relativistic QED with Coulomb interactions is independent of the coupling constant.

Pauli-Fierz 算子的时间演化（Markov 近似与 Rabi 周期）

Time evolution for the Pauli-Fierz operator (Markov approximation and Rabi cycle)

本文研究 Pauli-Fierz Hamiltonian 支配的非相对论 QED 系统在 Markov 与非 Markov 情形下的时间演化近似，给出误差控制，并在此基础上证明 Markov 情形下边缘跃迁概率的指数衰减以及非 Markov 情形下的 Rabi 周期。

Ionization of Atoms in a Thermal Field

We study the stationary states of a quantum mechanical system describing an atom coupled to black-body radiation at positive temperature. The stationary states of the non-interacting system are given by product states, where the particle is in a bound state corresponding to an eigenvalue of the particle Hamiltonian, and the field is in its equilibrium state. We show that if Fermi's Golden Rule predicts that a stationary state disintegrates after coupling to the radiation field then it is unstable, provided the coupling constant is sufficiently small (depending on the temperature). The result i…