Spectral Analysis of Relativistic Atoms – Interaction with the Quantized Radiation Field

تابش چرنکوف نسبیتی در حضور محیط دی‌الکتریک مغناطیده

In this paper, relativistic Cherenkov radiation was studied in a 3-D magneto-dielectric medium. Electric permittivity and magnetic permeability of the medium as functions of frequency, are assumed to satisfy Kramers- Kronig equations. A new interaction Hamiltonian, which is different from Hamiltonian term in non-relativistic state, was introduced by the quantized vector potential field and part...

Spectral Analysis for Systems of Atoms and Molecules coupled to the Quantized Radiation Field

Mourre Estimate and Spectral Theory for the Standard Model of Non-Relativistic QED

For a model of atoms and molecules made from static nuclei and non-relativistic electrons coupled to the quantized radiation field (the standard model of non-relativistic QED), we prove a Mourre estimate and a limiting absorption principle in a neighborhood of the ground state energy. As corollaries we derive local decay estimates for the photon dynamics, and we prove absence of (excited) eigen...

Spectral Theory for the Standard Model of Non-Relativistic QED

For a model of atoms and molecules made from static nuclei and non-relativistic electrons coupled to the quantized radiation field (the standard model of non-relativistic QED), we prove a Mourre estimate and a limiting absorption principle in a neighborhood of the ground state energy. As corollaries we derive local decay estimates for the photon dynamics, and we prove absence of (excited) eigen...

Asymptotic Electromagnetic Fields in Models of Quantum-Mechanical Matter Interacting with the Quantized Radiation Field

In models of (non-relativistic and pseudo-relativistic) electrons interacting with static nuclei and with the (ultraviolet-cutoff) quantized radiation field, the existence of asymptotic electromagnetic fields is established. Our results yield some mathematically rigorous understanding of Rayleigh scattering and of the phenomenon of relaxation of isolated atoms to their ground states. Our proofs...