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Journal of Modern Optics

Field theory reformulated without self-energy parts

Michel De Haan

Published Nov 10, 2005• 0 citations
Publisher

Abstract

The intuitive description of atomic levels requires the use of renormalized objects, with lifetime and dressed atomic levels. The reformulation of field theory for avoiding self-energy parts in the dynamical evolution enables us to provide such a description outside the scope of the usual quantum mechanics. That approach is illustrated here on a two-level system, interacting with a field, inside and outside the rotating wave approximation (RWA). A kinetic extension of the description is reached, enabling a statistical mixture to change its composition with time. The original reversible description is embedded in the new one and is recovered now from a restricted class of initial conditions. After dressing, the structure of the kinetic operators inside and outside the RWA is now common.

DOI
10.1080/09500340500275405

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The intuitive description of atomic levels requires the use of renormalized objects, with lifetime and dressed atomic levels. The reformulation of field theory for avoiding self-energy parts in the dynamical evolution enables us to provide such a description outside the scope of the usual quantum mechanics. That approach is illustrated here on a two-level system, interacting with a field, inside and outside the rotating wave approximation (RWA). A kinetic extension of the description is reached, enabling a statistical mixture to change its composition with time. The original reversible description is embedded in the new one and is recovered now from a restricted class of initial conditions. After dressing, the structure of the kinetic operators inside and outside the RWA is now common.
The compatibility of irreversibility, as expressed by the second law of thermodynamics, with ordinary quantum mechanics requires an extension of the latter. Such an extension of a reversible formalism is made possible by the presence of self-energy processes (already found in quantum electrodynamics), which allows for the widening of the dynamics through the introduction of specific additional variables leading to the recognition of such processes. A projection technique modeled on that introduced long ago by the Brussels group defines a subdynamics that is shown to contain the starting formulation in its entirety. (It corresponds to a restricted class of initial conditions, namely the reversible ones.) A new kinetic description is obtained in which, e.g., collision processes for privileged components arise from the original interaction. This method is applied successively to various models, and we focus in this paper on the possible presence of temporal behaviour excluded in ordinary quantum mechanics. Among the differences between this framework and that of ordinary quantum mechanics, the possibility appears for the purely exponential decay of a particle, while ordinary quantum mechanics requires long time tails associated with the finite lower bound in the spectrum of the Hamiltonian.
Interactions between a source of light and atoms are ubiquitous in nature. The study of them is interesting on the fundamental level as well as for applications. They are at the core of quantum information processing tasks and quantum thermodynamics protocols. However, even for a two-level atom interacting with a field in rotating wave approximation there exists no exact solution. This touches upon a basic problem in quantum field theory, where we can only calculate the transitions in the time asymptotic limits (i.e., minus and plus infinity), while we are not able to trace the evolution. In this paper we want to get more insight into the time evolution of a total system of a two-level atom and a continuous-mode quantum field. We propose an approximation, which we are able to apply systematically to each order of Dyson expansion, resulting in a greatly simplified formula for the evolution of the combined system at any time. Our tools include a proposed non-Hermitian renormalization method. As a sanity check, by applying our framework, we derive the known optical Bloch equations.
The compatibility of irreversibility, as expressed by the second law of thermodynamics, with ordinary quantum mechanics is a challenging problem. Our solution requires an extension of the latter. Such an extension of a reversible formalism is made possible by the presence of self‐energy processes (already found in quantum electrodynamics) which enables the widening of the dynamics by the introduction of specific additionnal variables leading to the recognition of such processes. A projection technique modeled on the one introduced long ago by the Brussels group defines a subdynamics which is shown to contain entirely the starting formulation (it corresponds now to a restricted class of initial conditions, namely the reversible one). A new kinetic description is obtained in which e.g. collision processes for privileged components arise from the original interaction. This method is applied successively to various models and we focus in this paper on the possible presence of temporal behaviours excluded in ordinary quantum mechanics. Among those differences, the possibility appears of a purely exponential decay for a particle while ordinary quantum mechanics requires long time tails associated with the finite lower bound in the spectrum of the Hamiltonian.
Abstract A challenging problem facing physicists is the compatibility of irreversibility, as expressed by the second law of thermodynamics, with ordinary quantum mechanics. We present a solution through an extension of the latter. The presence of self‐energy processes (already found in quantum electrodynamics) is fully exploited to get an extension of a reversible formalism. They enable the widening of the dynamics by the introduction of specific auxiliary variables, leading to the recognition of such processes. A projection technique modeled on the one introduced long ago by the Brussels group defines a subdynamics that is shown to contain entirely the starting formulation (it corresponds to a restricted class of initial conditions, namely, the reversible one). A new kinetic description is obtained in which, for example, collision processes for privileged components arise from the original interaction. A very simple model and its generalizations are considered. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004
We use the path-integral technique to solve the quantum-mechanical problem of interaction of a single two-level atom with a single-mode quantized field without the rotating-wave approximation (RWA). We calculate the full spin-Bose propagator in the form of a matrix as an expansion around a path corresponding to the RWA. The effect of energy-nonconserving terms on the atomic population inversion is studied, and we show that even under the conditions in which the RWA is considered to be valid there is a significant effect on the atomic inversion due to these terms.
Abstract We investigate the applicability of the two major approximations which are most commonly employed in the study of the quantum Rabi model, namely the description of a resonant cavity mode as a single-mode quantized field and the use of the rotating wave approximation. Starting from the Hamiltonian of a two-level system interacting with a multi-mode quantized field, we perform the canonical transformation of the field operators. This allows one to partition the Hamiltonian of the system into two parts. The first part is the interaction of the two-level system with a single collective field mode, while the second one describes the interaction with field fluctuations. The first part is usually associated with the resonant cavity mode. This division enables us to determine the applicability condition of the single-mode approximation. In addition we identify simple approximate relations for the description of the eigenstates, eigenfunctions and the time evolution of the quantum Rabi model beyond the rotating wave approximation.