Second-order Formulation and Scaling in the Lossy Spin-Boson Model

In the Fleischmann–Pons experiment, energy is produced without commensurate energetic reaction products. To account for this we have proposed new models in which coherent energy exchange occurs between two-level systems with a large energy quantum, and an oscillator with a much smaller characteristic energy. In earlier work we demonstrated using perturbation theory that the lossy spin-boson model is capable of efficient coherent energy exchange when many oscillator quanta are exchanged for a two-level system quanta on resonance. Here we introduce a formulation that isolates nearly degenerate states in the lossy spin-boson model, and allows the computation of the self-energy and indirect coupling matrix elements. From calculations of simple lossy spin boson models we establish a scaling law and define the dimensionless coupling constant g for the system. Direct calculations using this approach is not possible for large models in which a great many oscillator quanta are exchanged, but the formulation provides a foundation for understanding this kind of model, and will allow us to develop more powerful approximate methods. © 2011 ISCMNS. All rights reserved.