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Interaction Representation
Published in David K. Ferry, An Introduction to Quantum Transport in Semiconductors, 2017
This last equation is known as Dyson’s equation and represents a resummation of the diagrams and perturbation theory. This is more easily expressed by taking the last term to the left-hand side and rewriting everything as () G(k,ω)=G0(k,ω)1−G0(k,ω)Σ(k,ω)=1[G0(k,ω)]−1−Σ(k,ω),
Quantum Dynamics of Phase and Charge in Josephson Junctions
Published in Andrei D. Zaikin, Dmitry S. Golubev, Dissipative Quantum Mechanics of Nanostructures, 2019
Andrei D. Zaikin, Dmitry S. Golubev
where in the last equation, we employed an extension of Poisson resummation theorem related to properties of Jacoby theta-function. Equation (6.48) demonstrates the equivalence of the two representations for the partition function (6.45) and (6.47) in the limit EC ≫ EJ since in this case, the energy bands are parabolic E(Q) ≃ Q2/2C with Q = Qx + 2ep.
Rigorous vibrational Fermi resonance criterion revealed: two different approaches yield the same result
Published in Molecular Physics, 2020
S. V. Krasnoshchekov, E. O. Dobrolyubov, M. A. Syzgantseva, R. V. Palvelev
The effect of divergence of a RSPT series is often considered as a drawback of an imperfect mathematical technique. Underappreciated is that the information contained in high-order divergent RSPT series contains valuable information about non-linear spectral properties of the Hamiltonian that can be extracted using an appropriate mathematical treatment. The common name of this family of methods of treating divergent series is ‘resummation’ [26–37]. Resummation techniques permit representing eigenvalues in a new non-linear multi-valued functional form, more appropriate to describing the physical picture of the problem.