Higher approximations in the theory of the average Hamiltonian

High-gain quantum free-electron laser: Emergence and exponential gain

“…III we then solve the resulting equations of motion in the short-time limit and observe an exponential gain of the laser intensity as well as a super-Poissonain behavior of the corresponding fluctuations. Moreover, we make use of the asymptotic method of canonical averaging [28,29] to calculate higher-order corrections to the deep quantum regime and we connect our results to the existing literature on the Quantum FEL [6]. Finally, we summarize our main results and conclude in Sec.…”

“…We first separate the slowly-varying dynamics from the rapid oscillations. For that we make use of the canonical variant [29] of the method of averaging, in which we directly work with the Hamiltonian instead of the equations of motion. To employ this technique, we decomposê H (t), Eq.…”

“…which we identify with the effective Hamiltonian in lowest order of the method of averaging [29], that isĤ eff ≡ εĤ (1) eff . If we interpretΥ 1,0 andΥ 0,1 as collective spin-flip operators, we observe that the expression for the effective Hamitonian in Eq.…”

Progress in spin dynamics solid-state nuclear magnetic resonance with the application of Floquet–Magnus expansion to chemical shift anisotropy

“…While the efficiency of Fer expansion seems obvious, more work is still required to allow the scheme to overcome difficulties such as cases involving non-periodic and non-cyclic cases. Other expansion approaches including Dison series 35 , Wilcox expansion 36 , secular averaging theory 26,51,53,54,55,56 , Van Vleck transformation 10,22,26,51 , Van Vleck-Primas 22,26,52 perturbation, static perturbation theory 10,26 and other emerging theoretical methods deserve further additional attention in the spin physics community.…”

Low-Temperature Nuclear Spin-Lattice Relaxation in Amorphous Materials

“…This term is responsible for a creation of the indirect interaction. According to [11], where the quantum-mechanical analogue of the classic method of averaging over fast movements is given, we get…”