Convergence of the Magnus expansion for time dependent two level systems
1987; American Institute of Physics; Volume: 86; Issue: 10 Linguagem: Inglês
10.1063/1.452541
ISSN1520-9032
Autores Tópico(s)Spectroscopy and Quantum Chemical Studies
ResumoThis paper derives criteria for the convergence of the Magnus expansion, applied to an arbitrary time dependent two level system, in terms of the eigenvalues of the Hamiltonian for that system. When a weak to moderate intensity field perturbs a two level system the resonance frequency of the system must lie below the frequency of the applied field for the series to converge. An alternative solution for the exponential form of the evolution operator is developed that converges for all values of the expansion parameter and clearly shows the singularities that lead to the failure of the Magnus solution. Finally, a simple unitary transformation is presented that extends considerably the radius convergence of the Magnus series, as illustrated by a spin 1/2 in a linearly polarized field.
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