Third order correction to localization in a two-level driven system

Abstract

A general result is presented on the lack of second order corrections and on the form of the leading order Floquet quasi-energies in the high-frequency approximation for a two-level driven system. Then, by a perturbative approach in the high-frequency approximation that uses dual Dyson series and renormalization group techniques [M. Frasca, Phys. Rev. B 68, 165315 (2003)], we obtain a third order correction for a sinusoidal driving field that is the same obtained by Barata and Wreszinski [Phys. Rev. Lett. 84, 2112 (2000)], confirming their result that localization deviates from the zeros of the zero-th order Bessel function when higher order terms are taken into account. Three different expressions for this correction are compared. An important consequence of this result is that gives complete support to the correctness of both methods. Finally, the limitation of high-frequency approximations is presented by comparison with numerical results for a sinusoidal driving field.

7 pages, 2 figures. Final version accepted for publication in Physical Review B

References in corpus (6)

• Location of crossings in the Floquet spectrum of a driven two-level system
• Strong Coupling Theory of Two Level Atoms in Periodic Fields
• Charge Transport Through Open, Driven Two-Level Systems with Dissipation
• Perturbative results on localization for a driven two-level system
• Perturbative Analysis of Dynamical Localisation
• Phase dependence of localization in the driven two-level model

Cited by in corpus (10)

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• Dissipative two-level systems under ultrastrong off-resonant driving
• Quasienergy spectrum and tunneling current in ac-driven triple quantum dot shuttles
• Charge localization and dynamical spin locking in double quantum dots driven by ac magnetic fields
• Majorana path integral for nonequilibrium dynamics of two-level systems
• Effect of a high-frequency magnetic field on the resonant behavior displayed by a spin-$1/2$ particle under the influence of a rotating magnetic field
• Continued fraction analysis of dressed systems: application to periodically driven optical lattices
• The Rabi problem with elliptic polarization
• Localization in a strongly disordered system: A perturbation approach