Floquet theory: exponential perturbative treatment

Casas, Fernando; Oteo, J. A.; Ros, J.

doi:10.1088/0305-4470/34/16/305

Cited by 126 publications

(179 citation statements)

References 15 publications

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“…In Section 4, we argue how, nevertheless, the general formalism of MMFT can still lead to valid results, in agreement with prior work [35,[45][46][47][49][50][51]. In Section 5, we derive a generalisation of the Floquet-Magnus expansion [52], which provides a perturbative exponential expansion of the time-evolution operator that has the desired structure. With this, we advocate the possibility to identify effective Hamiltonians that characterise well the effective dynamics of quasi-periodically driven systems in a fast-driving regime and exemplify in Section 6 the results with a quasi-periodically driven Lambda system.…”

Section: Introductionsupporting

confidence: 69%

“…In practice, this is often done through an expansion in terms of powers of |ω| −1 . In this section, we will derive a generalisation of the Floquet-Magnus expansion [52,58,59] to quasi-periodic systems and provide a perturbative exponential expansion of the time-evolution operator with the desired Floquet representation. This will allow us to identify H Q as the effective Hamiltonian that captures the dynamics of the system in a suitable fast-driving regime.…”

Section: Generalised Floquet-magnus Expansionmentioning

confidence: 99%

“…We start the derivation by reproducing the steps of the regular Floquet-Magnus expansion [52] and introducing the desired decomposition of the time-evolution operator † ( ) ( )…”

Section: Generalised Floquet-magnus Expansionmentioning

confidence: 99%

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Quasi-Periodically Driven Quantum Systems

Verdeny

Puig

Mintert

2016

Zeitschrift Für Naturforschung A

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Floquet theory provides rigorous foundations for the theory of periodically driven quantum systems. In the case of non-periodic driving, however, the situation is not so well understood. Here, we provide a critical review of the theoretical framework developed for quasi-periodically driven quantum systems. Although the theoretical footing is still under development, we argue that quasiperiodically driven quantum systems can be treated with generalisations of Floquet theory in suitable parameter regimes. Moreover, we provide a generalisation of the Floquet-Magnus expansion and argue that quasi-periodic driving offers a promising route for quantum simulations.

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Section: Introductionsupporting

confidence: 69%

Section: Generalised Floquet-magnus Expansionmentioning

confidence: 99%

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Quasi-Periodically Driven Quantum Systems

Verdeny

Puig

Mintert

2016

Zeitschrift Für Naturforschung A

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“…In the case of a linearly polarized pump, the latter introduces additional anisotropy in the system via renormalization of the parameters of the effective SOI Hamiltonian. In the high-frequency regime the formal derivation of the effective time-independent Hamiltonian can be performed in a rather intuitive way, and the rigorous mathematical procedure is based on either Floquet-Magnus expansion 39,40 or the BrillouinWigner perturbation theory 41 : If this is the case, Floquet bands are nearly uncoupled, while the corresponding Floquet Hamiltonian becomes almost block diagonal, which results in a very weak dependence on time of the effective Floquet operator. We solve directly the evolution equation that governs the dynamics of RashbaDresselhaus spin-orbit-coupled electron gas under an intense linearly polarized field.…”

Section: Hybrid Surface Waves Under Intense Pumpingmentioning

confidence: 99%

Hybrid surface waves in two-dimensional Rashba-Dresselhaus materials

2017

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We address the electromagnetic properties of two-dimensional electron gas confined by a dielectric environment in the presence of both Rashba and Dresselhaus spin-orbit interactions. It is demonstrated that off-diagonal components of the conductivity tensor resulting from a delicate interplay between Rashba and Dresselhaus couplings lead to the hybridization of transverse electric and transverse magnetic surface electromagnetic modes localized at the interface. We show that the characteristics of these hybrid surface waves can be controlled by additional intense external off-resonant coherent pumping.

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“…The Floquet Magnus expansion is a new theoretical tool for describing spin dynamics recently introduced in solid-state NMR and spin physics [34]- [36]. This unique approach (FME) is an extension of the popular Magnus expansion and average Hamiltonian theory and is useful to shed new lights on AHT and FLT [27] [28].…”

Section: Floquet-magnus Expansionmentioning

confidence: 99%

Theories in Spin Dynamics of Solid-State Nuclear Magnetic Resonance Spectroscopy

Mananga¹,

Moghaddasi²,

Sana³

et al. 2015

WJNST

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This short review article presents theories used in solid-state nuclear magnetic resonance spectroscopy. Main theories used in NMR include the average Hamiltonian theory, the Floquet theory and the developing theories are the Fer expansion or the Floquet-Magnus expansion. These approaches provide solutions to the time-dependent Schrodinger equation which is a central problem in quantum physics in general and solid-state nuclear magnetic resonance in particular. Methods of these expansion schemes used as numerical integrators for solving the time dependent Schrodinger equation are presented. The action of their propagator operators is also presented. We highlight potential future theoretical and numerical directions such as the time propagation calculated by Chebychev expansion of the time evolution operators and an interesting transformation called the Cayley method.

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Floquet theory: exponential perturbative treatment

Cited by 126 publications

References 15 publications

Quasi-Periodically Driven Quantum Systems

Quasi-Periodically Driven Quantum Systems

Hybrid surface waves in two-dimensional Rashba-Dresselhaus materials

Theories in Spin Dynamics of Solid-State Nuclear Magnetic Resonance Spectroscopy

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