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Linear response theory and optical conductivity of Floquet topological insulators

Physical Review B, 2020
Motivated by the quest for experimentally accessible dynamical probes of Floquet topological insulators, we formulate the linear response theory of a periodically driven system.
Martin Rodríguez-Vega, T Pereg-Barnea, Babak Seradjeh   +2 more
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Floquet theory in magnetic resonance: Formalism and applications

Progress in Nuclear Magnetic Resonance Spectroscopy, 2021
Floquet theory is an elegant mathematical formalism originally developed to solve time-dependent differential equations. Besides other fields, it has found applications in optical spectroscopy and nuclear magnetic resonance (NMR). This review attempts to give a perspective of the Floquet formalism as applied in NMR and shows how it allows one to solve ...
Konstantin L Ivanov, Kaustubh R Mote, Matthias Ernst   +2 more
exaly   +3 more sources

Canonical Floquet theory

Celestial Mechanics and Dynamical Astronomy, 1994
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
William E Wiesel
exaly   +3 more sources

Floquet Theory for a Volterra Equation

Journal of the London Mathematical Society, 1988
The authors discuss periodic solutions of the integrodifferential equation \[ dy(t)/dt=A(t)y(t)+\int^{t}_{0}C(t,s)y(s)ds+f(t), \] relating two different integrability properties of the resolvent to each other.
Becker, L. C., Burton, T. A., Krisztin, T.   +2 more
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Generalization of the Floquet theory

Nonlinear Analysis: Theory, Methods & Applications, 2009
Two systems of differential equations \(\omega\)-periodic in time are called topologically equivalent if there exists a mapping \(H(t,x)\) such that (i) \(H(t+\omega,x)=H(t,x)\); (ii) for any \(t\), \(H(t,. )\) is a homeomorphism; (iii) if \(x(t)\) is a solution of the first system, then \(H(t,x(t))\) is a solution of the second system.
Zou, Changwu, Shi, Jinlin
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Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators

Physical Review B, 2016
We construct a systematic high-frequency expansion for periodically driven quantum systems based on the Brillouin-Wigner (BW) perturbation theory, which generates an effective Hamiltonian on the projected zero-photon subspace in the Floquet theory ...
Takahiro Mikami, Sota Kitamura, Kenji Yasuda   +2 more
exaly   +2 more sources

Floquet Theory as a Computational Tool

SIAM Journal on Numerical Analysis, 2005
Summary: We describe how classical Floquet theory may be utilized, in a continuation framework, to construct an efficient Fourier spectral algorithm for approximating periodic orbits. At each continuation step, only a single square matrix, whose size equals the dimension of the phase-space, needs to be factorized; the rest of the required numerical ...
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Floquet Theory and Newton’s Method

Journal of Applied Mechanics, 1973
Application of Newton’s method to nonlinear vibration problems can lead to a sequence of nonhomogeneous ordinary differential equations with periodic coefficients. The form of the complementary solutions are known from Floquet theory. This paper suggests a method for avoiding “secular terms” that grow with time in the particular solution.
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A floquet theory of the linear synchronous machine

Journal of the Franklin Institute, 1983
Abstract The differential equation describing the three-phase linear synchronous machine containing an arbitrary stator MMF distribution is reformulated and solved as a perturbation theory problem. The solution algorithm presented also produces a transformation capable of reducing to constant coefficient form the differential equation describing the ...
J.L. Stensby, C.W. Brice, R.K. Cavin
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Floquet theory: exponential perturbative treatment

Journal of Physics A: Mathematical and General, 2001
A celebrated Floquet theorem states that the solution \(Z(t)\) to the linear matrix differential equation \[ \frac{dZ}{dt}=A(t)Z(t), \qquad Z(0)=I, \] with a complex \(n\times n\)-matrix \(A\) whose entries are integrable periodic functions of \(t\) with period \(T,\) has the form \[ Z(t)=P(t)\exp(tF), \] where \(F\) and \(P\) are \(n\times n ...
Casas, F., Oteo, J. A., Ros, J.
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