Related papers: Floquet-like theory and gauge transformations for …
Floquet's Theorem is a celebrated result in the theory of ordinary differential equations. Essentially, the theorem states that, when studying a linear differential system with $T$-periodic coefficients, we can apply a, possibly complex,…
In this paper, we study periodic linear systems on periodic time scales which include not only discrete and continuous dynamical systems but also systems with a mixture of discrete and continuous parts (e.g. hybrid dynamical systems). We…
A variational principle enabling one to compute individual Floquet states of a periodically time-dependent quantum system is formulated, and successfully tested against the benchmark system provided by the analytically solvable model of a…
Floquet theory is a powerful tool in the analysis of many physical phenomena, and extended to spatial coordinates provides the basis for Bloch's theorem. However, in its original formulation it is limited to linear systems with periodic…
Using the new periodicity concept based on shifts, we construct a unified Floquet theory for homogeneous and nonhomogeneous hybrid periodic systems on domains having continuous, discrete or hybrid structure. New periodicity concept based on…
Floquet modulations often yield effective Hamiltonians not easily accessible in traditional time-dependent systems, which brings opportunities for exploring novel physics of quantum dynamics. We investigate a Floquet system exhibiting…
The study of classical waves in time-periodic systems is experiencing a resurgence of interest, motivated by their rich physics and the new engineering opportunities they enable, with several analogies to parallel efforts in other branches…
Floquet engineering is the concept of tailoring a system by a periodic drive. It has been very successful in opening new classes of Hamiltonians to the study with ultracold atoms in optical lattices, such as artificial gauge fields,…
Dynamical quantum phase transitions (DQPTs) are characterized by nonanalytic behaviors of physical observables as functions of time. When a system is subject to time-periodic modulations, the nonanalytic signatures of its observables could…
Time-periodic dynamical systems occur commonly both in nature and as engineered systems. Large-scale linear time-periodic dynamical systems, for example, may arise through linearization of a nonlinear system about a given periodic solution…
We show that the time-dependence of electromagnetic field in a parametrically modulated cavity can be effectively analyzed using a $Floquet$ $map$. The map relates the field states separated by one period of the drive; iterative application…
The dynamics of qubits coupled to a harmonic oscillator with time-periodic coupling is investigated in the framework of Floquet theory. This system can be used to model nonadiabatic phenomena that require a periodic modulation of the…
Periodically driven quantum systems exhibit many fascinating phenomena absent in equilibrium systems, but their simulation is more challenging than that of static systems. Consequently, quantum simulation of these systems offers greater…
Floquet engineering, modulating quantum systems in a time periodic way, lies at the central part for realizing novel topological dynamical states. Thanks to the Floquet engineering, various new realms on experimentally simulating…
Periodic driving serves as an effective method for controlling the properties of physical systems. Called "Floquet engineering," it is a broad field of theoretical and experimental activity. Whereas original Floquet theory was proposed to a…
The classical and quantum dynamics in a high frequency field are found to be described by an effective time independent Hamiltonian. It is calculated in a systematic expansion in the inverse of the frequency ($\omega$) to order…
For a periodically driven open quantum system, the Floquet theorem states that the time evolution operator $\Lambda(t,0)$ of the system can be factorized as $\Lambda(t,0)=\mathcal{D}(t)e^{\mathcal{L}_{eff}t}$ with micro-motion operator…
Open quantum systems can display periodic dynamics at the classical level either due to external periodic modulations or to self-pulsing phenomena typically following a Hopf bifurcation. In both cases, the quantum fluctuations around…
Conformal field theories (CFT) play an important role in quantum field theories as they allow for exact studies that are hard to access without the conformal symmetries in place. A remarkable recent development is the application of…
We consider a quantum system periodically driven with a strength which varies slowly on the scale of the driving period. The analysis is based on a general formulation of the Floquet theory relying on the extended Hilbert space. It is shown…