Questions tagged [floquet-theory]

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Definition of Parahermitian Operators

In a few situations, such as Floquet systems and Bogoliubov transformations, I have heard the terms paraunitary transformations and then parahermitian operators. What is the formal definition of these ...
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Eigenvalues in Floquet theory

After calculating Floquet Hamiltonian and then it's eigenvalues I stumbled upon a problem with ordering of eigenvalues. I am using eigen library for c++ and for every Floquet Hamiltonian for given ...
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50 views

Meaning of time evolution of Floquet matrix

Consider the time-periodical Hamiltonian $H(t)=H(t+T)$. In the Floquet theorem, the Schrödinger equation has a solution of the form \begin{align} |\psi_\alpha(t)\rangle=e^{-i\epsilon_\alpha t}|\phi_\...
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Accessable introduction to Floquet theory of PDEs

I have been attempting to read "Floquet Theory for Partial Differential Equations" by Peter Kuchment. However, to put it mildly, it is hard to read. Any suggestions for more gentle ...
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Is dynamical localisation an interference effect?

The question refers to the well-known phenomenon of dynamical localisation due to an oscillating electric field, as explained in Dunlap & Kenkre, PRB 34,6 (1986). Here, a particle initially ...
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1answer
32 views

Clarifications about definition of Bravais lattice

I have a doubt about the definition of Bravais lattice for periodic materials. Precisely, here it is defined as: a discrete set of vectors closed under vector addition and subtraction If I look at ...
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1answer
154 views

Floquet bandstructure calculation

In this paper "Photonic Floquet Topological Insulators" the authors calculate the bandstructure of a time-periodic Hamiltonian. They create a time-dependent tight-binding Hamiltonian via the ...
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1answer
79 views

Time-reversal and its effect in the eigenfunctions of the Floquet operator

When time-reversal is present in a kicked Hamiltonian system (e.g. kicked rotator) it can be shown that there exists a basis in which the associated Floquet operator $U$ is symmetric. One can then try ...
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66 views

Which unitary transformation should I use to change the frame reference properly?

I'm dealing with time-periodic Hamiltonian $H(t)=H(t+T)$ , where $$ i\hbar \partial_t\psi(r,t)=H(r,t)\psi(r,t).$$ The periodicity lies on the potential (i.e. $V(t)=V(t+T)$ inside the $H(r,t)$). The ...
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1answer
896 views

Floquet State - Time Evolution

Is it possible to write the time evolution of a generic quantum state in terms of a floquet basis? It seems that the answer is yes, although this seems wrong. In general, time evolution in a system ...
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50 views

Usage of Floquet's Method

I'm treating with a nonlinear system of ODE, in which one of my fixed points is non-hyperbolic, that is, its eigenvalues has ($\Re(\lambda_{1,2}) = 0$). Therefore, I cannot say anything about its ...
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What is the relation between eigenstate thermalisation and infinite heating in Floquet systems?

Closed quantum systems with periodically changing parameters (Floquet systems) typically heat up to an infinite temperature at large times. I have read multiple times (the last time was here) that ...
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In Floquet theory, what is the physical significance of the Fourier coefficients?

Floquet theory is the study of (quasi)-periodic solutions of the time-dependent Schrödinger equation when the system is subjected to a time-periodic Hamiltonian.$\newcommand{\ket}[1]{\left|#1\right\...
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1answer
692 views

Magnus Expansion in Floquet theory [closed]

I wonder how to obtain the second equality as follows in Eq. (44) of Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering. M Bukov, ...
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220 views

Can different Floquet replicas be distinguished (within Floquet's theorem)?

According to Floquet's theorem, two quasi-energies separated by $n\hbar \omega$ represent the same state. According to this, I would think different replicas are indistinguishable experimentally. ...
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Are there exact expressions for the Floquet states of a periodically-forced, undamped harmonic oscillator?

For this question I was looking for the Floquet states of a quantum harmonic oscillator driven by a non-resonant harmonic force, and I had a rather harder time finding it than the simplicity of the ...
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1answer
616 views

How to observe Floquet state?

The Schrodinger equation is $$i\hbar\partial_t\psi(t)=H(t)\psi(t).$$ Now, given that the situation that the Hamiltonian is periodically driven, i.e., $H(t+T)=H(t)$, then the equation can be solved ...
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4k views

Floquet and Bloch's theorems : connection?

It is often stated that Bloch's theorem and Floquet's theorem are equivalent, even the Bloch's theorem is often referred as Floquet-Bloch theorem. However, it seems quite confusing to me since the ...
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3k views

Floquet quasienergy spectrum, continuous or discrete?

I haven't got a feeling about Floquet quasienergy, although it is talked by many people these days. Floquet theorem: Consider a Hamiltonian which is time periodic $H(t)=H(t+\tau)$. The Floquet ...