Questions tagged [floquet-theory]

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How to apply the Bloch-Floquet theorem for a square lattice in a magnetic field?

Generalizing the question here, if I have a square lattice in the homogeneous magnetic field $B$ as the given picture, how can we apply the Bloch-Floquet theorem in this periodic structures (with the ...
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How much information can be stored in a system with synthetic dimensions?

Okay this is a completely serious question and keep in mind I have a PhD in theoretical condensed matter physics, in which I have somewhat of a specialization in Floquet physics. So as the title says, ...
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The reason why the Nielsen-Nimiya Theorem doesn't have to hold true in the Floquet system?

According to the Nielsen-Ninomiya (NN) theorem, under appropriate assumptions, the number of right-handed and left-handed particles must be equal in a lattice system. On the other hand, in recent ...
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What is the physical meaning of Floquet quasi-energy? (to a near-layman)

I am doing a project for my undergrad physics course "Mathematical Methods in Physics". In the project, I need to write a computer program to calculate and plot graphs about Rabi ...
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Interpretation of Floquet Band Structure in Multi-band Models

Computing band structures inside Floquet formalism has become quite common, see e.g. [1]. While I think to fully understand it from a mathematical point of view, I'm lacking some physical ...
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What is the matrix representation of the Floquet and Rotation operators for kicked top model?

In this and other papers relating to the kicked top model, it is mentioned that spin coherent states can be expressed as: $$\left|\theta,\phi\right>=R(\theta,\phi)\left|j,j\right>$$ for given ...
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What is the thermal properties of Floquet system?

As we have learnt in stat-mech, the concepts of temperature, distribution, etc all rely on the fact that the system is in thermal equilibrium. However in Floquet physics, the periodically driven ...
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Transition probability in time-periodical system

There is a derivation of transition probability in Floquet system in the paper (PHYSICAL REVIEW B85, 184524 (2012)). They considered a time-periodical Hamiltonian $H(t+T)=H(t)$. According to Floquet ...
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Characteristic time scale in floquet system?

In Floquet formalism, we have quasi-energy spectrum instead of energy spectrum. However, if we have a driving force with a low frequency, we shall be able to use adiabatic approximation and regard the ...
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Spectrum of periodically driven Floquet operator

There is a periodically driven $XX$ model with alternating field. The piecewise Hamiltonian acts as following way \begin{equation} H_1 = \sum_{i=1}^{N-1}(\sigma^{x}_{i}\sigma^{x}_{i+1}+\sigma^{y}_{i}\...
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Basis state of non-interacting fermions

I am trying to calculate the periodic dynamics of many-body systems (spin-$1/2$ $XY$) Hamiltonian, where, \begin{equation} H_1 = \sum_{i=1}^{N-1}(\sigma^{x}_{i}\sigma^{x}_{i+1}+\sigma^{y}_{i}\sigma^{...
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What is Bloch-Floquet theory? [duplicate]

And specifically Bloch-Floquet boundary conditions? I would love to hear any explanation you guys might have.
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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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2 answers
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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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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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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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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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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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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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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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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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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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22 votes
1 answer
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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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3 votes
1 answer
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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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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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2 votes
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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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4 votes
1 answer
746 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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12 votes
2 answers
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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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10 votes
2 answers
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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 ...
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