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Floquet Theory and Quantum Quench

Floquet Theory and Quantum Quench are approaches to study systems far from equilibrium (e.g. periodic driving of a closed system). Floquet Theory helps to find a unitary operator $Q(t)$ such that it ...
ZHENGYAO HUANG's user avatar
4 votes
1 answer
233 views

Floquet Hilbert Space

Why do we need the extended Floquet Hilbert Space $\mathcal{F}$ to study the Time Periodic Hamiltonian (i.e., $H(t+T)=H(t)$)? What is the problem with the Normal Hilbert Space? Where we define the ...
Santanu Singh's user avatar
1 vote
1 answer
107 views

Intermediate step in Floquet-Magnus expansion

I am reading The Magnus expansion and some of its applications by Blanes et al. and I have a question about one equation regarding the Floquet-Magnus expansion. I. Defintions I use the same ...
Ivan's user avatar
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How can we determine if a given Floquet Hamiltonian has time-reversal symmetry?

In quantum mechanics, time reversal takes the form of an anti-unitary operator such that we preserve the canonical commutation relations. We can assign relations for each of the measurables like p and ...
Rob. D's user avatar
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5 votes
2 answers
194 views

How does one show that the ${\bf k}$-vector labeling a Bloch state is an arbitrary real vector?

I'm frustrated that I can't understand something that must be simple and fundamental. I'd appreciate any answer to the question, but also any clarifications of how my presentation of the theorem/proof,...
Ben H's user avatar
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0 answers
66 views

Topological Invariants of Floquet Topological Insulators

I've been working through the following sources: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.155118 https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.195303 where they derive new ...
Fred's user avatar
  • 195
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1 answer
192 views

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 ...
sara96's user avatar
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0 answers
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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, ...
ctimms137's user avatar
0 votes
1 answer
67 views

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 ...
Siam's user avatar
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4 votes
1 answer
539 views

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 ...
Mushroom1's user avatar
1 vote
0 answers
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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 ...
wayna's user avatar
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0 answers
39 views

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 ...
Taveren Sa's user avatar
0 votes
1 answer
65 views

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}\...
user123's user avatar
  • 31
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0 answers
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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^{...
user123's user avatar
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-1 votes
1 answer
1k views

What is Bloch-Floquet theory? [duplicate]

And specifically Bloch-Floquet boundary conditions? I would love to hear any explanation you guys might have.
citizen8567's user avatar
1 vote
2 answers
422 views

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 ...
rudzillaful's user avatar
2 votes
0 answers
143 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_\...
sotowa's user avatar
  • 21
2 votes
0 answers
62 views

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 ...
Quasilattice's user avatar
0 votes
1 answer
91 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 ...
Kinka-Byo's user avatar
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3 votes
1 answer
450 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 ...
JanJasper's user avatar
1 vote
1 answer
350 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 ...
user2820579's user avatar
0 votes
0 answers
224 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 ...
Leicam's user avatar
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2 votes
1 answer
1k 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 ...
speeze's user avatar
  • 51
1 vote
0 answers
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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 ...
Herr Schrödinger's user avatar
2 votes
0 answers
374 views

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 ...
Steven Mathey's user avatar
23 votes
1 answer
3k views

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\...
Emilio Pisanty's user avatar
3 votes
1 answer
861 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, ...
qc2014's user avatar
  • 421
7 votes
0 answers
307 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. ...
an offer can't refuse's user avatar
2 votes
0 answers
486 views

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 ...
Emilio Pisanty's user avatar
5 votes
1 answer
843 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 ...
pchenweis's user avatar
  • 261
14 votes
2 answers
6k 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 ...
hbaromega's user avatar
  • 307
12 votes
2 answers
4k 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 ...
an offer can't refuse's user avatar