# 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 ...
1 vote
55 views

### 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, ...
43 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 ...
82 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 ...
26 views

### Interpretation of Floquet Band Structure in Multi-band Models

Computing band structures inside Floquet formalism has become quite common, see e.g. . While I think to fully understand it from a mathematical point of view, I'm lacking some physical ...
24 views

### 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 ...
22 views

### 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 ...
1 vote
46 views

### 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 ...
1 vote
27 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 ...
34 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}\...
51 views

### 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^{...
155 views

### What is Bloch-Floquet theory? [duplicate]

And specifically Bloch-Floquet boundary conditions? I would love to hear any explanation you guys might have.
1 vote
40 views

### 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 ...
1 vote
212 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 ...
86 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_\...
53 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 ...
47 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 ...
282 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 ...
1 vote
174 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 ...
136 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 ...
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 ...
1 vote
55 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 ...