1.00
0.50
1.00
0.00
Time: 0 T
|c₁|²: 1.000
|c₂|²: 0.000
Quasi-energy: –
|c₁|²: 1.000
|c₂|²: 0.000
Quasi-energy: –
Floquet Theorem
For H(t+T)=H(t), solutions ψ(t)=e^{−iεt}u(t) with u(t+T)=u(t). Quasi-energies ε are defined mod ω=2π/T — the "Brillouin zone of time". Resonance (ω≈2ω₀) causes exponential growth (Mathieu instability). Driven atoms can be dressed into Floquet-Bloch states; topological Floquet insulators emerge from periodically driven lattices.
For H(t+T)=H(t), solutions ψ(t)=e^{−iεt}u(t) with u(t+T)=u(t). Quasi-energies ε are defined mod ω=2π/T — the "Brillouin zone of time". Resonance (ω≈2ω₀) causes exponential growth (Mathieu instability). Driven atoms can be dressed into Floquet-Bloch states; topological Floquet insulators emerge from periodically driven lattices.