Effective Gaps in Continuous Floquet Hamiltonians

Singular Continuous Floquet Operator for Systems with Increasing Gaps

Consider the Floquet operator of a time independent quantum system, periodically perturbed by a rank one kick, acting on a separable Hilbert space: e0 e |φ〉〈φ| where T and κ are the period and the coupling constant respectively. Assume the spectrum of the self adjoint operator H0 is pure point, simple, bounded from below and the gaps between the eigenvalues (λn) grow like: λn+1 − λn ∼ Cn with d...

Weakly Regular Floquet Hamiltonians with Pure Point Spectrum

We study the Floquet Hamiltonian −i∂t + H + V (ωt), acting in L([ 0, T ],H, dt), as depending on the parameter ω = 2π/T . We assume that the spectrum of H in H is discrete, Spec(H) = {hm}m=1, but possibly degenerate, and that t 7→ V (t) ∈ B(H) is a 2π-periodic function with values in the space of Hermitian operators on H. Let J > 0 and set Ω0 = [ 89J, 98J ]. Suppose that for some σ > 0 it holds...

Effective Hamiltonians with Relativistic Corrections

Optimal control of effective Hamiltonians.

We present a systematic scheme for the optimization of quantum simulations. Specifically, we show how polychromatic driving can be used to significantly improve the driving of Raman transitions in the Lambda system, which opens new possibilities for controlled driving-induced effective dynamics.

Hyperoctahedral Chen calculus for effective Hamiltonians

We tackle the problem of unraveling the algebraic structure of computations of effective Hamiltonians. This is an important subject in view of applications to chemistry, solid state physics or quantum field theory. We show, among other things, that the correct framework for these computations is provided by the hyperoctahedral group algebras. We define several structures on these algebras and g...