The missing quantum number of the Floquet states

Abstract

We reformulate the Floquet theory for periodically driven quantum systems following a perfect analogy with the proof of Bloch theorem. We observe that the current standard method for calculating the Floquet eigenstates by the quasi-energy alone is incomplete and unstable, and pinpoint an overlooked quantum number, the average energy. This new quantum number resolves many shortcomings of the Floquet method stemming from the quasi-energy degeneracy issues, particularly in the continuum limit. Using the average energy quantum number we get properties similar to those of the static energy, including a unique lower-bounded ordering of the Floquet states, from which we define a ground state, and a variational method for calculating the Floquet states. This is a first step towards reformulating Floquet first-principles methods, that have long been thought to be incompatible due to the limitations of the quasi-energy.

References in corpus (5)

• Equilibrium states of generic quantum systems subject to periodic driving
• Statistical mechanics of Floquet systems with regular and chaotic states
• Comment on "Critique of the foundations of time-dependent density functional theory" [Phys. Rev.A. 75, 022513 (2007)]
• Defining a well-ordered Floquet basis by the average energy
• Variational principle for time-periodic quantum systems

Cited by in corpus (4)

• Geometric Floquet theory
• Level-crossing resonances on open atomic transitions in a buffered Cs vapor cell: Linewidth narrowing, high contrast and applications to atomic magnetometry
• Measuring a localization phase diagram controlled by the interplay of disorder and driving
• Floquet formulation of the dynamical Berry-phase approach to non-linear optics in extended systems