The missing quantum number of the Floquet states
- URL: http://arxiv.org/abs/2111.04288v2
- Date: Wed, 16 Feb 2022 06:55:12 GMT
- Title: The missing quantum number of the Floquet states
- Authors: Cristian M. Le and Ryosuke Akashi and Shinji Tsuneyuki
- Abstract summary: 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.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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