arXiv:hep-th/9212122

Geometrical phase,generalized quasienergy and Floquet operator as invariants

Vladimir I. Man’ko

Published Dec 21, 1992• 0 citations

Abstract

For time-periodical quantum systems generalized Floquet operator is found to be integral of motion.Spectrum of this invariant is shown to be quasienergy spectrum.Analogs of invariant Floquet operators are found for nonperiodical systems with several characteristic times.Generalized quasienergy states are introduced for these systems. Geometrical phase is shown to be integral of motion.

DOI: 10.48550/arxiv.hep-th/9212122

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arXiv:hep-th/9212122

Geometrical phase,generalized quasienergy and Floquet operator as invariants

Vladimir I. Man’ko

Published Dec 21, 1992• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.hep-th/9212122

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Jan 1, 20010 citations

We derive Floquet theory from quantum geometry. We identify quasienergy folding as a consequence of a broken gauge group of the adiabatic gauge potential

U(1){\mapsto}\mathbb{Z}

. Fixing instead the gauge freedom using the parallel-transport gauge uniquely decomposes Floquet dynamics into a purely geometric and a purely dynamical evolution. The dynamical average-energy operator provides an unambiguous sorting of the quasienergy spectrum, identifying a Floquet ground state and suggesting a way to define the filling of Floquet-Bloch bands. We exemplify the features of geometric Floquet theory using an exactly solvable XY model and a non-integrable kicked Ising chain. We elucidate the geometric origin of inherently nonequilibrium effects, like the

π

-quasienergy splitting in discrete time crystals or

π

-edge modes in anomalous Floquet topological insulators. The spectrum of the average-energy operator is a susceptible indicator for both heating and spatiotemporal symmetry-breaking transitions. Last, we demonstrate that the periodic lab frame Hamiltonian generates transitionless counterdiabatic driving for Floquet eigenstates. This work directly bridges seemingly unrelated areas of nonequilibrium physics.