Skip to content
DraconiticResearch
Search Sources API
181,686 studies31 sourcesUpdated 1 min ago
PreprintarXiv licencearXiv

The geometry of Floquet states

  • Vladimir Y. Cherynak
  • John R. Klein
Open at sourcePDFDOICite

Abstract

This paper studies the moduli space of "good" periodic Hamiltonians, i.e., periodic Hamiltonians with nondegenerate Floquet spectrum. The corresponding Floquet states determine a geometric model for the moduli space of such Hamiltonians. The model is expressed in terms of configuration spaces, flag manifolds, and principal bundles. A corollary of the main result is the complete determination of the rational cohomology ring of the space of good periodic Hamiltonians. The paper also considers the adiabatic driving of a 1-parameter family of good periodic Hamiltonians. We formulate two conjectures describing the resulting asymptotic quantum evolution. These are Floquet analogues of the adiabatic theorem in quantum mechanics.

Related

  1. Group averaging and the geometry of physical quantum states: from normalizable solutions to solvable loop quantum cosmology
    Alejandro Corichi
    arXivPreprintCC BY-NC-ND 4.0Full textMathematical physicsGravitation & general relativityarXiv
  2. Floquet instability near a stationary Euler flow in 3D
    Mimi Dai
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. Exact subsystem dynamics in the deterministic Floquet-PXP model
    Katja Klobas
    arXivPreprintarXiv licenceFull textMathematical physicsQuantum physics & quantum informationarXiv
  4. The Floquet-Magnus expansion of unbounded operators
    Daniel Burgarth, Robin Hillier, Davide Lonigro +1
    arXivPreprintarXiv licenceFull textAnalysis & PDEsMathematical physicsarXiv
  5. Cyclotomic Structure and Exact Recurrences in Floquet Many-Body Quantum Dynamics
    Amit Anand, Dinesh Valluri, Shohini Ghose
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryQuantum physics & quantum informationarXiv

Cite

BibTeXRIS
BibTeX
@misc{cherynak2026geometry,
  title = {{The geometry of Floquet states}},
  author = {Vladimir Y. Cherynak and John R. Klein},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38845},
  eprint = {2610.38845},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38845},
}
RIS
TY  - UNPB
TI  - The geometry of Floquet states
AU  - Vladimir Y. Cherynak
AU  - John R. Klein
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38845
UR  - https://arxiv.org/abs/2610.38845
AB  - This paper studies the moduli space of "good" periodic Hamiltonians, i.e., periodic Hamiltonians with nondegenerate Floquet spectrum. The corresponding Floquet states determine a geometric model for the moduli space of such Hamiltonians. The model is expressed in terms of configuration spaces, flag manifolds, and principal bundles. A corollary of the main result is the complete determination of the rational cohomology ring of the space of good periodic Hamiltonians. The paper also considers the adiabatic driving of a 1-parameter family of good periodic Hamiltonians. We formulate two conjectures describing the resulting asymptotic quantum evolution. These are Floquet analogues of the adiabatic theorem in quantum mechanics.
ER  -