On the Effective Reducibility of a Class of Quasi-Periodic Linear Hamiltonian Systems Close to Constant Coefficients

Xue, Nina; Zhao, Wencai

doi:10.1155/2018/5189873

Cited by 3 publications

(2 citation statements)

References 24 publications

(32 reference statements)

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“…In general, the resulting time evolution, U (t), is not quasiperiodic in t. However, in many instances, a multi-mode extension of Floquet's theorem applies [55] and allows U (t) can be reduced to a quasiperiodic modulation accompanied by a static Hamiltonian evolution, and several techniques [31,56] have been introduced to approximately construct the effective Hamiltonian in the weak driving or high frequency limit.…”

Section: Cut and Project Methodsmentioning

confidence: 99%

Topological edge modes without symmetry in quasiperiodically driven spin chains

Friedman,

Ware,

Vasseur

et al. 2020

Preprint

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We construct an example of a 1d quasiperiodically driven spin chain whose edge states can coherently store quantum information, protected by a combination of localization, dynamics, and topology. Unlike analogous behavior in static and periodically driven (Floquet) spin chains, this model does not rely upon microscopic symmetry protection: Instead, the edge states are protected purely by emergent dynamical symmetries. We explore the dynamical signatures of this Emergent Dynamical Symmetry-Protected Topological (EDSPT) order through exact numerics, time evolving block decimation, and analytic high-frequency expansion, finding evidence that the EDSPT is a stable dynamical phase protected by bulk many-body localization up to (at least) stretchedexponentially long time scales, and possibly beyond. We argue that EDSPTs are special to the quasiperiodically driven setting, and cannot arise in Floquet systems. Moreover, we find evidence of a new type of boundary criticality, in which the edge spin dynamics transition from quasiperiodic to chaotic, leading to bulk thermalization.

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Section: Cut and Project Methodsmentioning

confidence: 99%

Topological edge modes without symmetry in quasiperiodically driven spin chains

Friedman,

Ware,

Vasseur

et al. 2020

Preprint

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“…where R * is exponentially small in ε. Li and Xu [14] obtained the similar result for Hamiltonian systems. Later, Xue and Zhao [15] extended the result to the case of multiple eigenvalues.…”

Section: Introductionmentioning

confidence: 98%

On the Reducibility of Quasiperiodic Linear Hamiltonian Systems and Its Applications in Schrödinger Equation

Xue

Zhao

2020

Journal of Function Spaces

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In this paper, we consider the reducibility of the quasiperiodic linear Hamiltonian system ẋ=A+εQt, where A is a constant matrix with possible multiple eigenvalues, Qt is analytic quasiperiodic with respect to t, and ε is a small parameter. Under some nonresonant conditions, it is proved that, for most sufficiently small ε, the Hamiltonian system can be reduced to a constant coefficient Hamiltonian system by means of a quasiperiodic symplectic change of variables with the same basic frequencies as Qt. Applications to the Schrödinger equation are also given.

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