Quasiperiodic driving of Anderson localized waves in one dimension

Abstract

We consider a quantum particle in a one-dimensional disordered lattice with Anderson localization, in the presence of multi-frequency perturbations of the onsite energies. Using the Floquet representation, we transform the eigenvalue problem into a Wannier-Stark basis. Each frequency component contributes either to a single channel or a multi-channel connectivity along the lattice, depending on the control parameters. The single channel regime is essentially equivalent to the undriven case. The multi-channel driving substantially increases the localization length for slow driving, showing two different scaling regimes of weak and strong driving, yet the localization length stays finite for a finite number of frequency components.

Localization and hybridization across an effective mobility edge in periodically driven speckle potentials

“…Moreover, they also de-localize in the basis of the stationary Hamiltonian and exhibit signatures of the thermalization. Our results can be straightforwardly generalized to the case of non-harmonic periodic driving [16,17]. Finally, although the mobility edge in the used model is only an effective one (so that the quasi-extended states are not completely de-localized), our finding constitutes a step towards a much debated problem of the phenomenon of driven many-body localization in the presence of mobility edge [30][31][32].…”

“…In contrast, the high-frequency driving diminishes timeaveraged hopping amplitudes [11][12][13] and enhance the localization, an effect reminiscent of the dynamic localization [14,15]. Recently, it has been shown that the multifrequency driving can substantially increase the localization length [16], and the complete de-localization can be achieved with driven quasi-periodic potentials [17].…”

Chaos‐related Localization in Modulated Lattice Array

“…[12][13][14][15][16] In the previous works, theoretically and experimentally, the nonlinear driven system has exhibited some novel quantum tunneling and localization phenomena including nonlinear Landau-Zener tunneling, [17,18] Anderson localization (AL), [19,20] nonlinear CDT (NCDT) [21] and optical solitons. [22] Most importantly, Anderson localization in disordered systems has been studied intensively combining numerical and analytical arguments [23][24][25] and the transition of DOI: 10.1002/andp.201700218 localization-delocalization has been observed in models where only single elements (only driving, only nonlinearity) were considered. [26,27] To our knowledge, it has been clear that the localization and delocalization could coexist in a chaotic system and the transition could be realized by adjusting the driving frequency or other parameters.…”

Quasiperiodic Floquet-Thouless Energy Pump

“…The absence of time-translation symmetry gives the QFTEP features which have no analogue in equilibrium or Floquet systems. In particular, the QFTEP is protected by a combination of spatial and frequency localization [31][32][33][34][35][36], meaning the index ν can only change if this localization is destroyed. Here frequency localization is a phenomenon unique to quasiperiodically driven systems which arises only for sufficiently irrational ω 2 =ω 1 .…”

“…Frequency localization.-As a main result, this work shows that the model above is characterized by an integervalued topological invariant when it is localized in the spatial and frequency domains. The key to understanding such localization is a generalized Floquet theorem [31][32][33][34][35][36]: for the bichromatically driven systems we consider, a complete orthonormal basis of generalized (single-particle) Floquet states fjΦ n ðϕ 1 ; ϕ 2 Þig can be defined such that the time evolution of any state takes the form jψðtÞi ¼ P n κ n e −iε n t jΦ n ðω 1 t; ω 2 tÞi. Here each jΦ n ðϕ 1 ; ϕ 2 Þi is 2π periodic in each of its arguments while ε n is real valued and defines a generalized quasienergy.…”