# Driven Disordered Systems

Driving a localized system can create transitions between states that would barely communicate in a static Hamiltonian. It is tempting to conclude that enough driving must therefore restore ordinary diffusion. Agarwal and collaborators show why that inference can fail. The central distinctions are between motion within a drive cycle and transport over many cycles, between single-particle and interacting systems, and between extended states protected by topology and those arising from special disorder correlations.

### Figure to read

Resonant paths within a drive cycle and slow transport between them. [Figure 1 in the source paper](https://arxiv.org/pdf/1704.07390#page=2). Agarwal, Kartiek; Ganeshan, Sriram; Bhatt, R. N.. *Localization and transport in a strongly driven Anderson insulator*, Phys. Rev. B 96, 014201 (2017). Figure linked rather than reproduced; the archived manuscript does not provide an explicit open reproduction license.

Distinguish a closed sequence of Landau-Zener transitions from motion between different such orbits. Large intracycle excursions do not by themselves imply asymptotic diffusion.

### Floquet states and the time-domain trap

For a Hamiltonian repeated every period $T$, the one-period evolution operator defines Floquet eigenstates and quasienergies. These states organize long-time stroboscopic behavior, even when trajectories within one period are elaborate. A particle can move substantially during a cycle and return, or spread for an extended transient while its ultimate behavior remains constrained. The relevant observable and time window must therefore be specified before assigning a transport regime.

Agarwal, Ganeshan, and Bhatt analyze a monochromatically driven one-dimensional Anderson insulator at low frequency and strong amplitude. They map the Floquet problem to a hopping model with an additional harmonic-space coordinate. That mapping makes drive-induced resonances visible as couplings among photon sectors, but the resulting disorder is correlated; it is not simply an ordinary higher-dimensional random lattice. [1](https://doi.org/10.1103/PhysRevB.96.014201)

### Resonances without conventional diffusion

The paper identifies adiabatic Landau-Zener transitions at avoided crossings between localized states. Their proliferation can produce motion that appears diffusive on the scale of one cycle. Coherent evolution over successive cycles, however, changes the interpretation. The analyzed model remains localized, with slow transport associated with dephasing between these orbits and distant resonances. Short-time spreading is therefore an unreliable proxy for an indefinitely conducting Floquet phase. [1](https://doi.org/10.1103/PhysRevB.96.014201)

This distinction also clarifies why “strong driving” is incomplete information. Frequency, amplitude, spatial phase, localization length, and the structure of resonant crossings all influence the result. A spatially varying phase of the drive changes interference in a way that can reduce localization. The model thus offers several independently adjustable tests of mechanism rather than a single threshold at which disorder is assumed to stop mattering.

### Why the origin of a critical state matters

Ganeshan, Agarwal, and Bhatt later compare driven disordered bands that contain a subextensive set of extended states before driving. Their contrasting examples are a disordered Landau-level setting with a topologically protected critical energy and a random-dimer model whose extended states have a different origin. A naive mixing argument might predict enhanced delocalization in both. The computed Floquet behavior does not support that universal conclusion. [2](https://doi.org/10.1103/PhysRevB.102.134212)

The Landau-level model retains localized and delocalized or critical modes under the studied strong drives, with an enlarged spectral range of extended behavior. In the random-dimer setting, weak driving can instead localize the spectrum. This contrast ties the response to the protection mechanism of the original extended states. It connects the disorder branch to [topological materials](https://knowen.org/nodes/33549) without treating all extended wavefunctions as equivalent. [2](https://doi.org/10.1103/PhysRevB.102.134212)

### The wider driven-system landscape

Generic interacting Floquet systems raise an additional issue: sustained energy absorption. D'Alessio and Rigol's work analyzes the long-time behavior of periodically driven isolated interacting lattices, while rigorous prethermal theory identifies conditions for long-lived effective descriptions. Neither conclusion can be imported wholesale into the single-particle Anderson calculation. Interactions and the hierarchy of drive frequency to local energy scales change the physical problem. [3](https://doi.org/10.1103/PhysRevX.4.041048) [4](https://doi.org/10.1007/s00220-017-2930-x)

An instructive current comparison is the 2026 proposal to shape topological-insulator surface bands with circularly polarized light. There the aim is to engineer a useful dispersion and interaction-driven instability, rather than diagnose localization. Heating, occupation, and drive-induced changes in the band structure must all be assessed. [5](https://arxiv.org/abs/2607.27355)

The open methodological challenge is consistent long-time diagnosis. Compare Floquet eigenstate localization, multiple-cycle spreading, and sensitivity to drive phase; then add interactions or a bath deliberately. Read [symmetry engineering](https://knowen.org/nodes/33544) next for protocols that use periodic structure to protect selected dynamics instead of simply maximizing transport.

### References

1. Agarwal, Kartiek; Ganeshan, Sriram; Bhatt, R. N.. [Localization and transport in a strongly driven Anderson insulator](https://doi.org/10.1103/PhysRevB.96.014201). Phys. Rev. B 96, 014201 (2017). [Open manuscript](https://arxiv.org/abs/1704.07390).
2. Ganeshan, Sriram; Agarwal, Kartiek; Bhatt, R. N.. [Floquet dynamics of disordered bands with isolated critical energies](https://doi.org/10.1103/PhysRevB.102.134212). Phys. Rev. B 102, 134212 (2020). [Open manuscript](https://arxiv.org/abs/1912.12414).
3. D'Alessio, Luca; Rigol, Marcos. [Long-time behavior of periodically driven isolated interacting lattice systems](https://doi.org/10.1103/PhysRevX.4.041048). Phys. Rev. X 4, 041048 (2014). [Open manuscript](https://arxiv.org/abs/1402.5141).
4. Abanin, Dmitry; De Roeck, Wojciech; Ho, Wen Wei; Huveneers, Francois. [A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems](https://doi.org/10.1007/s00220-017-2930-x). Communications in Mathematical Physics 354, 809-827 (2017). [Open manuscript](https://arxiv.org/abs/1509.05386).
5. De, Suman Jyoti; Goutte, Leo; Agarwal, Kartiek; Pereg-Barnea, T.. [Flat-band formation and chiral superconductivity in driven topological insulators](https://arxiv.org/abs/2607.27355). Preprint, arXiv:2607.27355 (2026); journal publication not verified as of 5 September 2026. [Open manuscript](https://arxiv.org/abs/2607.27355).

*Independent research synthesis. Literature checked 5 September 2026; preprints are identified in the references.*

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# Parents

* Disorder, Localization & Slow Quantum Dynamics
* Non-equilibrium Control & Quantum State Preparation