# Kicked-Harper model versus on-resonance double-kicked rotor model: from spectral difference to topological equivalence.

@article{Wang2013KickedHarperMV, title={Kicked-Harper model versus on-resonance double-kicked rotor model: from spectral difference to topological equivalence.}, author={Hailong Wang and Derek Y H Ho and Wayne M. Lawton and Jiaozi Wang and Jiangbin Gong}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2013}, volume={88 5}, pages={ 052920 } }

Recent studies have established that, in addition to the well-known kicked-Harper model (KHM), an on-resonance double-kicked rotor (ORDKR) model also has Hofstadter's butterfly Floquet spectrum, with strong resemblance to the standard Hofstadter spectrum that is a paradigm in studies of the integer quantum Hall effect. Earlier it was shown that the quasienergy spectra of these two dynamical models (i) can exactly overlap with each other if an effective Planck constant takes irrational multiples…

## 23 Citations

### Floquet topological phases in a spin- 1/2 double kicked rotor

- PhysicsPhysical Review A
- 2018

The double kicked rotor model is a physically realizable extension of the paradigmatic kicked rotor model in the study of quantum chaos. Even before the concept of Floquet topological phases became…

### Non-Hermitian Floquet topological phases in the double-kicked rotor

- PhysicsPhysical Review A
- 2019

Dynamical kicking systems possess rich topological structures. In this work, we study Floquet states of matter in a non-Hermitian extension of double kicked rotor model. Under the on-resonance…

### Topological phases of the kicked Harper–Kitaev model with ultracold atoms

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2017

It is found that both Floquet Majorana modes and Hall chiral edge modes could appear at the sample boundary in the gaps between the quasienergy bands, and the competition of topological superconductor and Chern insulator states in the model is studied.

### Floquet topological phase transitions in a kicked Haldane-Chern insulator

- Physics
- 2018

We consider a periodically $\delta$-kicked Haldane type Chern insulator with the kicking applied in the $\hat{z}$ direction. This is known to behave as an inversion symmetry breaking perturbation,…

### Floquet systems with Hall effect: Topological properties and phase transitions

- PhysicsPhysical Review B
- 2019

We study the quantum topological properties of Floquet (time-periodic) systems exhibiting Hall effects due to perpendicular magnetic and electric fields. The systems are charged particles…

### Floquet Second-Order Topological Phases in Momentum Space

- PhysicsNanomaterials
- 2021

A momentum-space counterpart of HOTPs is revealed in time-periodic driven systems, which is demonstrated in a two-dimensional extension of the quantum double-kicked rotor and protected by chiral symmetry and characterized by a pair of topological invariants.

### Floquet topological phases with high Chern numbers in a periodically driven extended Su–Schrieffer–Heeger model

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2022

The high Chern number phases with the Chern number |C| > 1 are observed in this study of a periodically driven extended Su–Schrieffer–Heeger (E-SSH) model with a cyclic parameter. Besides the…

### Localization and delocalization properties in quasi-periodically perturbed Kicked Harper and Harper models

- Physics
- 2021

We numerically study the single particle localization and delocalization phenomena of an initially localized wave packet in the kicked Harper model (KHM) and Harper model subjected to quasiperiodic…

### Dynamical characterization of Weyl nodes in Floquet Weyl semimetal phases

- Physics
- 2020

Due to studies in nonequilibrium (periodically-driven) topological matter, it is now understood that some topological invariants used to classify equilibrium states of matter do not suffice to…

### Aspects of Floquet bands and topological phase transitions in a continuously driven superlattice

- Physics
- 2014

The recent creation of novel topological states of matter via periodic driving fields has attracted much attention. To contribute to the growing knowledge on this subject, we study the well-known…

## References

SHOWING 1-10 OF 52 REFERENCES

### Spectral relationships between kicked Harper and on-resonance double kicked rotor operators

- Mathematics
- 2009

Kicked Harper operators and on-resonance double kicked rotor operators model quantum systems whose semiclassical limits exhibit chaotic dynamics. Recent computational studies indicate a striking…

### Exponential quantum spreading in a class of kicked rotor systems near high-order resonances.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

It is found that the existence of a flat band is one important feature behind why and how the exponential dynamics emerges and a quantitative prediction of the exponential spreading rate based on an interesting and simple pseudoclassical map may be inaccurate.

### Extended and localized states of generalized kicked Harper models.

- MathematicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1995

Basic properties of quantum states for generalized Harper models are studied using the phase-space translational symmetry of the problem, and it is shown that \ensuremath{\sigma} is always different from zero for qg1.

### General approach to the quantum kicked particle in a magnetic field: quantum-antiresonance transition.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

The quantum kicked particle in a magnetic field is studied in a weak-chaos regime under realistic conditions, i.e., for general values of the conserved coordinate x(c) of the cyclotron orbit center.…

### Antiresonance and localization in quantum dynamics.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

By considering exactly-solvable cases, numerical evidence is given that QAR-localization is an excellent approximation to DL sufficiently close to QAR, as the level of chaos is increased.

### General quantum resonances of the kicked particle.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

It is shown that QR can arise, in general, for any rational value of the Bloch quasimomentum, and this is illustrated in the case of the main QRs for arbitrary potentials.

### Topological singularities and transport in kicked Harper model.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

Quasienergy spectrum of kicked Harper model is found to exhibit a series of diabolic crossings, which suggest a correlation between the transport and the topological characteristics of the system.

### Dimer decimation and intricately nested localized-ballistic phases of a kicked Harper model.

- Computer Science, PhysicsPhysical review letters
- 2001

A new decimation scheme is introduced to study localization transitions in tight binding models with long range interaction and the renormalization tools provide a new method to compute quasienergy spectrum.

### Sub-Fourier characteristics of a δ-kicked-rotor resonance.

- PhysicsPhysical review letters
- 2010

A theoretical analysis shows that for an accelerating potential the width of the resonance in acceleration space depends on 1/N3, a property which is verified experimentally and could be useful for high precision gravity measurements.