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# Many-body dynamical localisation of coupled quantum kicked rotors

TL;DR: In this paper, the quantum motion of coupled kicked rotors is mapped to an interacting lattice model supporting many-body localised (MBL) phases, which predicts that a similar effect takes place in momentum space.

Abstract: The quantum motion of $N$ coupled kicked rotors is mapped to an interacting $N$-particle Anderson-Aubry-Andr$e$ tight-binding problem supporting many-body localised (MBL) phases. Interactions in configuration space are known to be insufficient for destroying Anderson localisation in a system in the MBL phase. The mapping we establish here predicts that a similar effect takes place in momentum space and determines the quantum dynamics of the coupled kicked rotors. Due to the boundedness of the Floquet quasi-energy spectrum there exists limitations on the interacting lattice models that can be mapped to quantum kicked rotors; in particular, no extensive observable can be mapped in the thermodynamic limit.

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TL;DR: In this article, the authors introduce quantum mechanics of classically chaotic systems, or quantum chaos for short, with experimental or numerical examples of microwave billiard experiments, initiated by the author and his group.

Abstract: This book introduces the quantum mechanics of classically chaotic systems, or quantum chaos for short. The author's philosophy has been to keep the discussion simple and to illustrate theory, wherever possible, with experimental or numerical examples. The microwave billiard experiments, initiated by the author and his group, play a major role in this respect. Topics covered include the various types of billiard experiment, random matrix theory, systems with periodic time dependences, the analogy between the dynamics of a one-dimensional gas with a repulsive interaction and spectral level dynamics, where an external parameter takes the role of time, scattering theory distributions and fluctuation, properties of scattering matrix elements, semiclassical quantum mechanics, periodic orbit theory, and the Gutzwiller trace formula. This book will be of great value to anyone working in quantum chaos.

912 citations

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01 Jan 1979

TL;DR: In this paper, a survey of the Henon-Heiles Hamiltonian with applications to related examples can be found, including a question about the localized mode due to a light impurity and the role of periodic orbits in semiclassical quantization.

Abstract: Integrable and stochastic behaviour in dynamical astronomy.- Adiabatic and stochastic motion of charged particles in the field of a single wave.- Numerical study of particle motion in two waves.- Stochastic ion heating by a perpendicularly propagating electrostatic wave.- Preservation of conditionally periodic movements with small change in the Hamilton function.- On resonant hamiltonians with two degrees of freedom near an equilibrium point.- A survey of the Henon-Heiles Hamiltonian with applications to related examples.- Ergodic components in the stochastic region in a Hamiltonian system.- A question about the localized mode due to a light impurity.- Nonlinear oscillation regimes in some physical problems.- Metric universality in nonlinear recurrence.- Magnetic flux annihilation in a large Josephson junction.- Some non-linear physics in crystallographic structures.- Laser instabilities - an example from synergetics.- Dynamics and ergodicity of the infinite harmonic crystal a review of some salient features.- Geodesic correction to stochastic parallel displacement of tensors.- The method of Dirichlet forms.- Regular and irregular spectra of molecules.- Semiclassical studies of bound states and molecular dynamics.- The role of periodic orbits in semiclassical quantization.- Semiclassical eigenvalues for rotating triatomic molecules.- Semiclassical calculation of vibrational energy levels for nonseparable potentials.- Classical quantization conditions for a dynamical system with stochastic behavior?.- Semi-classical ergodicity of quantum eigenstates in the Wigner representation.- Stochastic behavior of a quantum pendulum under a periodic perturbation.- Periodic solutions of arbitrary period, variational methods.

489 citations

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01 Jan 1998

Abstract: Introduction. Hydrodynamic simulation of semiconductor devices. Simulation of semiclassical transport. Cellular automata in high-field semiconductor transport. Quantum transport theory. Density matrix theory of coherent ultrafast dynamics. Dynamic and nonlinear transport in mesoscopic structures. Transport in systems with chaotic dynamics: lateral superlattices. Bloch oscillations and Wannier-Stark localization in semiconductor superlattices. Vertical transport and domain formation in multiple quantum wells. Scattering processes in low-dimensional semiconductor structures.

190 citations

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01 Jan 2008

TL;DR: In this paper, the physical minimum is defined as the number of atoms that can be present in the system at a given moment in time, and the role of the Franz-Keldysh effect is discussed.

Abstract: 0. Preface 1. Recollections 2. Once again on the "Physical Minimum" 3. Hybrid Organic-Inorganic Nanostructures and Light-Matter Interaction 4. The acoustic-wave driven quantum processor 5. On the problem of many-body localization 6. Raman scattering by LO phonons in semiconductors: the role of the Franz-Keldysh effect 7. Phenomena in cold exciton gases: from theory to experiments 8. Composite Fermions and Fractional Quantum Hall effect in two-dimensional electron system 9. Microcavities with quantum dots: weak and strong coupling regimes 10. Dynamics of cold excitons and electron-hole ensembles in direct-gap semiconductors studied by mid-infrared pump and probe spectroscopy 11. Exciton Coherence 12. Inelastic Light Scattering by Low-lying Excitations of Quantum Hall Fluids 13. Remarks on Surface-atoms Forces in London and Lifshitz Limits 14. Modern trends in semiconductor spintronics 15. Excitonic insulators, electron-hole liquids and metal-insulator transitions 16. Electron-hole liquid in semiconductors 17. Collective state of interwell excitons in double quantum wells heterostructures 18. Bose-Einstein condensation of excitons: Promise and disappointment 19. Acoustically induced superlattices: from photons and electrons to excitons and polaritons 20. Inelastic tunneling spectroscopy of single surface adsorbed molecules

17 citations

### "Many-body dynamical localisation of..." refers background in this paper

...However, in 2006, Basko, Aleiner, and Altshuler showed that under suitable conditions interactions are insufficient to thermalise the system and localisation can in fact persist in a disordered quantum many-body system [39, 40]....

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