Many-body energy localization transition in periodically driven systems

According to the second law of thermodynamics the total entropy of a system is increased during almost any dynamical process. The positivity of the specific heat implies that the entropy increase is associated with heating. This is generally true both at the single particle level, like in the Fermi acceleration mechanism of charged particles reflected by magnetic mirrors, and for complex systems in everyday devices. Notable exceptions are known in noninteracting systems of particles moving in periodic potentials. Here the phenomenon of dynamical localization can prevent heating beyond certain threshold. The dynamical localization is known to occur both at classical (Fermi–Ulam model) and at quantum levels (kicked rotor). However, it was believed that driven ergodic systems will always heat without bound. Here, on the contrary, we report strong evidence of dynamical localization transition in both classical and quantum periodically driven ergodic systems in the thermodynamic limit. This phenomenon is reminiscent of many-body localization in energy space.     

Periodically driven ergodic and many-body localized quantum systems

We study dynamics of isolated quantum many-body systems whose Hamiltonian is switched between two different operators periodically in time. The eigenvalue problem of the associated Floquet operator maps onto an effective hopping problem. Using the effective model, we establish conditions on the spectral properties of the two Hamiltonians for the system to localize in energy space. We find that ergodic systems always delocalize in energy space and heat up to infinite temperature, for both local and global driving. In contrast, many-body localized systems with quenched disorder remain localized at finite energy. We support our conclusions by numerical simulations of disordered spin chains. We argue that our results hold for general driving protocols, and discuss their experimental implications.     

Tunnelling in periodically driven systems

Tunnelling in periodically driven bistable symmetric potential wells is investigated in an analytical approximation in a domain where the driving frequency is large compared to the tunnelling frequency and only the four lowest lying levels contribute significantly. The influence of finite level widths is taken into account, and a smooth variation of the amplitude of the driving field is allowed for.     

Hall resistance and the diamagnetic moment of periodically modulated two-dimensional systems

It is argued that the Hall resistance of macroscopic samples can be directly obtained by ensemble averaged transport properties of mesoscopic systems. The resulting formula relates the Hall current to the part of the magnetic moment of Fermi electrons, which originates in macroscopic currents only. As one of the possible application the Hall resistance of the periodically modulated two-dimensional electron system in the strong magnetic field is briefly discussed.     

Survival probability and saturation energy in periodically driven quantum chaotic systems

We study characteristics of the steady state of a random-matrix model with periodical pumping, where the energy increase saturates by quantum localization. We study the dynamics by making use of the survival probability. We found that Floquet eigenstates are separated into the localized and extended states, and the former governs the dynamics.     

Atom localization in a four-level atomic system with an assisting radio-frequency driven field

We propose a scheme for atom localization in a four-level atomic system by means of a radio-frequency field driving a hyperfine transition within the two ground states. It is found that, due to the quantum disturbed effect induced by the radio-frequency field, the property of atom localization can be significantly controlled. This scheme shows some characteristics that other schemes of atom localization do not have, which may provide some possibilities for the technological applications in atom nano-lithography.     

Many-body localization in disorder-free systems: The importance of finite-size constraints

Recently it has been suggested that many-body localization (MBL) can occur in translation-invariant systems, and candidate 1D models have been proposed. We find that such models, in contrast to MBL systems with quenched disorder, typically exhibit much more severe finite-size effects due to the presence of two or more vastly different energy scales. In a finite system, this can artificially split the density of states (DOS) into bands separated by large gaps. We argue for such models to faithfully represent the thermodynamic limit behavior, the ratio of relevant coupling must exceed a certain system-size depedent cutoff, chosen such that various bands in the DOS overlap one another. Setting the parameters this way to minimize finite-size effects, we study several translation-invariant MBL candidate models using exact diagonalization. Based on diagnostics including entanglement and local observables, we observe thermal (ergodic), rather than MBL-like behavior. Our results suggest that MBL in translation-invariant systems with two or more very different energy scales is less robust than perturbative arguments suggest, possibly pointing to the importance of non-perturbative effects which induce delocalization in the thermodynamic limit.     

Phase separation dynamics in driven diffusive systems

We study phase separation dynamics in a driven diffusive system. Our simulations are based on the Cahn-Hilliard equation with an additional flux term due to an external field. We study the dynamical scaling parallel and perpendicular to the field. A crossover is observed from isotropic domains at early times to extremely anisotropic domains at later times. We find that the inverse interfacial density (an isotropic measure of the domain size) increases ast , with =1/3, from early times independent of the field strength, even though we do not observe dynamical scaling during these times. Our results indicate that a growth exponent =1/3 may be more universal than previously expected. We analyze the dynamics in terms of surface driven instabilities and one-dimensional solitary waves.     

Activated escape of periodically driven systems

We discuss activated escape from a metastable state of a system driven by a time-periodic force. We show that the escape probabilities can be changed very strongly even by a comparatively weak force. In a broad parameter range, the activation energy of escape depends linearly on the force amplitude. This dependence is described by the logarithmic susceptibility, which is analyzed theoretically and through analog and digital simulations. A closed-form explicit expression for the escape rate of an overdamped Brownian particle is presented and shown to be in quantitative agreement with the simulations. We also describe experiments on a Brownian particle optically trapped in a double-well potential. A suitable periodic modulation of the optical intensity breaks the spatio-temporal symmetry of an otherwise spatially symmetric system. This has allowed us to localize a particle in one of the symmetric wells. (c) 2001 American Institute of Physics.     

Anomalous localization in low-dimensional systems with correlated disorder

This review presents a unified view on the problem of Anderson localization in one-dimensional weakly disordered systems with short-range and long-range statistical correlations in random potentials. The following models are analyzed: the models with continuous potentials, the tight-binding models of the Anderson type, and various Kronig–Penney models with different types of perturbations. Main attention is paid to the methods of obtaining the localization length in dependence on the controlling parameters of the models. Specific interest is in an emergence of effective mobility edges due to certain long-range correlations in a disorder. The predictions of the theoretical and numerical analysis are compared to recent experiments on microwave transmission through randomly filled waveguides.     

Energy transduction in periodically driven non-hermitian systems

We show a new mechanism to extract energy from nonequilibrium fluctuations typical of periodically driven non-Hermitian systems. The transduction of energy between the driving force and the system is revealed by an anomalous behavior of the susceptibility, leading to a diminution of the dissipated power and consequently to an improvement of the transport properties. The general framework is illustrated by the analysis of some relevant cases.     

Enumeration of many-body skeleton diagrams

The many-body dynamics of interacting electrons in condensed matter and quantum chemistry is often studied at the quasiparticle level, where the perturbative diagrammatic series is partially resummed. Based on Hedin's equations for self-energy, polarization, propagator, effective potential, and vertex function, dressed (skeleton) Feynman diagrams are enumerated. Such diagram counts provide useful simple checks for extensions of the theory for future realistic simulations.     

Strong-coupling theory of periodically driven two-level systems

We present a simple but highly efficient iterating approach for strong-coupling periodically driven two-level systems. The obtained explicit approximating analytical solution reproduces accurately the exact numerical solution in the strong-coupling regime for a wide frequency range including resonance, far-off resonance, harmonic, and subharmonic cases. Our theory is suitable for single- and multi-period periodic driving and for the periodic driving with a few-cycle pulse as well, and it gives a general formula for calculating the strong-field ac Stark effect in such diverse situations.     

Coherent transport in a periodically driven bistable system

The quantum dynamics of a quartic double well, subjected to a harmonically oscillating field, is studied in the framework of the Floquet formalism. The modifications of the familiar tunneling process due to the driving are investigated numerically and explained in terms of the structure of the corresponding local quasienergy spectrum. In particular, there is a one-dimensional manifold in the parameter space spanned by the amplitude and frequency of the driving force, where tunneling is almost completely suppressed by the coherent driving. The quantal dynamics in the semiclassical regime as well as the influence of weak incoherent processes are briefly discussed.     

Few- and many-body methods in nuclear physics

In this contribution a brief overview of the status and perspectives of the theoretical methods for studying light and heavy nuclear systems is presented.     

Scaling and decay in periodically driven scattering systems

We investigate irregular scattering in a periodically driven Hamiltonian system of one degree of freedom. The potential is asymptotically attracting, so there exist parabolically escaping scattering orbits, i.e. orbits with asymptotic energy E(out)=0. The scattering functions (i.e. the asymptotic out-variables as functions of an asymptotic in-variable) show a characteristic algebraic scaling in the vicinity of these orbits. This behavior is explained by asymptotic properties of the interaction. As a consequence, the number N(Deltat) of temporarily bound particles decays algebraically with the delay time Deltat, although no KAM scenario can be found in phase space. On the other hand, we find the number N(n) of temporarily bound particles to decay exponentially with the number n of zeros of x(t).     

Long-lasting exponential spreading in periodically driven quantum systems

Using a dynamical model relevant to cold-atom experiments, we show that long-lasting exponential spreading of wave packets in momentum space is possible. Numerical results are explained via a pseudoclassical map, both qualitatively and quantitatively. Possible applications of our findings are also briefly discussed.     

Quantum mechanics of rapidly and periodically driven systems

This review deals with the dynamics of quantum systems that are subject to high frequency external perturbations. Though the problem may look hopelessly time-dependent, and poised on the extreme opposite side of adiabaticity, there exists a ‘Kapitza Window’ over which the dynamics can be treated in terms of effective time-independent Hamiltonians. The consequent results are important in the context of atomic traps as well as quantum optic properties of atoms in intense and high-frequency electromagnetic fields.      

Semiclassical theory for many-body fermionic systems

We present a treatment of many-body fermionic systems that facilitates an expression of well-known quantities in a series expansion inħ. The ensuing semiclassical result contains, to a leading order of the response function, the classical time correlation function of the observable followed by the Weyl-Wigner series; on top of these terms are the periodic-orbit correction terms. The treatment given here starts from linear response assumption of the many-body theory and in its connection with semiclassical theory, it assumes that the one-body quantal system has a classically chaotic dynamics. Applications of the framework are also discussed.