Resonance Effects in the Nonadiabatic Nonlinear Quantum Dimer

The quantum nonlinear dimer consisting of an electron shuttling between the two sites and in weak interaction with vibrations, is studied numerically under the application of a DC electric field. A field-induced resonance phenomenon between the vibrations and the electronic oscillations is found to influence the electronic transport greatly. For initially delocalization of the electron, the resonance has the effect of a dramatic increase in the transport. Nonlinear frequency mixing is identified as the main mechanism that influences transport. A characterization of the frequency spectrum is also presented.Comment: 7 pages, 6 figure

Zener transitions between dissipative Bloch bands. II: Current Response at Finite Temperature

We extend, to include the effects of finite temperature, our earlier study of the interband dynamics of electrons with Markoffian dephasing under the influence of uniform static electric fields. We use a simple two-band tight-binding model and study the electric current response as a function of field strength and the model parameters. In addition to the Esaki-Tsu peak, near where the Bloch frequency equals the damping rate, we find current peaks near the Zener resonances, at equally spaced values of the inverse electric field. These become more prominenent and numerous with increasing bandwidth (in units of the temperature, with other parameters fixed). As expected, they broaden with increasing damping (dephasing).Comment: 5 pages, LateX, plus 5 postscript figure

Extended States in a One-dimensional Generalized Dimer Model

The transmission coefficient for a one dimensional system is given in terms of Chebyshev polynomials using the tight-binding model. This result is applied to a system composed of two impurities located between $N$ sites of a host lattice. It is found that the system has extended states for several values of the energy. Analytical expressions are given for the impurity site energy in terms of the electron's energy. The number of resonant states grows like the number of host sites between the impurities. This property makes the system interesting since it is a simple task to design a configuration with resonant energy very close to the Fermi level $E_F$.Comment: 4 pages, 3 figure

Scaling Properties of 1D Anderson Model with Correlated Diagonal Disorder

Statistical and scaling properties of the Lyapunov exponent for a tight-binding model with the diagonal disorder described by a dichotomic process are considered near the band edge. The effect of correlations on scaling properties is discussed. It is shown that correlations lead to an additional parameter governing the validity of single parameter scaling.Comment: 5 pages, 3 figures, RevTe

Holstein polarons in a strong electric field: delocalized and stretched states

The coherent dynamics of a Holstein polaron in strong electric fields is considered under different regimes. Using analytical and numerical analysis, we show that even for small hopping constant and weak electron-phonon interaction, the original discrete Wannier-Stark (WS) ladder electronic states are each replaced by a semi-continuous band if a resonance condition is satisfied between the phonon frequency and the ladder spacing. In this regime, the original localized WS states can become {\em delocalized}, yielding both `tunneling' and `stretched' polarons. The transport properties of such a system would exhibit a modulation of the phonon replicas in typical tunneling experiments. The modulation will reflect the complex spectra with nearly-fractal structure of the semi-continuous band. In the off-resonance regime, the WS ladder is strongly deformed, although the states are still localized to a degree which depends on the detuning: Both the spacing between the levels in the deformed ladder and the localization length of the resulting eigenfunctions can be adjusted by the applied electric field. We also discuss the regime beyond small hopping constant and weak coupling, and find an interesting mapping to that limit via the Lang-Firsov transformation, which allows one to extend the region of validity of the analysis.Comment: 10 pages, 13 figures, submitted to PR

ac-Field-Controlled Anderson Localization in Disordered Semiconductor Superlattices

An ac field, tuned exactly to resonance with the Stark ladder in an ideal tight binding lattice under strong dc bias, counteracts Wannier-Stark localization and leads to the emergence of extended Floquet states. If there is random disorder, these states localize. The localization lengths depend non-monotonically on the ac field amplitude and become essentially zero at certain parameters. This effect is of possible relevance for characterizing the quality of superlattice samples, and for performing experiments on Anderson localization in systems with well-defined disorder.Comment: 10 pages, Latex; figures available on request from [email protected]

Self-induced and induced transparencies of two-dimensional and three- dimensional superlattices

The phenomenon of transparency in two-dimensional and three-dimensional superlattices is analyzed on the basis of the Boltzmann equation with a collision term encompassing three distinct scattering mechanisms (elastic, inelastic and electron-electron) in terms of three corresponding distinct relaxation times. On this basis, we show that electron heating in the plane perpendicular to the current direction drastically changes the conditions for the occurrence of self-induced transparency in the superlattice. In particular, it leads to an additional modulation of the current amplitudes excited by an applied biharmonic electric field with harmonic components polarized in orthogonal directions. Furthermore, we show that self-induced transparency and dynamic localization are different phenomena with different physical origins, displaced in time from each other, and, in general, they arise at different electric fields.Comment: to appear in Physical Review

Upper bounds on wavepacket spreading for random Jacobi matrices

A method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix. As an application, one obtains sharp upper bounds on the diffusion exponents for random polymer models, coinciding with the lower bounds obtained in a prior work. The second application is an elementary argument (not using multiscale analysis or the Aizenman-Molchanov method) showing that under the condition of uniformly positive Lyapunov exponents, the moments of the position operator grow at most logarithmically in time.Comment: final version, to appear in CM

Localization of interacting electrons in quantum dot arrays driven by an ac-field

We investigate the dynamics of two interacting electrons moving in a one-dimensional array of quantum dots under the influence of an ac-field. We show that the system exhibits two distinct regimes of behavior, depending on the ratio of the strength of the driving field to the inter-electron Coulomb repulsion. When the ac-field dominates, an effect termed coherent destruction of tunneling occurs at certain frequencies, in which transport along the array is suppressed. In the other, weak-driving, regime we find the surprising result that the two electrons can bind into a single composite particle -- despite the strong Coulomb repulsion between them -- which can then be controlled by the ac-field in an analogous way. We show how calculation of the Floquet quasienergies of the system explains these results, and thus how ac-fields can be used to control the localization of interacting electron systems.Comment: 7 pages, 6 eps figures V2. Minor changes, this version to be published in Phys. Rev.

Hidden dimers and the matrix maps: Fibonacci chains re-visited

The existence of cycles of the matrix maps in Fibonacci class of lattices is well established. We show that such cycles are intimately connected with the presence of interesting positional correlations among the constituent `atoms' in a one dimensional quasiperiodic lattice. We particularly address the transfer model of the classic golden mean Fibonacci chain where a six cycle of the full matrix map exists at the centre of the spectrum [Kohmoto et al, Phys. Rev. B 35, 1020 (1987)], and for which no simple physical picture has so far been provided, to the best of our knowledge. In addition, we show that our prescription leads to a determination of other energy values for a mixed model of the Fibonacci chain, for which the full matrix map may have similar cyclic behaviour. Apart from the standard transfer-model of a golden mean Fibonacci chain, we address a variant of it and the silver mean lattice, where the existence of four cycles of the matrix map is already known to exist. The underlying positional correlations for all such cases are discussed in details.Comment: 14 pages, 2 figures. Submitted to Physical Review