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Miroshnichenko A.E.,Australian National University | Flach S.,Max Planck Institute For Physik Komplexer Systeme | Kivshar Y.S.,Australian National University
Reviews of Modern Physics | Year: 2010

Modern nanotechnology allows one to scale down various important devices (sensors, chips, fibers, etc.) and thus opens up new horizons for their applications. The efficiency of most of them is based on fundamental physical phenomena, such as transport of wave excitations and resonances. Short propagation distances make phase-coherent processes of waves important. Often the scattering of waves involves propagation along different paths and, as a consequence, results in interference phenomena, where constructive interference corresponds to resonant enhancement and destructive interference to resonant suppression of the transmission. Recently, a variety of experimental and theoretical work has revealed such patterns in different physical settings. The purpose of this review is to relate resonant scattering to Fano resonances, known from atomic physics. One of the main features of the Fano resonance is its asymmetric line profile. The asymmetry originates from a close coexistence of resonant transmission and resonant reflection and can be reduced to the interaction of a discrete (localized) state with a continuum of propagation modes. The basic concepts of Fano resonances are introduced, their geometrical and/or dynamical origin are explained, and theoretical and experimental studies of light propagation in photonic devices, charge transport through quantum dots, plasmon scattering in Josephson-junction networks, and matter-wave scattering in ultracold atom systems, among others are reviewed. © 2010 The American Physical Society.

Cherstvy A.G.,Max Planck Institute For Physik Komplexer Systeme
European Biophysics Journal | Year: 2011

We analyze looping of thin charged elastic filaments under applied torques and end forces, using the solution of linear elasticity theory equations. In application to DNA, we account for its polyelectrolyte character and charge renormalization, calculating electrostatic energies stored in the loops. We argue that the standard theory of electrostatic persistence is only valid when the loop's radius of curvature and close-contact distance are much larger than the Debye screening length. We predict that larger twist rates are required to trigger looping of charged rods as compared with neutral ones. We then analyze loop shapes formed on charged filaments of finite length, mimicking DNA looping by proteins with two DNA-binding domains. We find optimal loop shapes at different salt amounts, minimizing the sum of DNA elastic, DNA electrostatic, and protein elastic energies. We implement a simple model where intercharge repulsions do not affect the loop shape directly but can choose the energy-optimized shape from the allowed loop types. At low salt concentrations more open loops are favored due to enhanced repulsion of DNA charges, consistent with the results of computer simulations on formation of DNA loops by lac repressor. Then, we model the precise geometry of DNA binding by the lac tetramer and explore loop shapes, varying the confined DNA length and protein opening angle. The characteristics of complexes obtained, such as the total loop energy, stretching forces required to maintain its shape, and the reduction of electrostatic energy with increment of salt, are in good agreement with the outcomes of more elaborate numerical calculations for lac-repressor-induced DNA looping. © 2010 European Biophysical Societies' Association.

Arevalo E.,Max Planck Institute For Physik Komplexer Systeme
Physical Review Letters | Year: 2010

X waves are spatiotemporal optical waves with intriguing superluminal and subluminal characteristics. Here we theoretically show that for a given initial carrier frequency of the system localized waves with genuine superluminal or subluminal group velocity can emerge from initial X waves in nonlinear optical systems with normal group velocity dispersion. Moreover, we show that this temporal behavior depends on the wave detuning from the carrier frequency of the system and not on the particular X-wave biconical form. A spatial counterpart of this behavior is also found when initial X waves are boosted in the plane transverse to the direction of propagation, so a fully spatiotemporal motion of localized waves can be observed. © 2010 The American Physical Society.

Flach S.,Max Planck Institute For Physik Komplexer Systeme
Chemical Physics | Year: 2010

We analyze mechanisms and regimes of wave packet spreading in nonlinear disordered media. We predict that wave packets can spread in two regimes of strong and weak chaos. We discuss resonance probabilities, nonlinear diffusion equations, and predict a dynamical crossover from strong to weak chaos. The crossover is controlled by the ratio of nonlinear frequency shifts and the average eigenvalue spacing of eigenstates of the linear equations within one localization volume. We consider generalized models in higher lattice dimensions and obtain critical values for the nonlinearity power, the dimension, and norm density, which influence possible dynamical outcomes in a qualitative way. © 2010 Elsevier B.V. All rights reserved.

Pollmann F.,Max Planck Institute For Physik Komplexer Systeme | Turner A.M.,University of Amsterdam
Physical Review B - Condensed Matter and Materials Physics | Year: 2012

A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped symmetric phases in one-dimensional (1D) systems can be completely characterized using tools related to projective representations of the symmetry groups. We explain two ways to detect these symmetry protected topological phases in 1D. First, we give a numerical approach for directly extracting the projective representations from a matrix-product state representation. Second, we derive nonlocal order parameters for time-reversal and inversion symmetry, and discuss a generalized string order for local symmetries for which the regular string-order parameter cannot be applied. We furthermore point out that the nonlocal order parameter for these topological phases is actually related to topological surfaces. © 2012 American Physical Society.

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