arXiv subjects
Publications and source records attributed to Sergej Flach.
We study the scaling of the localization length of two interacting particles in a one-dimensional random lattice with the single particle localization length. We obtain several regimes, among them one interesting weak Fock space disorder regime. In this regime we derive a weak logarithmic scaling law. Numerical data support the absence of any strong enhancement of the two particle localization length.
We present computational data on the thermal conductivity of nonlinear waves in disordered chains. Disorder induces Anderson localization for linear waves and results in a vanishing conductivity. Cubic nonlinearity restores normal conductivity, but with a strongly temperature-dependent conductivity $κ(T)$. We find indications for an asymptotic low-temperature $κ\sim T^4$ and intermediate temperature $κ\sim T^2$ laws. These findings are in accord with theoretical studies of wave packet spreading, where a regime of strong chaos is found to be intermediate, followed by an asymptotic regime of weak chaos (EPL 91 (2010) 30001).
We review recent studies about quantum discrete breathers. We describe their basic properties in comparison with their classical counterparts, and the ways they may be addressed theoretically in different quantum lattice models including either bosonic or fermionic excitations. We also review recent experimental work in the field.
We investigate anomalous energy transport processes in the Fermi-Pasta-Ulam $β$ lattice. They are determined by the maximum sound velocity of the relevant weakly damped energy carriers. That velocity can be numerically resolved by measuring the propagating fronts of the correlation functions of energy/momentum fluctuations at different times. The numerical results are compared with the predictions for solitons and effective (renormalized) phonons, respectively. Excellent agreement has been found for the prediction of effective long wavelength phonons, giving strong evidence that the energy carriers should be effective phonons rather than solitons.
We study the dynamics of few interacting bosons in a one-dimensional lattice with dc bias. In the absence of interactions the system displays single particle Bloch oscillations. For strong interaction the Bloch oscillation regime reemerges with fractional Bloch periods which are inversely proportional to the number of bosons clustered into a bound state. The interaction strength is affecting the oscillation amplitude. Excellent agreement is found between numerical data and a composite particle dynamics approach. For specific values of the interaction strength a particle will tunnel from the interacting cloud to a well defined distant lattice location.
Nowadays nanotechnology allows to scale-down various important devices (sensors, chips, fibres, etc), and, thus, opens up new horizon for their applications. Nevertheless, the efficiency most of them is still based on the fundamental physical phenomena, such as resonances. Thus, the understanding of the resonance phenomena will be beneficial. One of the well-known examples is the resonant enhancement of the transmission known as Breit-Wigner resonances, which can be described by a Lorentzian function. But, in many physical systems 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 branches of physics. The purpose of this Review is to demonstrate that this kind of resonant scattering is related to the Fano resonances, known from atomic physics. One of the main features of the Fano resonances is the asymmetric profile. The asymmetry comes from the close coexistence of resonant transmission and resonant reflection. Fano successfully explained such a phenomenon in his seminal paper in 1961 in terms of interaction of a discrete (localized) state with a continuum of propagation modes. It allows to describe both resonant enhancement and resonant suppression in a unified manner. All of these properties can be demonstrated in the frame of a very simple model, which will be used throughout the Review to show that resonant reflections observed in different complex systems are indeed closely related to the Fano resonances.
We study the evolution of a wave packet in a nonlinear Schrödinger lattice equation subject to a dc bias. In the absence of nonlinearity all normal modes are spatially localized giving rise to a Stark ladder with an equidistant eigenvalue spectrum and Bloch oscillations. Nonlinearity induces frequency shifts and mode-mode interactions and destroys localization. With increasing strength of nonlinearity we observe: (I) localization as a transient, with subsequent subdiffusion (weak mode-mode interactions); (II) immediate subdiffusion (strong mode-mode interactions); (III) single site trapping as a transient, with subsequent explosive spreading, followed by subdiffusion. For single mode excitations and weak nonlinearities stability intervals are predicted and observed upon variation of the dc bias strength, which affect the short and long time dynamics.
In one-dimensional quantum lattice models with open boundaries, we find and study localization at the lattice edge. We show that edge-localized eigenstates can be found in both bosonic and fermionic systems, specifically, in the Bose-Hubbard model with on-site interactions and in the spinless fermion model with nearest-neighbor interactions. We characterize the localization through spectral studies via numerical diagonalization and perturbation theory, through considerations of the eigenfunctions, and through the study of explicit time evolution. We concentrate on few-particle systems, showing how more complicated edge states appear as the number of particles is increased.
We investigate the spectrum and eigenstates of a Bose-Hubbard chain containing two bosons with fixed boundary conditions. In the noninteracting case the eigenstates of the system define a two-dimensional normal-mode space. For the interacting case weight functions of the eigenstates are computed by perturbation theory and numerical diagonalization. We identify paths in the two-dimensional normal-mode space which are rims for the weight functions. The decay along and off the rims is algebraic. Intersection of two paths (rims) leads to a local enhancement of the weight functions. We analyze nonperturbative effects due to the degeneracies and the formation of two-boson bound states.
We study the localization of bosonic atoms in an optical lattice, which interact in a spatially confined region. The classical theory predicts that there is no localization below a threshold value for the strength of interaction that is inversely proportional to the number of participating atoms. In a full quantum treatment, however, we find that localized states exist for arbitrarily weak attractive or repulsive interactions for any number ($>1$) of atoms. We further show, using an explicit solution of the two-particle bound state and an appropriate measure of entanglement, that the entanglement tends to a finite value in the limit of weak interactions. Coupled with the non-existence of localization in an optimized quantum product state, we conclude that the localization exists by virtue of entanglement.
We study the rectification process of interacting quantum particles in a periodic potential exposed to the action of an external ac driving. The breaking of spatio-temporal symmetries leads to directed motion already in the absence of interactions. A hallmark of quantum ratcheting is the appearance of resonant enhancement of the current (Europhys. Lett. 79 (2007) 10007 and Phys. Rev. A 75 (2007) 063424). Here we study the fate of these resonances within a Gross-Pitaevskii equation which describes a mean field interaction between many particles. We find, that the resonance is i) not destroyed by interactions, ii) shifting its location with increasing interaction strength. We trace the Floquet states of the linear equations into the nonlinear domain, and show that the resonance gives rise to an instability and thus to the appearance of new nonlinear Floquet states, whose transport properties differ strongly as compared to the case of noninteracting particles.
It is shown that elastic resonance scattering of light by a finite-size obstacle with weak dissipation is analogous to quantum scattering by a potential with quasi-discrete levels and exhibits Fano resonances. Localized plasmons (polaritons), exited in the obstacle by the incident light, are equivalent to the quasi-discrete levels, while the radiative decay of these excitations plays exactly the same role as tunnelling from the quasi-discrete levels for the quantum problem. Mie scattering of light by a spherical particle and an exactly solvable discrete model with nonlocal coupling simulating wave scattering in systems with reduced spatial dimensionality are discussed as examples.
We study the spectrum and eigenstates of the quantum discrete Bose-Hubbard Hamiltonian in a finite one-dimensional lattice containing two bosons. The interaction between the bosons leads to an algebraic localization of the modified extended states in the normal mode space of the noninteracting system. Weight functions of the eigenstates in the space of normal modes are computed by using numerical diagonalization and perturbation theory. We find that staggered states do not compactify in the dilute limit for large chains.
We study nonlinear surface modes in two-dimensional {\em anisotropic} periodic photonic lattices and demonstrate that, in a sharp contrast to one-dimensional discrete surface solitons, the mode threshold power is lower at the surface, and two-dimensional discrete solitons can be generated easier near the lattice corners and edges. We analyze the crossover between effectively one- and two-dimensional regimes of the surface-mediated beam localization in the lattice.
Upon initial excitation of a few normal modes the energy distribution among all modes of a nonlinear atomic chain (the Fermi-Pasta-Ulam model) exhibits exponential localization on large time scales. At the same time resonant anomalies (peaks) are observed in its weakly excited tail for long times preceding equipartition. We observe a similar resonant tail structure also for exact time-periodic Lyapunov orbits, coined q-breathers due to their exponential localization in modal space. We give a simple explanation for this structure in terms of superharmonic resonances. The resonance analysis agrees very well with numerical results and has predictive power. We extend a previously developed perturbation method, based essentially on a Poincare-Lindstedt scheme, in order to account for these resonances, and in order to treat more general model cases, including truncated Toda potentials. Our results give qualitative and semiquantitative account for the superharmonic resonances of q-breathers and natural packets.
We study the transport of atoms across a localized Bose-Einstein condensate in a one-dimensional optical lattice. For atoms scattering off the condensate we predict total reflection as well as full transmission for certain parameter values on the basis of an exactly solvable model. The findings of analytical and numerical calculations are interpreted by a tunable Fano-like resonance and may lead to interesting applications for blocking and filtering atom beams.
We propose a setup to observe soliton ratchet effects using discrete cavity solitons in a one-dimensional array of coupled waveguide optical resonators. The net motion of solitons can be generated by an adiabatic shaking of the holding beam with zero average inclination angle. The resulting soliton velocity can be controlled by different parameters of the holding beam.
We study the two-dimensional extension of the Fano-Anderson model on the basis of a two-dimensional optical waveguide array with a bi-modal defect. We demonstrate numerically the persistence of the Fano resonance in wavepacket scattering process by the defect. An analytical approximation is derived for the total scattered light power.