Goran Gligorić

WAVE INTERACTIONS IN LOCALIZING MEDIA — A COIN WITH MANY FACES

A variety of heterogeneous potentials are capable of localizing linear noninteracting waves. In this work, we review different examples of heterogeneous localizing potentials which were realized in experiments. We then discuss the impact of nonlinearity induced by wave interactions, in particular, its destructive effect on the localizing properties of the heterogeneous potentials.

Stable Periodic Density Waves in Dipolar Bose-Einstein Condensates Trapped in Optical Lattices

Density-wave patterns in discrete media with local interactions are known to be unstable. We demonstrate that stable double- and triple-period patterns (DPPs and TPPs), with respect to the period of the underlying lattice, exist in media with nonlocal nonlinearity. This is shown in detail for dipolar Bose-Einstein condensates, loaded into a deep one-dimensional optical lattice. The DPP and TPP emerge via phase transitions of the second and first kind, respectively. The emerging patterns may be stable if the dipole-dipole interactions are repulsive and sufficiently strong, in comparison with the local repulsive nonlinearity. Within the set of the considered states, the TPPs realize a minimum of the free energy. A vast stability region for the TPPs is found in the parameter space, while the DPP stability region is relatively narrow. The same mechanism may create stable density-wave patterns in other physical media featuring nonlocal interactions.

Influence of boundary conditions on quantum escape

It has recently been established that quantum statistics can play a crucial role in quantum escape. Here we demonstrate that boundary conditions can be equally important —moreover, in certain cases, may lead to a complete suppression of the escape. Our results are exact and hold for arbitrarily many particles.

Interactions destroy dynamical localization with strong and weak chaos

Bose-Einstein condensates loaded into kicked optical lattices can be treated as quantum kicked-rotor systems. Noninteracting rotors show dynamical localization in momentum space. The experimentally tunable condensate interaction is included in a qualitative Gross-Pitaevskii–type model based on two-body interactions. We observe strong- and weak-chaos regimes of wave packet spreading in momentum space. In the intermediate strong-chaos regime the condensate energy grows as t1/2. In the asymptotic weak-chaos case the growth crosses over into a t1/3 law. The results do not depend on the details of the kicking.

Kinks and bell-type solitons in microtubules

In the present paper, we study the nonlinear dynamics of microtubules relying on the known u-model. As a mathematical procedure, we use the simplest equation method. We recover some solutions obtained earlier using less general methods. These are kink solitons. In addition, we show that the solution of the crucial differential equation, describing nonlinear dynamics of microtubules, can be a bell-type soliton. The discovery of this new solution is supported by numerical analysis.

Discrete localized modes supported by an inhomogeneous defocusing nonlinearity.

We report that infinite and semi-infinite lattices with spatially inhomogeneous self-defocusing (SDF) onsite nonlinearity, whose strength increases rapidly enough toward the lattice periphery, support stable unstaggered (UnST) discrete bright solitons, which do not exist in lattices with the spatially uniform SDF nonlinearity. The UnST solitons coexist with stable staggered (ST) localized modes, which are always possible under the defocusing onsite nonlinearity. The results are obtained in a numerical form and also by means of variational approximation (VA). In the semi-infinite (truncated) system, some solutions for the UnST surface solitons are produced in an exact form. On the contrary to surface discrete solitons in uniform truncated lattices, the threshold value of the norm vanishes for the UnST solitons in the present system. Stability regions for the novel UnST solitons are identified. The same results imply the existence of ST discrete solitons in lattices with the spatially growing self-focusing nonlinearity, where such solitons cannot exist either if the nonlinearity is homogeneous. In addition, a lattice with the uniform onsite SDF nonlinearity and exponentially decaying intersite coupling is introduced and briefly considered. Via a similar mechanism, it may also support UnST discrete solitons. The results may be realized in arrayed optical waveguides and collisionally inhomogeneous Bose-Einstein condensates trapped in deep optical lattices. A generalization for a two-dimensional system is briefly considered.

High- and low-frequency phonon modes in dipolar quantum gases trapped in deep lattices

We study normal modes propagating on top of the stable uniform background in arrays of dipolar Bose-Einstein condensate (BEC) droplets trapped in a deep optical lattice. Both the on-site mean-field dynamics of the droplets and their displacement due to the repulsive dipole-dipole interactions (DDIs) are taken into account. Dispersion relations for two modes, \textit{viz}., high- and low- frequency counterparts of optical and acoustic phonon modes in condensed matter, are derived analytically and verified by direct simulations, for both cases of the repulsive and attractive contact interactions. The (counterpart of the) optical-phonon branch does not exist without the DDIs. These results are relevant in the connection to emerging experimental techniques enabling real-time imaging of the condensate dynamics and direct experimental measurement of phonon dispersion relations in BECs.

Localized modes in mini-gaps opened by periodically modulated intersite coupling in two-dimensional nonlinear lattices

Spatially periodic modulation of the intersite coupling in two-dimensional (2D) nonlinear lattices modifies the eigenvalue spectrum by opening mini-gaps in it. This work aims to build stable localized modes in the new bandgaps. Numerical analysis shows that single-peak and composite two- and four-peak discrete static solitons and breathers emerge as such modes in certain parameter areas inside the mini-gaps of the 2D superlattice induced by the periodic modulation of the intersite coupling along both directions. The single-peak solitons and four-peak discrete solitons are stable in a part of their existence domain, while unstable stationary states (in particular, two-soliton complexes) may readily transform into robust localized breathers.

Make slow fast —How to speed up interacting disordered matter

Anderson and dynamical localization have been experimentally observed with ultra-cold atomic matter. Feshbach resonances are used to efficiently control the strength of interactions between atoms. This allows to study the delocalization effect of interactions for localized wave packets. The delocalization processes are subdiffusive and slow, thereby limiting the quantitative experimental and numerical analysis. We propose an elegant solution of the problem by proper ramping the interaction strength in time. We demonstrate that subdiffusion is speeded up to normal diffusion for interacting disordered and kicked atomic systems. The door is open to test these theoretical results experimentally, and to attack similar computational quests in higher space dimensions

On Moving Discrete Modes in Nonlinear Lattices

In this paper we summarize the results of our investigation of the moving localized structures in lattice like systems. Dynamics of discrete localized modes in cubic, cubic‐quintic, saturable photorefractive lattice and in the Bose‐Einstein condensate modelled by the nonpolynomial Schrodinger equation are considered in the framework of the Peierls‐Nabarro barrier. Two approaches are numerically tested: free‐energy approach and mapping analysis. We show that only the last one is appropriate.