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 inter-site coupling is introduced and briefly considered too. Via a similar mechanism, it may also support UnST discrete solitons, under the action of the SDF nonlinearity. 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 too.Comment: 14 pages, 7 figures, accepted for publication in PR

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.Comment: Physical Review A, in pres

Discrete solitons in an array of quantum dots

We develop a theory for the interaction of classical light fields with an a chain of coupled quantum dots (QDs), in the strong-coupling regime, taking into account the local-field effects. The QD chain is modeled by a one-dimensional (1D) periodic array of two-level quantum particles with tunnel coupling between adjacent ones. The local-field effect is taken into regard as QD depolarization in the Hartree-Fock-Bogoliubov approximation. The dynamics of the chain is described by a system of two discrete nonlinear Schr\"{o}dinger (DNLS) equations for local amplitudes of the probabilities of the ground and first excited states. The two equations are coupled by a cross-phase-modulation cubic terms, produced by the local-field action, and by linear terms too. In comparison with previously studied DNLS systems, an essentially new feature is a phase shift between the intersite-hopping constants in the two equations. By means of numerical solutions, we demonstrate that, in this QD chain, Rabi oscillations (RO) self-trap into stable bright\textit{\ Rabi solitons} or \textit{Rabi breathers}. Mobility of the solitons is considered too. The related behavior of observable quantities, such as energy, inversion, and electric-current density, is given a physical interpretation. The results apply to a realistic region of physical parameters.Comment: 12 pages, 10 figures, Phys. Rev. B, in pres

Spectroscopic characteristics of highly selective manganese catalysis in acqueous polyurethane systems

The latest investigations on producing more efficient catalytic aqueous polyurethane systems are in the domain of metal complexes with mixed ligands. In our previous research works, the high selectivity for the isocyanate-hydroxyl reaction in aqueous polyurethane systems has been shown by the manganese(III) mixed-ligand complexes. The two new complexes have been prepared with two acetylacetonate (acac) ligands and one maleate ligand and its hydroxylamine derivative of the general formula [Mn(C5H7O2)(2)L]. Their structures have been established by using the fundamental analyses, the FTIR and UV/VIS spectroscopic methods, as well as the magnetic measurements. In order to explain the different selectivity of the manganese(III) mixed-ligand complexes, the UV and ESR spectroscopy have been employed to determine the kinetics of the complexes' decomposition. The thermal stability of the complexes has been determined by way of the dynamic TG method at the heating rate of 5 degrees C.min(-1) and at the temperature ranged 20-550 degrees C. It suggests the decomposition of the complexes by loss of acid ligand. The main factor in the selective catalysis control in the aqueous polyurethane systems is the nature of the acid ligands and their impact on the manganese(II)/manganese(III) equilibrium

Thermal stability of aqueous polyurethanes depending on the applied catalysts

The thermal stability of aqueous polyurethanes has been measured applying the thermogravimetric analysis. The aqueous polyurethanes (aqPUR) with catalysts of different selectivity have been studied by use of the dynamic method. To obtain degradations of 0.025, 0.05, and 0.10, employing the dynamic method, the heating rates of 0.5, 1, 2, 5, and 10 degrees C min(-1) have been used in the range of 30-500 degrees C. Using the more selective catalysts in the aqueous polyurethanes, the total resulting time of the decompositon has been on the increase at all degrees of the degradation and at the particular starting temperature. This paper shows that the dynamic method based on the thermogravimetric analysis can be used to assess the thermal stability of the aqueous polyurethanes using the catalysts of different selectivity

Nonlinear symmetry breaking of Aharonov-Bohm cages

We study the influence of mean-field cubic nonlinearity on Aharonov-Bohm caging in a diamond lattice with synthetic magnetic flux. For sufficiently weak nonlinearities, the Aharonov-Bohm caging persists as periodic nonlinear breathing dynamics. Above a critical nonlinearity, symmetry breaking induces a sharp transition in the dynamics and enables stronger wave-packet spreading. This transition is distinct from other flatband networks, where continuous spreading is induced by effective nonlinear hopping or resonances with delocalized modes and is in contrast to the quantum limit, where two-particle hopping enables arbitrarily large spreading. This nonlinear symmetry-breaking transition is readily observable in femtosecond laser-written waveguide arrays