Narrow Results

We study transport dynamics of quantum systems with long-range steps on the Watts–Strogatz network (WSN) which is generated by rewiring links of the regular ring. First, we probe physical systems modeled by the discrete nonlinear schrödinger (DNLS) equation. Using the localized initial condition, we compute the time-averaged occupation probability of the initial site, which is related to the nonlinearity, the long-range steps and rewiring links. Self-trapping transitions occur at large (small) nonlinear parameters for coupling $ϵ=-1$ (1), as long-range interactions are intensified. The structure disorder induced by random rewiring, however, has dual effects for $ϵ=-1$ and inhibits the self-trapping behavior for $ϵ=1$. Second, we investigate continuous-time quantum walks (CTQW) on the regular ring ruled by the discrete linear schrödinger (DLS) equation. It is found that only the presence of the long-range steps does not affect the efficiency of the coherent exciton transport, while only the allowance of random rewiring enhances the partial localization. If both factors are considered simultaneously, localization is greatly strengthened, and the transport becomes worse.

We examine numerically the long-time average probability in a two-site system, for finding an electron staying at an initially occupied site for an asymmetric quantum Holstein electron-phonon coupled model. The principal finding is the existence of quantum-mechanical resonant tunnelling channels in the electron localization phenomenon. Based on a strong-coupling perturbative analysis, we have explained the presence of the channels as a consequence of a general resonant effect on an effective two-level system. Finally, a comparison of the quantum problem with the semiclassical description given by the Discrete Nonlinear Schrödinger equation is performed.

In this paper, we discuss coherent atomic oscillations between two weakly coupled Bose–Einstein condensates that are energetically different. The weak link is notionally provided by a laser barrier in a (possibly asymmetric) multi-well trap or by Raman coupling between condensates in different hyperfine levels. The resultant boson Josephson junction dynamics is described by a double-well nonlinear Gross–Pitaevskii equation. On the basis of a new set of Jacobian elliptic function solutions, we describe the period of the oscillations as well as associated quantities and predict novel observable consequences of the interplay of the energy difference and initial phase difference between the two condensate populations.

The ground state energies and the derivates of the acoustic polaron in cylindrical quantum wire systems are performed by using the Huybrechts-like variational approach. The criterions for presence of the self-trapping transition of the acoustic polaron in cylindrical quantum wires are determined qualitatively. It is found that the critical coupling constant for the discontinuous transition from a quasi-free state to a trapped state of the acoustic polaron in cylindrical quantum wires tends to shift toward the weaker electron–phonon coupling with the increasing of cutoff wave vector. Detailed numerical results confirm that the self-trapping transition is expected to occur in the cylindrical quantum wire systems of alkali halides and wide-band-gap semiconductors.

Self-trapping transition of the acoustic polaron in slab is researched by calculating the polaron ground state energy and the first derivative of the ground state energy with respect to the electron–phonon coupling. It is indicated that the possibility of self-trapping transition for acoustic polaron in slab fall in between 3D and 2D systems. The electron may be self-trapped in slab systems of GaN, AlN and alkali halides, if the slab systems are thinner than one over ten of the length unit ℏ/mc.

We theoretically study the conditions for realization of trapping of a femtosecond pulse inside a one-dimensional photonic crystal with the relaxing cubic nonlinearity. A number of variants is considered: focusing and defocusing nonlinearities of the layers, a half-linear system, structures with differing values of nonlinearity parameters of periodically alternating layers. The results seem to be useful to make the optimal choice of the system characteristics to obtain self-trapping.

Amorphous bulk composites were prepared by doping azo-dye Disperse Red 13 (DR13) in poly(methyl methacrylate) (PMMA) matrices. Photo-induced anisotropy of such kind of bulk polymer material was investigated experimentally by measuring the birefringence when irradiating it with linearly polarized green light. We report the first observation of self-trapping of an optical vortex based on such effect in bulk poly(methyl methacrylate) materials containing photosensitive azo-dye molecules. The dependence of the average core width of a single-charge optical vortex versus time and input power was investigated in detail.