Scaling behavior of the momentum distribution of a quantum Coulomb system in a confining potential

We calculate the single-particle momentum distribution of a quantum many-particle system in the presence of the Coulomb interaction and a confining potential. The region of intermediate momenta, where the confining potential dominates, marks a crossover from a Gaussian distribution valid at low momenta to a power-law behavior valid at high momenta. We show that for all momenta the momentum distribution can be parametrized by a $q$-Gaussian distribution whose parameters are specified by the confining potential. Furthermore, we find that the functional form of the probability of transitions between the confined ground state and the $n^{th}$ excited state is invariant under scaling of the ratio $Q^2/\nu_n$, where $Q$ is the transferred momentum and $\nu_n$ is the corresponding excitation energy. Using the scaling variable $Q^2/\nu_n$ the maxima of the transition probabilities can also be expressed in terms of a $q$-Gaussian.Comment: 6 pages, 5 figure

Penentration of dynamic localized states in DC-driven Josephson junction ladders by discrete jumps

We give a theoretical study of unusual resistive (dynamic) localized states in anisotropic Josephson junction ladders, driven by a DC current at one edge. These states comprise nonlinearly coupled rotating Josephson phases in adjacent cells, and with increasing current they are found to expand into neighboring cells by a sequence of sudden jumps. We argue that the jumps arise from instabilities in the ladder's superconducting part, and our analytic expressions for the peculiar voltage (rotational frequency) ratios and I-V curves are in very good agreement with direct numerical simulations.Comment: Accepted, Physical Review E. 5 pages, 5 figures. Revtex, with postscript figure

Optical creation of vibrational intrinsic localized modes in anharmonic lattices with realistic interatomic potentials

Using an efficient optimal control scheme to determine the exciting fields, we theoretically demonstrate the optical creation of vibrational intrinsic localized modes (ILMs) in anharmonic perfect lattices with realistic interatomic potentials. For systems with finite size, we show that ILMs can be excited directly by applying a sequence of femtosecond visible laser pulses at THz repetition rates. For periodic lattices, ILMs can be created indirectly via decay of an unstable extended lattice mode which is excited optically either by a sequence of pulses as described above or by a single picosecond far-infrared laser pulse with linearly chirped frequency. In light of recent advances in experimental laser pulse shaping capabilities, the approach is experimentally promising.Comment: 20 pages, 7 eps figures. Accepted, Phys. Rev.

Solitons in Triangular and Honeycomb Dynamical Lattices with the Cubic Nonlinearity

We study the existence and stability of localized states in the discrete nonlinear Schr{\"o}dinger equation (DNLS) on two-dimensional non-square lattices. The model includes both the nearest-neighbor and long-range interactions. For the fundamental strongly localized soliton, the results depend on the coordination number, i.e., on the particular type of the lattice. The long-range interactions additionally destabilize the discrete soliton, or make it more stable, if the sign of the interaction is, respectively, the same as or opposite to the sign of the short-range interaction. We also explore more complicated solutions, such as twisted localized modes (TLM's) and solutions carrying multiple topological charge (vortices) that are specific to the triangular and honeycomb lattices. In the cases when such vortices are unstable, direct simulations demonstrate that they turn into zero-vorticity fundamental solitons.Comment: 17 pages, 13 figures, Phys. Rev.