Exact dynamics and thermalization of an open bosonic quantum system in presence of a quantum phase transition induced by the environment

We derive the exact out-of-equilibrium Wigner function of a bosonic mode linearly coupled to a bosonic bath of arbitrary spectral density. Our solution does not rely on any master equation approach and it therefore also correctly describes a bosonic mode which is initially entangled with its environment. It has been recently suggested that non-Markovian quantum effects lead to dissi- pationless dynamics in the case of a strong coupling to a bath whose spectral density has a support bounded from below. We show in this work that such a system undergoes a quantum phase transi- tion at some critical bath coupling strength. The apparent dissipationless dynamics then correspond to the relaxation towards the new ground-state.Comment: 8 page

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

Generation of Intrinsic Vibrational Gap Modes in Three-Dimensional Ionic Crystals

The existence of anharmonic localization of lattice vibrations in a perfect 3-D diatomic ionic crystal is established for the rigid-ion model by molecular dynamics simulations. For a realistic set of NaI potential parameters, an intrinsic localized gap mode vibrating in the [111] direction is observed for fcc and zinc blende lattices. An axial elastic distortion is an integral feature of this mode which forms more readily for the zinc blende than for the fcc structure. Molecular dynamics simulations verify that in each structure this localized mode may be stable for at least 200 cycles.Comment: 5 pages, 4 figures, RevTeX, using epsf.sty. To be published in Phys. Rev. B. Also available at http://www.msc.cornell.edu/~kiselev

Critical Langevin dynamics of the O(N)-Ginzburg-Landau model with correlated noise

We use the perturbative renormalization group to study classical stochastic processes with memory. We focus on the generalized Langevin dynamics of the \phi^4 Ginzburg-Landau model with additive noise, the correlations of which are local in space but decay as a power-law with exponent \alpha in time. These correlations are assumed to be due to the coupling to an equilibrium thermal bath. We study both the equilibrium dynamics at the critical point and quenches towards it, deriving the corresponding scaling forms and the associated equilibrium and non-equilibrium critical exponents \eta, \nu, z and \theta. We show that, while the first two retain their equilibrium values independently of \alpha, the non-Markovian character of the dynamics affects the dynamic exponents (z and \theta) for \alpha < \alpha_c(D, N) where D is the spatial dimensionality, N the number of components of the order parameter, and \alpha_c(x,y) a function which we determine at second order in 4-D. We analyze the dependence of the asymptotic fluctuation-dissipation ratio on various parameters, including \alpha. We discuss the implications of our results for several physical situations

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

Nonlinear Modulation of Multi-Dimensional Lattice Waves

The equations governing weakly nonlinear modulations of $N$-dimensional lattices are considered using a quasi-discrete multiple-scale approach. It is found that the evolution of a short wave packet for a lattice system with cubic and quartic interatomic potentials is governed by generalized Davey-Stewartson (GDS) equations, which include mean motion induced by the oscillatory wave packet through cubic interatomic interaction. The GDS equations derived here are more general than those known in the theory of water waves because of the anisotropy inherent in lattices. Generalized Kadomtsev-Petviashvili equations describing the evolution of long wavelength acoustic modes in two and three dimensional lattices are also presented. Then the modulational instability of a $N$-dimensional Stokes lattice wave is discussed based on the $N$-dimensional GDS equations obtained. Finally, the one- and two-soliton solutions of two-dimensional GDS equations are provided by means of Hirota's bilinear transformation method.Comment: Submitted to PR

Asymmetric gap soliton modes in diatomic lattices with cubic and quartic nonlinearity

Nonlinear localized excitations in one-dimensional diatomic lattices with cubic and quartic nonlinearity are considered analytically by a quasi-discreteness approach. The criteria for the occurence of asymmetric gap solitons (with vibrating frequency lying in the gap of phonon bands) and small-amplitude, asymmetric intrinsic localized modes (with the vibrating frequency being above all the phonon bands) are obtained explicitly based on the modulational instabilities of corresponding linear lattice plane waves. The expressions of particle displacement for all these nonlinear localized excitations are also given. The result is applied to standard two-body potentials of the Toda, Born-Mayer-Coulomb, Lennard-Jones, and Morse type. The comparison with previous numerical study of the anharmonic gap modes in diatomic lattices for the standard two-body potentials is made and good agreement is found.Comment: 24 pages in Revtex, 2 PS figure

Breathers on lattices with long range interaction

We analyze the properties of breathers (time periodic spatially localized solutions) on chains in the presence of algebraically decaying interactions $1/r^s$. We find that the spatial decay of a breather shows a crossover from exponential (short distances) to algebraic (large distances) decay. We calculate the crossover distance as a function of $s$ and the energy of the breather. Next we show that the results on energy thresholds obtained for short range interactions remain valid for $s>3$ and that for $s < 3$ (anomalous dispersion at the band edge) nonzero thresholds occur for cases where the short range interaction system would yield zero threshold values.Comment: 4 pages, 2 figures, PRB Rapid Comm. October 199

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.