Relaxation and coarsening of weakly-interacting breathers in a simplified DNLS chain

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Stationary discrete solitons in circuit QED

We demonstrate that stationary localized solutions (discrete solitons) exist in a one dimensional Bose-Hubbard lattices with gain and loss in the semiclassical regime. Stationary solutions, by defi- nition, are robust and do not demand for state preparation. Losses, unavoidable in experiments, are not a drawback, but a necessary ingredient for these modes to exist. The semiclassical calculations are complemented with their classical limit and dynamics based on a Gutzwiller Ansatz. We argue that circuit QED architectures are ideal platforms for realizing the physics developed here. Finally, within the input-output formalism, we explain how to experimentally access the different phases, including the solitons, of the chain.Comment: 10 pages including appendix, 7 figure

A Chain, a Bath, a Sink and a Wall

This research did not receive any funding. Stefano Lepri acknowledges hospitality of the Institut Henri Poincaré-Centre Emile Borel during the trimester Stochastic Dynamics Out of Equilibrium where part of this work was elaborated.Peer reviewe

Symmetry Breaking in Linearly Coupled Dynamical Lattices

We examine one- and two-dimensional (1D and 2D) models of linearly coupled lattices of the discrete-nonlinear-Schr{\"{o}}dinger type. Analyzing ground states of the systems with equal powers in the two components, we find a symmetry-breaking phenomenon beyond a critical value of the squared $l^2$-norm. Asymmetric states, with unequal powers in their components, emerge through a subcritical pitchfork bifurcation, which, for very weakly coupled lattices, changes into a supercritical one. We identify the stability of various solution branches. Dynamical manifestations of the symmetry breaking are studied by simulating the evolution of the unstable branches. The results present the first example of spontaneous symmetry breaking in 2D lattice solitons. This feature has no counterpart in the continuum limit, because of the collapse instability in the latter case.Comment: 9 pages, 9 figures, submitted to Phys. Rev. E, Apr, 200

Non-standard Hubbard models in optical lattices: a review

Originally, the Hubbard model has been derived for describing the behaviour of strongly-correlated electrons in solids. However, since over a decade now, variations of it are also routinely being implemented with ultracold atoms in optical lattices. We review some of the rich literature on this subject, with a focus on more recent non-standard forms of the Hubbard model. After an introduction to standard (fermionic and bosonic) Hubbard models, we discuss briefly common models for mixtures, as well as the so called extended Bose-Hubbard models, that include interactions between neighboring sites, next-neighboring sites, and so on. The main part of the review discusses the importance of additional terms appearing when refining the tight-binding approximation on the original physical Hamiltonian. Even when restricting the models to the lowest Bloch band is justified, the standard approach neglects the density-induced tunneling (which has the same origin as the usual on-site interaction). The importance of these contributions is discussed for both contact and dipolar interactions. For sufficiently strong interactions, also the effects related to higher Bloch bands become important even for deep optical lattices. Different approaches that aim at incorporating these effects, mainly via dressing the basis Wannier functions with interactions, leading to effective, density-dependent Hubbard-type models, are reviewed. We discuss also examples of Hubbard-like models that explicitly involve higher $p$-orbitals, as well as models that couple dynamically spin and orbital degrees of freedom. Finally, we review mean-field nonlinear-Schr\"odinger models of the Salerno type that share with the non-standard Hubbard models the nonlinear coupling between the adjacent sites. In that part, discrete solitons are the main subject of the consideration. We conclude by listing some future open problems.Comment: expanded version 47pp, accepted in Rep. Prog. Phy

"Market making" behaviour in an order book model and its impact on the bid-ask spread

It has been suggested that marked point processes might be good candidates for the modelling of financial high-frequency data. A special class of point processes, Hawkes processes, has been the subject of various investigations in the financial community. In this paper, we propose to enhance a basic zero-intelligence order book simulator with arrival times of limit and market orders following mutually (asymmetrically) exciting Hawkes processes. Modelling is based on empirical observations on time intervals between orders that we verify on several markets (equity, bond futures, index futures). We show that this simple feature enables a much more realistic treatment of the bid-ask spread of the simulated order book.Comment: 17 pages, 9 figure

Space Plasma Phenomena at the Collisional/Noncollisional Interplay

We present the final report of the workshop on "Space Plasma Phenomena at the Collisional/Non-collisional Interplay" held at the "Chateau" of Meudon Observatory dur- ing June 18-29, 2001. The workshop allowed 15 scientists belonging to 13 institutions from the Czech Republic, France, Germany, Italy, United Kingdom and USA to gather and to tackle a number of problems in Plasma Physics at various degrees of collisionality typical of the Space environment. Three broad areas were considered involving three working groups: a) \u27Vlasov Plasma Theory and Simulations\u27 (i.e. novel and critical ap- proaches to Vlasov plasma theory); b) \u27Kinetic effects on MHD wave propagation\u27 (i.e. the problem of the \u27hybrid treatment of plasmas\u27); c) \u27Fluid phenomena in plasmas\u27 (i.e. the fluid treatment of fast particle populations). The main results of the workshop were: i) the concomitant and successful benchmarking and tuning of several numerical codes on a suite of kinetic, \u27hybrid\u27 and fluid plasma problems (including the exchange of several such codes by participants); ii) theoretically new and numerically compact approach to Vlasov Plasma theory (\u27q-space\u27 and Chebyshev approaches); iii) a novel approach to the effect of correlations in plasmas (i.e. a revision of the foundations of Vlasov theory); iv) a study of MHD turbulence at high numerical resolution (i.e. novel results on the long standing riddle of the small-scale MHD turbulent power spectrum). Nine publications were laid out during the workshop to be authored by participants belonging to different institutions. The total cost of the workshop was FFr. 53,300

Analysis, testing, and evaluation of faulted and unfaulted Wye, Delta, and open Delta connected electromechanical actuators

Mathematical models capable of simulating the transient, steady state, and faulted performance characteristics of various brushless dc machine-PSA (power switching assembly) configurations were developed. These systems are intended for possible future use as primemovers in EMAs (electromechanical actuators) for flight control applications. These machine-PSA configurations include wye, delta, and open-delta connected systems. The research performed under this contract was initially broken down into the following six tasks: development of mathematical models for various machine-PSA configurations; experimental validation of the model for failure modes; experimental validation of the mathematical model for shorted turn-failure modes; tradeoff study; and documentation of results and methodology