Unknown Coupling Strength Research Articles

Perturbative quantum gravity induced scalar coupling to electromagnetism

Physicists working on atom interferometers are interested in scalar couplings to electromagnetism of dimensions 5 and 6 which might be induced by quantum gravity. There is a widespread belief that such couplings can only be induced by conjectured non-perturbative effects, resulting in unknown coupling strengths. In this letter we exhibit a completely perturbative mechanism through which quantum gravity induces dimension six couplings with precisely calculable coefficients.

Pinning control of complex network synchronization: A recurrent neural network approach

Using recurrent high order neural networks for identification, a new scheme for pinning control of complex networks with changing unknown coupling strengths is proposed for achieving synchronization. The robust behavior of the control system is investigated via simulations.

Adaptive Mean Field Games for Large Population Coupled ARX Systems with Unknown Coupling Strength

This paper is concerned with decentralized tracking-type games for large population multi-agent systems with mean-field coupling. The individual dynamics are described by stochastic discrete-time auto-regressive models with exogenous inputs (ARX models), and coupled by terms of the unknown population state average (PSA) with unknown coupling strength. A two-level decentralized adaptive control law is designed. On the high level, the PSA is estimated based on the Nash certainty equivalence (NCE) principle. On the low level, the coupling strength is identified based on decentralized least squares algorithms and the estimate of the PSA. The decentralized control law is constructed by combining the NCE principle and Certainty equivalence (CE) principle. By probability limit theory, under mild conditions, it is shown that: (a) the closed-loop system is stable almost surely; (b) as the number of agents increases to infinity, the estimates of both the PSA and the coupling strength are asymptotically strongly consistent and the decentralized control law is an almost sure asymptotic Nash-equilibrium.

Multipath interferometer with ultracold atoms trapped in an optical lattice

We study an ultra-cold gas of $N$ bosons trapped in a one dimensional $M$-site optical lattice perturbed by a spatially dependent potential $g\cdot x^j$, where the unknown coupling strength $g$ is to be estimated. We find that the measurement uncertainty is bounded by $\Delta g\propto\frac1{N (M^j-1)}$. For a typical case of a linear potential, the sensitivity improves as $M^{-1}$, which is a result of multiple interferences between the sites -- an advantage of multi-path interferometers over the two-mode setups. Next, we calculate the estimation sensitivity for a specific measurement where, after the action of the potential, the particles are released from the lattice and form an interference pattern. If the parameter is estimated by a least-square fit of the average density to the interference pattern, the sensitivity still scales like $M^{-1}$ for linear potentials and can be further improved by preparing a properly correlated initial state in the lattice.

Adiabatic passage and ensemble control of quantum systems

This paper considers population transfer between eigenstates of a finite quantum ladder controlled by a classical electric field. Using an appropriate change of variables, we show that this setting can be set in the framework of adiabatic passage, which is known to facilitate ensemble control of quantum systems. Building on this insight, we present a mathematical proof of robustness for a control protocol—chirped pulse—practised by experimentalists to drive an ensemble of quantum systems from the ground state to the most excited state. We then propose new adiabatic control protocols using a single chirped and amplitude-shaped pulse, to robustly perform any permutation of eigenstate populations, on an ensemble of systems with unknown coupling strengths. These adiabatic control protocols are illustrated by simulations on a four-level ladder.

Distributed robust adaptive control for a class of dynamical complex networks against imperfect communications

In this article, a robust tracking control problem of a class of dynamical complex networks is presented through a distributed adaptive approach. Uncertain network topology with unknown coupling strength, delayed and perturbed communications and external disturbances are considered, while the bounds of channel noises and coupling delays and disturbances are assumed to be unknown. Adaptation laws are proposed to estimate the network coupling strength and the upper and lower bounds of communication state errors and disturbances on-line. Based on the information from adaptive schemes, a class of distributed robust adaptive controllers is constructed to automatically compensate for the imperfect network and disturbance effects. Then, according to the Lyapunov stability theory, it is shown that the achievement of tracking for complex networks is effective on imperfect communications and disturbances. The effectiveness of the proposed design is illustrated via a decoupled longitudinal model of an F-18 aircraft.

Phase dynamics of coupled oscillators reconstructed from data

We systematically develop a technique for reconstructing the phase dynamics equations for coupled oscillators from data. For autonomous oscillators and for two interacting oscillators we demonstrate how phase estimates obtained from general scalar observables can be transformed to genuine phases. This allows us to obtain an invariant description of the phase dynamics in terms of the genuine, observable-independent phases. We discuss the importance of this transformation for characterization of strength and directionality of interaction from bivariate data. Moreover, we demonstrate that natural (autonomous) frequencies of oscillators can be recovered if several observations of coupled systems at different, yet unknown coupling strengths are available. We illustrate our method by several numerical examples and apply it to a human electrocardiogram and to a physical experiment with coupled metronomes.

Analysis of vector-meson photoproduction in terms of a multichannel impact-parameter formalism

An analysis of high-energy data on ρ0, ω0 and ϕ0 photoproduction on protons is carried out in the context of the multichannel impact-parameter formalism which had been successfully applied previously to Compton scattering on protons and neutrons providing a unified theoretical description for all these photon-induced diffractive processes. Particular attention has been devoted to the determination of the helicity-flip structure for the asymptotically leading,i.e. Pomeranchuk, part of vector-meson photoproduction amplitudes. The proposedK-matrix description allows the existence of a helicity-flip contribution to Pomeranchuk exchange albeit with unknown coupling strength. ϕ0 photoproduction is especially suited to investigate in detail the nature of the Pomeranchuk coupling in diffractive photoproduction processes since no lower-lying trajectories can contribute here. The analysis lends support to the presence of a substantial helicity-flip contribution for the nucleons in high-energy vector-meson photoproduction which is to be associated with Pomeranchuk exchange.