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In this letter, we provide new insight into Willems et al.'s fundamental lemma by studying the concept of universal inputs. An input is called universal if, when applied to any controllable system, it leads to input-output data that parametrizes all finite trajectories of the system. By the fundamental lemma, inputs that are persistently exciting of sufficiently high order are universal. The main contribution of this work is to prove the converse. Therefore, universality and persistency of excitation are equivalent.

We consider a competition between $d+1$ players, and aim to identify the "most exciting game'' of this kind. This is translated, mathematically, into a stochastic optimization problem over martingales that live on the $d$-dimensional subprobability simplex $Δ$ and terminate on the vertices of $Δ$ (so-called win-martingales), with a cost function related to a scaling limit of Shannon entropies. We uncover a surprising connection between this problem and the seemingly unrelated field of Monge-Ampère equations: If $g$ solves \begin{equation*} \begin{cases} g(x)=\log \det\left(\frac{1}{2} abla^2 g(x)\right), \quad \, \ \ \ \ \, \, \, \, x \in Δ, \\ g(x)=\infty, \quad \quad \quad \quad \ \ \ \ \ \quad \quad \, \ \ \ \ \ x\in \partial Δ, \end{cases} \end{equation*} then the winning-probability of the players in the most exciting game is described by $$dM_s=\sqrt{\frac{2 ( abla^2 g(M_s))^{-1}}{1-s} } \, dB_s.$$ To formalize this, a detailed quantitative analysis of the Monge-Ampère equation for $g$ is crucial. This is then leveraged to prove that $M$ is indeed an optimal win-martingale.

We study the morphology of the 511 keV signal that could be produced by exciting dark matter (XDM) in the Milky Way. In this model, collisions between dark matter particles excite the dark matter to a state that can then decay back to the ground state, releasing an electron-positron pair. These electrons and positrons would then annihilate, producing 511 keV photons that could explain the 511 keV signal seen by INTEGRAL at the Galactic Center. We compare the resulting flux with the most recent INTEGRAL data, performing the first full statistical analysis of the exciting dark matter model. We focus on exciting dark matter in the mass and cross section ranges 100 GeV $\lesssim m_χ \lesssim$ 3 TeV and $10^{-19}$ cm$^3$ s$^{-1} \lesssim \langle σv \rangle \lesssim 10^{-16}$ cm$^3$ s$^{-1}$. We show that exciting dark matter can provide a significantly better fit than the simpler case of annihilating dark matter, with $Δχ^2 > 16$ for all but one of the density profiles we consider.

In the context of data-driven control, persistence of excitation (PE) of an input sequence is defined in terms of a rank condition on the Hankel matrix of the input data. For nonlinear systems, recent results employed rank conditions involving collected input and state/output data, for which no guidelines are available on how to satisfy them a priori. In this paper, we first show that a set of discrete impulses is guaranteed to be persistently exciting for any controllable LTI system. Based on this result, for certain classes of nonlinear systems, we guarantee persistence of excitation of sequences of basis functions a priori, by design of the physical input only.

We studied magneto-optical resonances caused by excited-state level crossings in a nonzero magnetic field. Experimental measurements were performed on the transitions of the $D_2$ line of rubidium. These measured signals were described by a theoretical model that takes into account all neighboring hyperfine transitions, the mixing of magnetic sublevels in an external magnetic field, the coherence properties of the exciting laser radiation, and the Doppler effect. Good agreement between the experimental measurements and the theoretical model could be achieved over a wide range of laser power densities. We further showed that the contrasts of the level-crossing peaks can be sensitive to changes in the frequency of the exciting laser radiation as small as several tens of megahertz when the hyperfine splitting of the exciting state is larger than the Doppler broadening.

The Hawkes process is a simple point process, whose intensity function depends on the entire past history and is self-exciting and has the clustering property. The Hawkes process is in general non-Markovian. The linear Hawkes process has immigration-birth representation. Based on that, Fierro et al. recently introduced a generalized linear Hawkes model with different exciting functions. In this paper, we study the convergence to equilibrium, large deviation principle, and moderate deviation principle for this generalized model. This model also has connections to the multivariate linear Hawkes process. Some applications to finance are also discussed.

Linearized augmented planewaves combined with local-orbitals (LAPW+lo) are arguably the most precise basis set to represent Kohn-Sham states. When employed within real-time time-dependent density functional theory (RT-TDDFT), they promise ultimate precision achievable for exploring the evolution of electronic excitations. In this work, we present an implementation of RT-TDDFT in the full-potential LAPW+lo code exciting. We benchmark our results against those obtained by linear-response TDDFT with exciting and by RT-TDDFT calculations with the Octopus code, finding a satisfactory level of agreement. To illustrate possible applications of our implementation, we have chosen three examples: the dynamic behavior of excitations in MoS$_2$ induced by a laser pulse, the third harmonic generation in silicon, and a pump-probe experiment in diamond.

Ehrenfest Dynamics combined with real-time time-dependent density functional theory has proven to be a reliable tool to study non-adiabatic molecular dynamics with a reasonable computational cost. Among other possibilities, it allows for assessing in real time electronic excitations generated by ultra-fast laser pulses, as e.g., in pump-probe spectroscopy, and their coupling to the nuclear vibrations even beyond the linear regime. In this work, we present its implementation in the all-electron full-potential package exciting. Three cases are presented as examples: diamond and cubic BN relaxed after an initial lattice distortion, and cubic BN exposed to a laser pulse. Comparison with the Octopus code exhibits good agreement.

This paper presents a new approach to deal with the dual problem of system identification and regulation. The main feature consists of breaking the control input to the system into a regulator part and a persistently exciting part. The former is used to regulate the plant using a robust MPC formulation, in which the latter is treated as a bounded additive disturbance. The identification process is executed by a simple recursive least squares algorithm. In order to guarantee sufficient excitation for the identification, an additional non-convex constraint is enforced over the persistently exciting part.

We start a series of studies of the excitation of an optical target by quantum light. In this first part, we introduce the problematic and address the first case of interest, that of exciting the quantum harmonic oscillator, corresponding to, e.g., a single-mode passive cavity or a non-interacting bosonic field. We introduce a mapping of the Hilbert space that allows to chart usefully the accessible regions. We then consider the quantum excitation from single photon sources in the form of a two-level system under various regimes of (classical) pumping: incoherent, coherent and in the Mollow triplet regime. We close this first opus with an overview of the material to be covered in the subsequent papers.

The non-sinusoidal character oscillations appear in the transmitted, reflected and absorbed light fluxes when light pulses irradiate a semiconductor quantum well (QW), containing a large number of the equidistant energy levels of electronic excitations. A damping echo of the exciting pulse appears through the time intervals $2π\hbar/ΔE$ in the case of the very short light pulses $γ_l^{-1}\ll\hbar/ΔE$.

We consider exciting surface plasmon polaritons in the Kretschmann configuration. Contrary to common belief, we show that a plane wave incident at an angle greater than the angle of total internal reflection does not excite surface plasmon polaritons. These excitations do arise, however, if the incident light forms a narrow beam composed of an infinite number of plane waves. The surface plasmon polariton is formed at the geometrical edge of the beam as a result of interference of reflected plane waves.

The problem of parameter estimation from a standard vector linear regression equation in the absence of sufficient excitation in the regressor is addressed. The first step to solve the problem consists in transforming this equation into a set of scalar ones using the well-known dynamic regressor extension and mixing technique. Then a novel procedure to generate new scalar exciting regressors is proposed.} The superior performance of a classical gradient estimator using this new regressor, instead of the original one, is illustrated with comprehensive simulations.

On chip exciting electric modes in individual plasmonic nanostructures are realized widely; nevertheless, the excitation of their magnetic counterparts is seldom reported. Here, we propose a highly efficient on chip excitation approach of the magnetic dipole mode of an individual split ring resonator (SRR) by integrating it onto a photonic crystal nanocavity (PCNC). A high excitation efficiency of up to 58% is realized through the resonant coupling between the modes of the SRR and PCNC. A further fine adjustment of the excited magnetic dipole mode is demonstrated by tuning the relative position and twist angle between the SRR and PCNC. Finally, a structure with a photonic crystal waveguide side coupled with the hybrid SRR PCNC is illustrated, which could excite the magnetic dipole mode with an in plane coupling geometry and potentially facilitate the future device application. Our result may open a way for developing chip integrated photonic devices employing a magnetic field component in the optical field.

We study ground and radial excitations of flavor singlet and flavored pseudoscalar mesons within the framework of the rainbow-ladder truncation using an infrared massive and finite interaction in agreement with recent results for the gluon-dressing function from lattice QCD and Dyson-Schwinger equations. Whereas the ground-state masses and decay constants of the light mesons as well as charmonia are well described, we confirm previous observations that this truncation is inadequate to provide realistic predictions for the spectrum of excited and exotic states. Moreover, we find a complex conjugate pair of eigenvalues for the excited $D_{(s)}$ mesons, which indicates a non-Hermiticity of the interaction kernel in the case of heavy-light systems and the present truncation. Nevertheless, limiting ourselves to the leading contributions of the Bethe-Salpeter amplitudes, we find a reasonable description of the charmed ground states and their respective decay constants.

We study the excitation of a two-level system (2LS) by quantum light, thereby bringing our previous studies~(see part~I. of this series) to a target that is quantum itself. While there is no gain for the quantum state of the target as compared to driving it with classical light, its dynamical features, such as antibunching, can be improved. We propose a chain of two-level systems, i.e., setting the emission of each 2LS as the driving source of the following one, as an arrangement to provide better single-photon sources. At a fundamental level, we discuss the notion of strong-coupling between quantum light from a source and its target, and the several versions of the Mollow triplet that follow from various types of driving light. We discuss the Heitler effect of antibunched photons from the scattered light off a laser.

We reconsider the proposal of excited dark matter (DM) as an explanation for excess 511 keV gamma rays from positrons in the galactic center. We quantitatively compute the cross section for DM annihilation to nearby excited states, mediated by exchange of a new light gauge boson with off-diagonal couplings to the DM states. In models where both excited states must be heavy enough to decay into e^+ e^- and the ground state, the predicted rate of positron production is never large enough to agree with observations, unless one makes extreme assumptions about the local circular velocity in the Milky Way, or alternatively if there exists a metastable population of DM states which can be excited through a mass gap of less than 650 keV, before decaying into electrons and positrons.

This is the final talk of NSTAR2011 conference. It is not a summary talk, but rather a looking forward to what still needs to be done in excited baryon physics. In particular, we need to hone our tools connecting experimental inputs with QCD. At present we rely on models that often have doubtful connections with the underlying theory, and this needs to be dramatically improved, if we are to reach definitive conclusions about the relevant degrees of freedom of excited baryons. Conclusions that we want to have by NSTAR2021.