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Ultrafast reaction processes take place when resonant features of nonlinear model systems are taken into account. In the targeted energy or electron transfer dimer model this is accomplished through the implementation of nonlinear oscillators with opposing types of nonlinearities, one attractive while the second repulsive. In the present work we show that this resonant behavior survives if we take into account the vibrational degrees of freedom as well. After giving a summary on the basic formalism of chemical reactions we show that resonant electron transfer can be assisted by vibrations. We find the condition for this efficient transfer and show that in the case of additional interaction with noise a distinct non-Arrhenius behavior develops that is markedly different from the usual Kramers-like activated transfer.

The heart beats due to the synchronized contraction of cardiomyocytes triggered by a periodic sequence of electrical signals called action potentials, which originate in the sinoatrial node and spread through the heart's electrical system. A large body of work is devoted to modeling the propagation of the action potential and to reproducing reliably its shape and duration. Connection of computational modeling of cells to macroscopic phenomenological curves such as the electrocardiogram has been also intense, due to its clinical importancce in analyzing cardiovascular diseases. In this work we simulate the dynamics of action potential propagation using the three-variable Fenton-Karma model that can account for both normal and damaged cells through spatially inhomogeneous voltage diffusion coefficient. We monitor the action potential propagation in the cardiac tissue and calculate the pseudo-electrocardiogram that reproduces the R and T waves. The R wave amplitude varies according to a double exponential law as a function of the (spatially homogeneous, for an isotropic tissue) diffusion coefficient. The addition of spatial inhomogeneity in the diffusion coefficient by means of a defected region representing damaged cardiac cells, may result in T-wave inversion in the calculated pseudo-electrocardiogram. The transition from positive to negative polarity of the T-wave is analyzed as a function of the length and the depth of the defected region., Comment: 12 pages, figures, 39 references

We report an experimental and theoretical study of spin noise correlations in a $^{87}$Rb-$^{133}$Cs unpolarized alkali-metal vapor dominated by spin-exchange collisions. We observe strong unequal-time inter-species correlations and account for these with a first-principles theoretical model. Since the two atomic species have different spin precession frequencies, the dual-species vapor enables the use of an additional experimental handle, the applied magnetic field, for untangling various sub-types of spin correlations. In particular, the measured cross-correlation and auto-correlation spectra shed light on a number of spin-dynamic effects involving intra-atom, inter-atom, intra-species and inter-species correlations. Cross-correlation coefficients exceeding $60\%$ have been observed at low-magnetic fields, where the two spin species couple strongly via spin-exchange collisions. The understanding of such spontaneously generated correlations can motivate the design of quantum-enhanced measurements with single or multi-species spin-polarized alkali-metal vapors used in quantum sensing applications.

We investigate the use of Quantum Neural Networks for discovering and implementing quantum error-correcting codes. Our research showcases the efficacy of Quantum Neural Networks through the successful implementation of the Bit-Flip quantum error-correcting code using a Quantum Autoencoder, effectively correcting bit-flip errors in arbitrary logical qubit states. Additionally, we employ Quantum Neural Networks to restore states impacted by Amplitude Damping by utilizing an approximative 4-qubit error-correcting codeword. Our models required modification to the initially proposed Quantum Neural Network structure to avoid barren plateaus of the cost function and improve training time. Moreover, we propose a strategy that leverages Quantum Neural Networks to discover new encryption protocols tailored for specific quantum channels. This is exemplified by learning to generate logical qubits explicitly for the bit-flip channel. Our modified Quantum Neural Networks consistently outperformed the standard implementations across all tasks.

We theoretically demonstrated the possible emergence of slow-light self-induced transparency solitons in the infinite one-dimensional coupled cavity array, with each cavity containing a single qubit. We have predicted a substantial dependence of pulse transparency on its dimensionless width $\tau_0$. In particular, short pulses whose widths range from $\tau_0\ll 1$ to $\tau_0\lesssim 1$ exhibit simple, almost linear dispersion law with a finite frequency gap of the order of the cavity array photonic band gap. That is, the medium is opaque for very short pulses with carrier wave frequency below the photonic gap. When the pulse width exceeds the critical one, a twin transparency window separated by a finite band gap appears in the soliton pulse dispersion law. Observation of predicted effects within the proposed setup would be of interest for understanding the properties of self-induced transparency effect in general and future applications in the design of quantum technological devices.

Artificial intelligence in the form of deep learning is now very popular and directly implemented in many areas of science and technology. In the present work we study time evolution of Discrete Breathers in one-dimensional nonlinear chains using the framework of Convolutional Neural Networks. We focus on differentiating discrete breathers which are localized nonlinear modes from linearized phonon modes. The breathers are localized in space and time-periodic solutions of non-linear discrete lattices while phonons are the linear collective oscillations of interacting atoms and molecules. We show that deep learning neural networks are indeed able not only to distinguish breather from phonon modes but also determine with high accuracy the underlying nonlinear on-site potentials that generate breathers. This work can have extensions to more complex natural systems.

In quantum targeted energy transfer, bosons are transferred from a certain crystal site to an alternative one, utilizing a nonlinear resonance configuration similar to the classical targeted energy transfer. We use a novel computational method based on machine learning algorithms in order to investigate selectivity as well as efficiency of the quantum transfer in the context of a dimer and a trimer system. We find that our method identifies resonant quantum transfer paths that allow boson transfer in unison. The method is readily extensible to larger lattice systems involving nonlinear resonances., Comment: REVTeX 4.2, 9 pages, 7 figures

We study quantum features of electromagnetic radiation propagating in the one-dimensional superconducting quantum metamaterial comprised of an infinite chain of charge qubits placed within two-stripe massive superconductive resonators. The Quantum-mechanical model is derived assuming weak fields and that, at low temperatures, each qubit is either unoccupied ($N=0$) or occupied by a single Cooper pair ($N=1$). Based on this assumption we demonstrate the emergence of two bands of single-photon-qubit bound states with the energy lying within (lower branch) or outside (higher) the photon continuum. The emergence of bound states may cause radiation trapping which could be of interest for the control of photon transport in these systems.

We focus on chaotic dynamical systems and analyze their time series with the use of autoencoders, i.e., configurations of neural networks that map identical output to input. This analysis results in the determination of the latent space dimension of each system and thus determines the minimal number of nodes necessary to capture the essential information contained in the chaotic time series. The constructed chaotic autoencoders generate similar maximal Lyapunov exponents as the original chaotic systems and thus encompass their essential dynamical information.

The nonlinear dimer obtained through the nonlinear Schr{\"o}dinger equation has been a workhorse for the discovery the role nonlinearity plays in strongly interacting systems. While the analysis of the stationary states demonstrates the onset of a symmetry broken state for some degree of nonlinearity, the full dynamics maps the system into an effective $\phi^4$ model. In this latter context, the self-trapping transition is an initial condition dependent transfer of a classical particle over a barrier set by the nonlinear term. This transition has been investigated analytically and mathematically it is expressed through the hyperbolic limit of Jacobian elliptic functions. The aim of the present work is to recapture this transition through the use of methods of Artificial Intelligence (AI). Specifically, we used a physics motivated machine learning model that is shown to be able to capture the original dynamic self-trapping transition and its dependence on initial conditions. Exploitation of this result in the case of the non-degenerate nonlinear dimer gives additional information on the more general dynamics and helps delineate linear from nonlinear localization. This work shows how AI methods may be embedded in physics and provide useful tools for discovery.

For an ensemble of nonlinear systems that model, for instance, molecules or photonic systems, we propose a method that finds efficiently the configuration that has prescribed transfer properties. Specifically, we use physics-informed machine-learning (PIML) techniques to find the parameters for the efficient transfer of an electron (or photon) to a targeted state in a non-linear dimer. We create a machine learning model containing two variables, $\chi_D$, and $\chi_A$, representing the non-linear terms in the donor and acceptor target system states. We then introduce a data-free physics-informed loss function as $1.0 - P_j$, where $P_j$ is the probability, the electron being in the targeted state, $j$. By minimizing the loss function, we maximize the occupation probability to the targeted state. The method recovers known results in the Targeted Energy Transfer (TET) model, and it is then applied to a more complex system with an additional intermediate state. In this trimer configuration, the PIML approach discovers desired resonant paths from the donor to acceptor units. The proposed PIML method is general and may be used in the chemical design of molecular complexes or engineering design of quantum or photonic systems.

The spread of COVID-19 during the initial phase of the first half of 2020 was curtailed to a larger or lesser extent through measures of social distancing imposed by most countries. In this work, we link directly, through machine learning techniques, infection data at a country level to a single number that signifies social distancing effectiveness. We assume that the standard SIR model gives a reasonable description of the dynamics of spreading, and thus the social distancing aspect can be modeled through time-dependent infection rates that are imposed externally. We use an exponential ansatz to analyze the SIR model, find an exact solution for the time-independent infection rate, and derive a simple first-order differential equation for the time-dependent infection rate as a function of the infected population. Using infected number data from the "first wave" of the infection from eight countries, and through physics-informed machine learning, we extract the degree of linear dependence in social distancing that led to the specific infections. We find that in the two extremes are Greece, with the highest decay slope on one side, and the US on the other with a practically flat "decay". The hierarchy of slopes is compatible with the effectiveness of the pandemic containment in each country. Finally, we train our network with data after the end of the analyzed period, and we make week-long predictions for the current phase of the infection that appear to be very close to the actual infection values.

A one-dimensional metamaterial with parity-time (${\cal PT}$) symmetry that relies on balanced gain and loss is introduced, comprising of magnetically coupled split-ring resonators (SRRs). A particular topology that combines a non-trivial (topological) dimer configuration with a trivial (non-topological) dimer configuration which are separated by a central SRR with neither gain or loss, is investigated. By focusing on the dynamical aspects of such a topological ${\cal PT}$ metamaterial (PTMM), the existence of {\em topologically protected interface states} which are localized at the central SRR is demonstrated numerically. The solution of the corresponding {\em quadratic eigenvalue problem} reveals that the protected state is actually a robust eigenmode of the topological PTMM, whose eigenvalue is isolated in the middle of the gap (mid-gap state) of the two-band frequency spectrum. Direct numerical simulations have been further used to determine the robustness and dynamic stability of these states in the parameter space of the {\em dimerization strength} and the {\em gain-loss coefficient}., Comment: 8 pages, 7 figures, 45 references. Accepted by Physical Review B as Regular Article

The COVID-19 pandemic has affected all countries of the world producing a substantial number of fatalities accompanied by a major disruption in their social, financial, and educational organization. The strict disciplinary measures implemented by China were very effective and thus were subsequently adopted by most world countries to various degrees. The infection duration and number of infected persons are of critical importance for the battle against the pandemic. We use the quantitative landscape of the disease spreading in China as a benchmark and utilize infection data from eight countries to estimate the complete evolution of the infection in each of these countries. The analysis predicts successfully both the expected number of daily infections per country and, perhaps more importantly, the duration of the epidemic in each country. Our quantitative approach is based on a Gaussian spreading hypothesis that is shown to arise as a result of imposed measures in a simple dynamical infection model. This may have consequences and shed light in the efficiency of policies once the phenomenon is over.

We develop an approach on how to define single-point interactions under the application of external fields. The essential feature relies on an asymptotic method based on the one-point approximation of multi-layered heterostructures that are subject to bias potentials. In this approach , the zero-thickness limit of the transmission matrices of specific structures is analyzed and shown to result in matrices connecting the two-sided boundary conditions of the wave function at the origin. The reflection and transmission amplitudes are computed in terms of these matrix elements as well as biased data. Several one-point interaction models of two- and three-terminal devices are elaborated. The typical transistor in the semiconductor physics is modeled in the "squeezed limit'' as a $\delta$- and a $\delta'$-potentialand referred to as a "point" transistor. The basic property of these one-point interaction models is the existence of several extremely sharp peaks as an applied voltage tunes, at which the transmission amplitude is non-zero, while beyond these resonance values, the heterostructure behaves as a fully reflecting wall. The location of these peaks referred to as a "resonance set" is shown to depend on both system parameters and applied voltages. An interesting effect of resonant transmission through a $\delta$-like barrier under the presence of an adjacent well is observed. This transmission occurs at a countable set of the well depth values., Comment: 6 figures, to appear in Frontiers in Physics

Planar and linear arrays of SQUIDs (superconducting quantum interference devices), operate as nonlinear magnetic metamaterials in microwaves. Such {\em SQUID metamaterials} are paradigmatic systems that serve as a test-bed for simulating several nonlinear dynamics phenomena. SQUIDs are highly nonlinear oscillators which are coupled together through magnetic dipole-dipole forces due to their mutual inductance; that coupling falls-off approximately as the inverse cube of their distance, i.~e., it is non-local. However, it can be approximated by a local (nearest-neighbor) coupling which in many cases suffices for capturing the essentials of the dynamics of SQUID metamaterials. For either type of coupling, it is numerically demonstrated that chimera states as well as other spatially non-uniform states can be generated in SQUID metamaterials under time-dependent applied magnetic flux for appropriately chosen initial conditions. The mechanism for the emergence of these states is discussed in terms of the multistability property of the individual SQUIDs around their resonance frequency and the attractor crowding effect in systems of coupled nonlinear oscillators. Interestingly, generation and control of chimera states in SQUID metamaterials can be achieved in the presence of a constant (dc) flux gradient with the SQUID metamaterial initially at rest., Comment: 15 PAGES, 14 FIGURES, submitted to Frontiers in Applied Mathematics and Statistics

SQUID (Superconducting QUantum Interference Device) metamaterials, subject to a time-independent (dc) flux gradient and driven by a sinusoidal (ac) flux field, support chimera states that can be generated with zero initial conditions. The dc flux gradient and the amplitude of the ac flux can control the number of desynchronized clusters of such a generated chimera state (i.e., its `heads') as well as their location and size. The combination of three measures, i.e., the synchronization parameter averaged over the period of the driving flux, the incoherence index, and the chimera index, is used to predict the generation of a chimera state and its multiplicity on the parameter plane of the dc flux gradient and the ac flux amplitude. Moreover, the full-width half-maximum of the distribution of the values of the synchronization parameter averaged over the period of the ac driving flux, allows to distinguish chimera states from non-chimera, partially synchronized states., Comment: 7 pages, 5 figures, submitted to Physical Review E

A theoretical investigation of the ultrafast processes and dynamics of the excited carriers upon irradiation of GaAs with femtosecond (fs) pulsed lasers is performed in conditions that induce material damage and eventually surface modification of the heated solid. A parametric study is followed to correlate the produced transient carrier density with the damage threshold for various pulse duration values {\tau}p (it increases as ~ at relatively small values of {\tau}p while it drops for pulse durations of the order of some picoseconds) based on the investigation of the fundamental multiscale physical processes following fs-laser irradiation. Moreover, fluence values for which the originally semiconducting material demonstrates a metallic behaviour are estimated. It is shown that a sufficient number of carriers in the conduction band are produced to excite Surface Plasmon (SP) waves that upon coupling with the incident beam and a fluid-based surface modification mechanism lead to the formation of sub-wavelength periodic structures orientated perpendicularly to the laser beam polarization. Experimental results for the damage threshold and the frequencies of induced periodic structures show a good agreement with the theoretical predictions., Comment: 11 color pages To appear in the Physical Review B

Chimeras and branching are two archetypical complex phenomena that appear in many physical systems; because of their different intrinsic dynamics, they delineate opposite non-trivial limits in the complexity of wave motion and present severe challenges in predicting chaotic and singular behavior in extended physical systems. We report on the long-term forecasting capability of Long Short-Term Memory (LSTM) and reservoir computing (RC) recurrent neural networks, when they are applied to the spatiotemporal evolution of turbulent chimeras in simulated arrays of coupled superconducting quantum interference devices (SQUIDs) or lasers, and branching in the electronic flow of two-dimensional graphene with random potential. We propose a new method in which we assign one LSTM network to each system node except for "observer" nodes which provide continual "ground truth" measurements as input; we refer to this method as "Observer LSTM" (OLSTM). We demonstrate that even a small number of observers greatly improves the data-driven (model-free) long-term forecasting capability of the LSTM networks and provide the framework for a consistent comparison between the RC and LSTM methods. We find that RC requires smaller training datasets than OLSTMs, but the latter requires fewer observers. Both methods are benchmarked against Feed-Forward neural networks (FNNs), also trained to make predictions with observers (OFNNs).

The conditions leading to flat dispersionless frequency bands in truly one-dimensional parity-time ($\cal PT$) symmetric metamaterials comprising split-ring resonators (SRRs) arranged in a binary pattern are obtained analytically. In this paradigmatic system, in which the SRRs are coupled through both electric and magnetic dipole-dipole forces, flat-bands may arise from tailoring its natural parameters (such as, e.g., the coupling coefficients between SRRs) and not from geometrical effects. For sets of parameters which values are tailored to flatten the upper band of the spectrum, the solution of the corresponding quadratic eigenvalue problem reveals the existence of compact, two-site localized eigenmodes. Numerical simulations confirm the existence and the dynamic stability of such modes, which can be formed through the evolution of single-site initial excitations without disorder or nonlinearity., Comment: to be published in Scientific Reports (2019)

Graphene as well as more generally Dirac solids constitute two dimensional materials where the electronic flow is ultra relativistic. When a Dirac solid is deposited on a different substrate surface with roughness, a local random potential develops through an inhomogeneous charge impurity distribution. This external potential affects profoundly the charge flow and induces a chaotic pattern of current branches that develops through focusing and defocusing effects produced by the randomness of the surface. An additional bias voltage may be used to tune the branching pattern of the charge carrier currents. We employ analytical and numerical techniques in order to investigate the onset and the statistical properties of carrier branches in Dirac solids. We find a specific scaling-type relationship that connects the physical scale for the occurrence of branches with the characteristic medium properties, such as disorder and bias field. We use numerics to test and verify the theoretical prediction as well as a perturbative approach that gives a clear indication of the regime of validity of the approach. This work is relevant to device applications and may be tested experimentally.

Metamaterials (MMs), i.e. artificial media designed to achieve properties not available in natural materials, have been the focus of intense research during the last two decades. Many properties have been discovered and multiple designs have been devised that lead to multiple conceptual and practical applications. Superconducting MMs have the advantage of ultra low losses, a highly desirable feature. The additional use of the Josephson effect and SQUID configurations produce further specificity and functionality. SQUID-based MMs are both theoretically investigated but also fabricated and analyzed experimentally in many labs and exciting new phenomena have been found both in the classical and quantum realms. The SQUID is a unique nonlinear oscillator that can be manipulated through multiple external means. This flexibility is inherited to SQUID-based MMs, i.e. extended units that contain a large arrangement of SQUIDs. Such an assembly of weakly coupled nonlinear oscillators presents a nonlinear dynamics laboratory where numerous complex spatio-temporal phenomena may be explored. We focus primarily on SQUID-based MMs and present basic properties related to their individual and collective responses to external drives. We start by showing how a SQUID-based system acts as a genuine MM, demonstrate that the Josephson nonlinearity leads to wide-band tunability, intrinsic nonlinear as well as flat band localization. We explore further properties such as multistability and self-organization and the emergence of chimera states. We then dwell into the truly quantum regime and explore the interaction of electromagnetic pulses with superconducting qubits where the coupling between the two yields self-induced transparency and superradiance. We thus attempt to present the rich behavior of coupled superconducting units and point to their basic properties and practical utility., Comment: review article, to appear in Physics Reports: 84 pages, 36 figures, 350 references

A SQUID (Superconducting QUantum Interference Device) metamaterial on a Lieb lattice with nearest-neighbor coupling supports simultaneously stable dissipative breather families which are generated through a delicate balance of input power and intrinsic losses. Breather multistability is possible due to the peculiar snaking flux ampitude - frequency curve of single dissipative-driven SQUIDs, which for relatively high sinusoidal flux field amplitudes exhibits several stable and unstable solutions in a narrow frequency band around resonance. These breathers are very weakly interacting with each other, while multistability regimes with different number of simultaneously stable breathers persist for substantial intervals of frequency, flux field amplitude, and coupling coefficients. Moreover, the emergence of chimera states as well as novel temporally chaotic states exhibiting spatial homogeneity within each sublattice of the Lieb lattice is demonstrated., Comment: 11 pages, 9 figures, submitted to Physical Review E

The dynamics of a large array of coupled semiconductor lasers is studied for a nonlocal coupling scheme. Our focus is on chimera states, a self-organized spatio-temporal pattern of co-existing coherence and incoherence. In laser systems, such states have been previously found for global and nearest-neighbor coupling, mainly in small networks. The technological advantage of large arrays has motivated us to study a system of 200 nonlocally coupled lasers with respect to the emerging collective dynamics. The crucial parameters are the coupling strength, the coupling phase and the range of the nonlocal interaction. We find that chimera states with multiple (in)coherent domains exist in a wide region of the parameter space. We provide quantitative characterization for the obtained chimeras and other spatio-temporal patterns.

The dynamic equations for the fluxes through the SQUIDs that form a two-dimensional metamamaterial on a Lieb lattice are derived, and then linearized around zero flux to obtain the linear frequency spectrum according to the standard procedure. That spectrum, due to the Lieb lattice geometry, possesses a frequency band structure exhibiting two characteristic features; two dispersive bands, which form a Dirac cone at the corners of the first Brillouin zone, and a flat band crossing the Dirac points. It is demonstrated numerically that localized states can be excited in the system when it is initialized with single-site excitations; depending on the amplitude of those initial states, the localization is either due to the flat-band or to nonlinear effects. Flat-band localized states are formed in the nearly linear regime, while localized excitations of the discrete breather type are formed in the nonlinear regime. These two regimes are separated by an intermediate turbulent regime for which no localization is observed. Notably, initial single-site excitations of only edge SQUIDs of a unit cell may end-up in flat-band localized states; no such states are formed for initial single-site excitations of a corner SQUID of a unit cell. The degree of localization of the resulting states is in any case quantified using well-established measures such as the energetic participation ratio and the second moment., Comment: 11 pages, 9 figures

We address light propagation properties in complex media consisting of random distributions of lenses that have specific focusing properties. We present both analytical and numerical techniques that can be used to study emergent properties of light organization in these media. As light propagates, it experiences multiple scattering leading to the formation of light bundles in the form of branches; these are random yet occur systematically in the the medium, particularly in the weak scattering limit. On the other hand, in the strong scattering limit we find that coalescence of branches may lead to the formation of extreme waves of the "rogue wave" type. These waves appear at specific locations and arise in the linear as well as in the nonlinear regimes. We present both the weak and strong scattering limit and show that these complex phenomena can be studied numerically and analytically through simple models., Comment: This is a Chapter from the book: Quodons in Mica: Nonlinear localized traveling excitations in crystals. Springer Series in Materials Science

We propose a superconducting metamaterial design consisting of meta-atoms (MAs) which are each composed of a direct current (dc) superconducting quantum interference device (SQUID) and a superconducting rod. This design provides negative refraction index behavior for a wide range of structure parameters., Comment: 4 pages, 5 figures, 20 references. Accepted for publication by Applied Physics A

We report on the emergence of robust multi-clustered chimera states in a dissipative-driven system of symmetrically and locally coupled identical SQUID oscillators. The "snake-like" resonance curve of the single SQUID (Superconducting QUantum Interference Device) is the key to the formation of the chimera states and is responsible for the extreme multistability exhibited by the coupled system that leads to attractor crowding at the geometrical resonance (inductive-capacitive) frequency. Until now, chimera states were mostly believed to exist for nonlocal coupling. Our findings provide theoretical evidence that nearest neighbor interactions are indeed capable of supporting such states in a wide parameter range. SQUID metamaterials are the subject of intense experimental investigations and we are highly confident that the complex dynamics demonstrated in this manuscript can be confirmed in the laboratory.

We investigate the entanglement dynamics between two distant qubits by analyzing correlations in the quantum Ising model. Starting from the spin system in a paramagnetic regime enforced by the external magnetic field $B$, we then switch on the ferromagnetic spin-spin coupling $J$. Using the large coordination number expansion, we consider two limiting switching regimes: (1) adiabatic, which monitors the evolution of the ground state through the quantum transition to an ordered state; and (2) instantaneous (quench) which monitors instead the propagation of quantum fluctuations and simulates the generation of long range correlations. In particular, we find that quantum fluctuations propagate with twice the group speed of excitations in the equilibrium state of the system., Comment: 5 pages, 8 figures

Superconducting QUantum Interference Device (SQUID) metamaterials are superconducting artificial media whose function relies both on their geometry and the extraordinary properties of superconductivity and the Josephson effect. Recent experiments on one- and two-dimensional radio-frequency (rf) SQUID metamaterials have revealed their wide-band tuneability, significantly reduced losses, dynamic multistability, and tunable broadband transparency. The simplest version of an rf SQUID involves a superconducting ring interrupted by a Josephson junction; this device is a highly nonlinear resonator with a strong response to applied magnetic fields. SQUID metamaterials exhibit peculiar magnetic properties such as negative diamagnetic permeability, predicted both for the quantum and the classical regime. The applied alternating fields induce (super)currents in the SQUID rings, which are therefore coupled through dipole-dipole magnetic forces. This interaction is weak due to its magnetic nature. However, it couples the SQUIDs non-locally since it falls-off as the inverse cube of their center-to-center distance., Comment: arXiv admin note: text overlap with arXiv:1408.6072

Quantum bits (qubits) are at the heart of quantum information processing schemes. Currently, solid-state qubits, and in particular the superconducting ones, seem to satisfy the requirements for being the building blocks of viable quantum computers, since they exhibit relatively long coherence times, extremely low dissipation, and scalability. The possibility of achieving quantum coherence in macroscopic circuits comprising Josephson junctions, envisioned by Legett in the 1980's, was demonstrated for the first time in a charge qubit; since then, the exploitation of macroscopic quantum effects in low-capacitance Josephson junction circuits allowed for the realization of several kinds of superconducting qubits. Furthermore, coupling between qubits has been successfully achieved that was followed by the construction of multiple-qubit logic gates and the implementation of several algorithms. Here it is demonstrated that induced qubit lattice coherence as well as two remarkable quantum coherent optical phenomena, i.e., self-induced transparency and Dicke-type superradiance, may occur during light-pulse propagation in quantum metamaterials comprising superconducting charge qubits. The generated qubit lattice pulse forms a compound "quantum breather" that propagates in synchrony with the electromagnetic pulse. The experimental confirmation of such effects in superconducting quantum metamaterials may open a new pathway to potentially powerful quantum computing., Comment: Manuscript: 9 pages, 3 figures, 31 references + Supplementary Information: 11 pages, 4 figures

Surface plasmon polaritons (SPPs) are coherent electromagnetic surface waves trapped on an insulator-conductor interface. The SPPs decay exponentially along the propagation due to conductor losses, restricting the SPPs propagation length to few microns. Gain materials can be used to counterbalance the aforementioned losses. We provide an exact expression for the gain, in terms of the optical properties of the interface, for which the losses are eliminated. In addition, we show that systems characterized by lossless SPP propagation are related to PT symmetric systems. Furthermore, we derive an analytical critical value of the gain describing a phase transition between lossless and prohibited SPPs propagation. The regime of the aforementioned propagation can be directed by the optical properties of the system under scrutiny. Finally, we perform COMSOL simulations verifying the theoretical findings.

Ocean rogue waves (RW) -huge solitary waves- have for long triggered the interest of scientists. RWs emerge in a complex environment and it is still dubious the importance of linear versus nonlinear processes. Recent works have demonstrated that RWs appear in various other physical systems such as microwaves, nonlinear crystals, cold atoms, etc. In this work we investigate optical wave propagation in strongly scattering random lattices embedded in the bulk of transparent glasses. In the linear regime we observe the appearance of RWs that depend solely on the scattering properties of the medium. Interestingly, the addition of nonlinearity does not modify the RW statistics, while as the nonlinearities are increased multiple-filamentation and intensity clamping destroy the RW statistics. Numerical simulations agree nicely with the experimental findings and altogether prove that optical rogue waves are generated through the linear strong scattering in such complex environments.

We investigate wave transport properties of Parity-Time (PT) symmetric lattices that are periodically modulated along the direction of propagation. We demonstrate that in the regime of unbroken PT-symmetry the system Floquet-Bloch modes may interfere constructively leading to either controlled oscillations or linear power absorption and amplification occurring exactly at the phase transition point. The differential power response is effected by the overlap of the gain and loss system distribution with wave intensity pattern that is formed through Rabi oscillations engaging the coupled Floquet-Bloch modes.

The physics of activated escape of objects out of a metastable state plays a key role in diverse scientific areas involving chemical kinetics, diffusion and dislocation motion in solids, nucleation, electrical transport, motion of flux lines superconductors, charge density waves, and transport processes of macromolecules, to name but a few. The underlying activated processes present the multidimensional extension of the Kramers problem of a single Brownian particle. In comparison to the latter case, however, the dynamics ensuing from the interactions of many coupled units can lead to intriguing novel phenomena that are not present when only a single degree of freedom is involved. In this review we report on a variety of such phenomena that are exhibited by systems consisting of chains of interacting units in the presence of potential barriers. In the first part we consider recent developments in the case of a deterministic dynamics driving cooperative escape processes of coupled nonlinear units out of metastable states. The ability of chains of coupled units to undergo spontaneous conformational transitions can lead to a self-organised escape. The mechanism at work is that the energies of the units become re-arranged, while keeping the total energy conserved, in forming localised energy modes that in turn trigger the cooperative escape. We present scenarios of significantly enhanced noise-free escape rates if compared to the noise-assisted case. The second part deals with the collective directed transport of systems of interacting particles overcoming energetic barriers in periodic potential landscapes. Escape processes in both time-homogeneous and time-dependent driven systems are considered for the emergence of directed motion. It is shown that ballistic channels immersed in the associated high-dimensional phase space are the source for the directed long-range transport.

Regular lattices comprising superconducting quantum interference devices (SQUIDs) form magnetic metamaterials exhibiting extraordinary properties, including tunability, dynamic multistability, and negative magnetic permeability. The SQUIDs in a metamaterial interact through nonlocal, magnetic dipole-dipole forces that makes it possible for counter-intuitive dynamic states referred to as chimera states to appear; the latter feature clusters of SQUIDs with synchronous dynamics which coexist with clusters exhibiting asynchronous behavior. The spontaneous appearance of chimera states is demonstrated numerically for one-dimensional SQUID metamaterials driven by an alternating magnetic field in which the fluxes threading the SQUID rings are randomly initialized; then, chimera states appear generically for sufficiently strong initial excitations, which exhibit relatively long lifetimes. The synchronization and metastability levels of the chimera states are discussed in terms of appropriate measures. Given that both one- and two-dimensional SQUID metamaterials have been already fabricated and investigated in the laboratory, the presence of a chimera state could in principle be detected with presently available experimental setups., Comment: 8 pages, 8 figures

Nonequilibrium, quasi-stationary states of a one-dimensional "hard" $\phi^4$ deterministic lattice, initially thermalized to a particular temperature, are investigated when brought into contact with a stochastic thermal bath at lower temperature. For lattice initial temperatures sufficiently higher than those of the bath, energy localization through the formation of nonlinear excitations of the breather type during the cooling process occurs. These breathers keep the nonlinear lattice away from thermal equilibrium for relatively long times. In the course of time some breathers are destroyed by fluctuations, allowing thus the lattice to reach another nonequilibrium state of lower energy. The number of breathers thus reduces in time; the last remaining breather, however, exhibits amazingly long life-time demonstrated by extensive numerical simulations using a quasi-symplectic integration algorithm. For the single-breather states we have calculated the lattice velocity distribution unveiling non-gaussian features describable in a closed functional form. Moreover, the influence of the coupling constant on the life-time of a single breather has been explored. The latter exhibits power-law behaviour as the coupling constant approaches the anticontinuous limit., Comment: 5 pages, 10 figures

${\mathcal PT}-$symmetric dimers with a time-periodic gain/loss function in a balanced configuration where the amount of gain equals that of loss are investigated analytically and numerically. Two prototypical dimers in the linear regime are investigated: a system of coupled classical oscillators, and a Schr\"{o}dinger dimer representing the coupling of field amplitudes; each system representing a wide class of physical models. Through a thorough analysis of their stability behaviour, we find that turning on the coupling parameter in the classical dimer system, leads initially to decreased stability but then to re-entrant transitions from the exact to the broken ${\mathcal PT}-$phase and vice versa, as it is increased beyond a critical value. On the other hand, the Schr\"{o}dinger dimer behaves more like a single oscillator with time-periodic gain/loss. In addition, we are able to identify the conditions under which the behaviour of the two dimer systems coincides and/or reduces to that of a single oscillator., Comment: 9 pages, 9 figures, META14 Conference, subm. Special Issue Appl. Phys. A

Superconducting metamaterials comprising rf SQUIDs (Superconducting QUantum Interference Devices) have been recently realized and investigated with respect to their tuneability, permeability and dynamic multistability properties. These properties are a consequence of intrinsic nonlinearities due to the sensitivity of the superconducting state to external stimuli. SQUIDs, made of a superconducting ring interrupted by a Josephson junction, possess yet another source of nonlinearity, which makes them widely tuneable with an applied dc dlux. A model SQUID metamaterial, based on electric equivalent circuits, is used in the weak coupling approximation to demonstrate the dc flux tuneability, dynamic multistability, and nonlinear transmission in SQUID metamaterials comprising non-hysteretic SQUIDs. The model equations reproduce the experimentally observed tuneability patterns, and predict tuneability with the power of an applied ac magnetic magnetic field. Moreover, the results indicate the opening of nonlinear frequency bands for energy transmission through SQUID metamaterials, for sufficiently strong ac fields., Comment: 10 pages, 5 figures, submitted for the META 14 Conference

We use a simple dynamical model and explore coherent dynamics of wavepackets in complex networks of optical fibers. We start from a symmetric lattice and through the application of a Monte-Carlo criterion we introduce structural disorder and deform the lattice into a small-world network regime. We investigate in the latter both structural (correlation length) as well as dynamical (diffusion exponent) properties and find that both exhibit a rapid crossover from the ordered to the fully random regime. For a critical value of the structural disorder parameter $\rho \approx 0.25$ transport changes from ballistic to sub-diffusive due to the creation strongly connected local clusters and channels of preferential transport in the small world regime.

An overview of several dynamic properties of SQUID metamaterials is given in the presence of both constant and alternating magnetic field. The total current as a function of the driving frequency exhibits hysteretic effects which are favored by low levels of disorder. Multistability in the current states leads to multiple magnetic responses with different value of magnetic permeability. SQUID metamaterials exhibit wide-band tuneability which is periodic with the applied constant magnetic field; the numerical calculations reproduce fairly well recent experimental results. Current work also reveals the possibility for wave transmission through nonlinear bands, which is briefly discussed., Comment: META 2014 Conference, 20-23 May 2014, Singapore [3 pages, 3 figures]

The spatiotemporal complexity induced by perturbed initial excitations through the development of modulational instability in nonlinear lattices with or without disorder, may lead to the formation of very high amplitude, localized transient structures that can be named as extreme events. We analyze the statistics of the appearance of these collective events in two different universal lattice models; a one-dimensional nonlinear model that interpolates between the integrable Ablowitz-Ladik (AL) equation and the nonintegrable discrete nonlinear Schr\"odinger (DNLS) equation, and a two-dimensional disordered DNLS equation. In both cases, extreme events arise in the form of discrete rogue waves as a result of nonlinear interaction and rapid coalescence between mobile discrete breathers. In the former model, we find power-law dependence of the wave amplitude distribution and significant probability for the appearance of extreme events close to the integrable limit. In the latter model, more importantly, we find a transition in the the return time probability of extreme events from exponential to power-law regime. Weak nonlinearity and moderate levels of disorder, corresponding to weak chaos regime, favour the appearance of extreme events in that case., Comment: Invited Chapter in a Special Volume, World Scientific. 19 pages, 9 figures

We present numerical simulations for the propagation of surface plasmon polaritons in a dielectric-metal-dielectric waveguide using COMSOL multiphysics software. We show that the use of an active dielectric with gain that compensates metal absorption losses enhances substantially plasmon propagation. Furthermore, the introduction of the active material induces, for a specific gain value, a root in the imaginary part of the propagation constant leading to infinite propagation of the surface plasmon. The computational approaches analyzed in this work can be used to define and tune the optimal conditions for surface plasmon polariton amplification and propagation.

Metamaterials, i.e., artificially structured ("synthetic") media comprising weakly coupled discrete elements, exhibit extraordinary properties and they hold a great promise for novel applications including super-resolution imaging, cloaking, hyperlensing, and optical transformation. Nonlinearity adds a new degree of freedom for metamaterial design that allows for tuneability and multistability, properties that may offer altogether new functionalities and electromagnetic characteristics. The combination of discreteness and nonlinearity may lead to intrinsic localization of the type of discrete breather in metallic, SQUID-based, and ${\cal PT}-$symmetric metamaterials. We review recent results demonstrating the generic appearance of breather excitations in these systems resulting from power-balance between intrinsic losses and input power, either by proper initialization or by purely dynamical procedures. Breather properties peculiar to each particular system are identified and discussed. Recent progress in the fabrication of low-loss, active and superconducting metamaterials, makes the experimental observation of breathers in principle possible with the proposed dynamical procedures., Comment: 19 pages, 14 figures, Invited (Review) Chapter

Planar arrays of magnetoinductively coupled rf SQUIDs belong to the emergent class of superconducting metamaterials that encompass the Josephson effect. SQUID metamaterials acquire their electromagnetic properties from the resonant characteristics of their constitutive elements, i.e., the individual rf SQUIDs, which consist of a superconducting ring interrupted by a Josephson junction. We investigate the response of a two-dimensional SQUID metamaterial to frequency variation of an applied alternating magnetic field in the presence of disorder, arising from critical current fluctuations of the Josephson elements; in effect, the resonance frequencies of individual SQUIDs are distributed randomly around a mean value. Bistability is observed in the total current-frequency curves both in ordered and disordered SQUID metamaterials; moreover, bistability is favoured by disorder through the improvement of synchronization between SQUID oscillators. Relatively weak disorder widens significantly the bistability region by helping the system to self-organize itself and leads to nearly homogeneous states that change smoothly with varying frequency. Moreover, the total current of the metamaterial is enhanced compared with that of uncoupled SQUIDs, through the synergetic action of coupling and synchronization. Multistability of nearly homogeneous states allows the metamaterial to exhibit different magnetic responses corresponding to different values of the magnetic permeability. At low power of the incident field, high-current states exhibit extreme diamagnetic properties corresponding to negative magnetic permeability in a narrow frequency region., Comment: 10 pages, 14 figures. Subm. to Superconductor Science and Technology Focus Issue on "Superconducting Metamaterials" (2013)

A one dimensional, parity-time (${\cal PT}$)-symmetric magnetic metamaterial comprising split-ring resonators having both gain and loss is investigated. In the linear regime, the transition from the exact to the broken ${\cal PT}$-phase is determined through the calculation of the eigenfrequency spectrum for two different configurations; the one with equidistant split-rings and the other with the split-rings forming a binary pattern (${\cal PT}$ dimer chain). The latter system features a two-band, gapped spectrum with its shape determined by the gain/loss coefficient as well as the inter-element coupling. In the presense of nonlinearity, the ${\cal PT}$ dimer chain with balanced gain and loss supports nonlinear localized modes in the form of novel discrete breathers below the lower branch of the linear spectrum. These breathers, that can be excited from a weak applied magnetic field by frequency chirping, can be subsequently driven solely by the gain for very long times. The effect of a small imbalance between gain and loss is also considered. Fundamendal gain-driven breathers occupy both sites of a dimer, while their energy is almost equally partitioned between the two split-rings, the one with gain and the other with loss. We also introduce a model equation for the investigation of classical ${\cal PT}$ symmetry in zero dimensions, realized by a simple harmonic oscillator with matched time-dependent gain and loss that exhibits a transition from oscillatory to diverging motion. This behaviour is similar to a transition from the exact to the broken ${\cal PT}$ phase in higher-dimensional ${\cal PT}-$ symmetric systems. A stability condition relating the parameters of the problem is obtained in the case of piecewise constant gain/loss function that allows for the construction of a phase diagram with alternating stable and unstable regions., Comment: 10 pages, 11 figs, subm. to Applied Physics A for the Proceedings of the META13 Conference

We introduce a one dimensional parity-time (PT)-symmetric nonlinear magnetic metamaterial consisted of split ring dimers having both gain and loss. When nonlinearity is absent we find a transition between an exact to a broken PT-phase; in the former the system features a two band gapped spectrum with shape determined by the gain and loss coefficients as well as the inter-unit coupling. In the presence of nonlinearity we show numerically that as a result of the gain/dissipation matching a novel type of long-lived stable discrete breathers can form below the lower branch of the band with no attenuation. In these localized modes the energy is almost equally partitioned between two adjacent split rings on the one with gain and the other one with loss., Comment: 5 pages, 7 figures

Spatiotemporal complexity is induced in a two dimensional nonlinear disordered lattice through the modulational instability of an initially weakly perturbed excitation. In the course of evolution we observe the formation of transient as well as persistent localized structures, some of which have extreme magnitude. We analyze the statistics of occurrence of these extreme collective events and find that the appearance of transient extreme events is more likely in the weakly nonlinear regime. We observe a transition in the extreme events recurrence time probability from exponential, in the nonlinearity dominated regime, to power law for the disordered one., Comment: 5 figures, 5 pages

We investigate numerically the effect of the competition of disorder, nonlinearity, and boundaries on the Anderson localization of light waves in finite-size, one-dimensional waveguide arrays. Using the discrete Anderson - nonlinear Schr\"odinger equation, the propagation of the mode amplitudes up to some finite distance is monitored. The analysis is based on the calculated localization length and the participation number, two standard measures for the statistical description of Anderson localization. For relatively weak disorder and nonlinearity, a higher disorder strength is required to achieve the same degree of localization at the edge than in the interior of the array, in agreement with recent experimental observations in the linear regime. However, for relatively strong disorder and/or nonlinearity, this behavior is reversed and it is now easier to localize an excitation at the edge than in the interior., Comment: 5 double-column pages, 7 figures, submitted for publication