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Although much empirical evidence has demonstrated that p53 plays a key role in tumor suppression, the dynamics and function of the regulatory network centered on p53 have not yet been fully understood. Here, we develop a Boolean network model to reproduce the two-phase dynamics of the p53 network in response to DNA damage. In particular, we map the fates of cells into two types of Boolean attractors, and we find that the apoptosis attractor does not exist for minor DNA damage, reflecting that the cell is reparable. As the amount of DNA damage increases, the basin of the repair attractor shrinks, accompanied by the rising of the apoptosis attractor and the expansion of its basin, indicating that the cell becomes more irreparable with more DNA damage. For severe DNA damage, the repair attractor vanishes, and the apoptosis attractor dominates the state space, accounting for the exclusive fate of death. Based on the Boolean network model, we explore the significance of links, in terms of the sensitivity of the two-phase dynamics, to perturbing the weights of links and removing them. We find that the links are either critical or ordinary, rather than redundant. This implies that the p53 network is irreducible, but tolerant of small mutations at some ordinary links, and this can be interpreted with evolutionary theory. We further devised practical control schemes for steering the system into the apoptosis attractor in the presence of DNA damage by pinning the state of a single node or perturbing the weight of a single link. Our approach offers insights into understanding and controlling the p53 network, which is of paramount importance for medical treatment and genetic engineering.

Swarmalators are entities with the simultaneous presence of swarming and synchronization that reveal emergent collective behavior due to the fascinating bidirectional interplay between phase and spatial dynamics. Although different coupling topologies have already been considered, here we introduce time-varying competitive phase interaction among swarmalators where the underlying connectivity for attractive and repulsive coupling varies depending on the vision (sensing) radius. Apart from investigating some fundamental properties like conservation of center of position and collision avoidance, we also scrutinize the cases of extreme limits of vision radius. The concurrence of attractiveâ€"repulsive competitive phase coupling allows the exploration of diverse asymptotic states, like static Ď€, and mixed phase wave states, and we explore the feasible routes of those states through a detailed numerical analysis. In sole presence of attractive local coupling, we reveal the occurrence of static cluster synchronization where the number of clusters depends crucially on the initial distribution of positions and phases of each swarmalator. In addition, we analytically calculate the sufficient condition for the emergence of the static synchronization state. We further report the appearance of the static ring phase wave state and evaluate its radius theoretically. Finally, we validate our findings using Stuartâ€"Landau oscillators to describe the phase dynamics of swarmalators subject to attractive local coupling. [ABSTRACT FROM AUTHOR]

In a recent letter (Friedrich et al 2012 Phys. Rev. Lett. 109 138102), a minimal model swimmer has been proposed that propels itself at low Reynolds numbers by the revolving motion of a pair of spheres. The motion of the two spheres can synchronize by virtue of a hydrodynamic coupling that depends on the motion of the swimmer, but is rather independent of direct hydrodynamic interactions. This novel synchronization mechanism could account for the synchronization of a pair of flagella, e.g. in the green algae Chlamydomonas. In this paper, we discuss in detail how swimming and synchronization depend on the geometry of the model swimmer and compute the swimmer design for optimal synchronization. Our analysis highlights the role of broken symmetries in swimming and synchronization. [ABSTRACT FROM AUTHOR]

We study the mean-field dynamics and the reduced-dimension character of two-mode Bose-Einstein condensates (BECs) in highly anisotropic traps. By means of perturbative techniques, we show that the tightly confined (transverse) degrees of freedom can be decoupled from the dynamical equations at the expense of introducing additional effective three-body, attractive, intra- and inter-mode interactions into the dynamics of the loosely confined (longitudinal) degrees of freedom. These effective interactions are mediated by changes in the transverse wave function. The perturbation theory is valid as long as the nonlinear scattering energy is small compared to the transverse energy scales. This approach leads to reduced-dimension mean-field equations that optimally describe the evolution of a two-mode condensate in general quasi-one-dimensional (1D) and quasi-two-dimensional geometries.We use this model to investigate the relative phase and density dynamics of a two-mode, cigar- shaped 87Rb BEC. We study the relative-phase dynamics in the context of a nonlinear Ramsey interferometry scheme, which has recently been proposed as a novel platform for high-precision interferometry. Numerical integration of the coupled, time-dependent, three-dimensional, two-mode Gross-Pitaevskii equations for various atom numbers shows that this model gives a considerably more refined analytical account of the mean-field evolution than an idealized quasi-1D description. [ABSTRACT FROM AUTHOR]

We present a novel approach for recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series data. The main idea is to use a triplet analysis instead of the traditional pairwise one. Our technique reveals an effective phase connectivity which is generally not equivalent to a structural one. We demonstrate that by comparing the coupling functions from all possible triplets of oscillators, we are able to achieve in the reconstruction a good separation between existing and non-existing connections, and thus reliably reproduce the network structure. [ABSTRACT FROM AUTHOR]

This tutorial introduces the theoretical and experimental basics of electromagnetically induced transparency (EIT) in thermal alkali vapors. We first give a brief phenomenological description of EIT in simple three-level systems of stationary atoms and derive analytical expressions for optical absorption and dispersion under EIT conditions. Then we focus on how the thermal motion of atoms affects various parameters of the EIT system. Specifically, we analyze the Doppler broadening of optical transitions, ballistic versus diffusive atomic motion in a limited-volume interaction region, and collisional depopulation and decoherence. Finally, we discuss the common trade-offs important for optimizing an EIT experiment and give a brief 'walk-through' of a typical EIT experimental setup. We conclude with a brief overview of current and potential EIT applications. [ABSTRACT FROM AUTHOR]

We study a physical system consisting of a Bose–Einstein condensate confined to a ring shaped lattice potential interrupted by three weak links. The system is assumed to be driven by an effective flux piercing the ring lattice. By employing path integral techniques, we explore the effective quantum dynamics of the system in a pure quantum phase dynamics regime. Moreover, the effects of the density’s quantum fluctuations are studied through exact diagonalization analysis of the spectroscopy of the Bose–Hubbard model. We demonstrate that a clear two-level system emerges by tuning the magnetic flux at degeneracy. The lattice confinement, platform for the condensate, is realized experimentally employing a spatial light modulator. [ABSTRACT FROM AUTHOR]

Large-scale neurophysiological networks are often reconstructed from band-pass filtered time series derived from magnetoencephalography (MEG) data. Common practice is to reconstruct these networks separately for different frequency bands and to treat them independently. Recent evidence suggests that this separation may be inadequate, as there can be significant coupling between frequency bands (interlayer connectivity). A multilayer network approach offers a solution to analyze frequency-specific networks in one framework. We propose to use a recently developed network reconstruction method in conjunction with phase oscillator models to estimate interlayer connectivity that optimally fits the empirical data. This approach determines interlayer connectivity based on observed frequency-specific time series of the phase and a connectome derived from diffusion weighted imaging. The performance of this interlayer reconstruction method was evaluated in-silico. Our reconstruction of the underlying interlayer connectivity agreed to very high degree with the ground truth. Subsequently, we applied our method to empirical resting-state MEG data obtained from healthy subjects and reconstructed two-layered networks consisting of either alpha-to-beta or theta-to-gamma band connectivity. Our analysis revealed that interlayer connectivity is dominated by a multiplex structure, i.e. by one-to-one interactions for both alpha-to-beta band and theta-to-gamma band networks. For theta–gamma band networks, we also found a plenitude of interlayer connections between distant nodes, though weaker connectivity relative to the one-to-one connections. Our work is an stepping stone towards the identification of interdependencies across frequency-specific networks. Our results lay the ground for the use of the promising multilayer framework in this field with more-informed and justified interlayer connections. [ABSTRACT FROM AUTHOR]

Josephson effects are commonly studied in quantum systems in which dissipation or noise can be neglected or do not play a crucial role. In contrast, here we discuss a setup where dissipative interactions do amplify a photonic Josephson current, opening a doorway to dissipation-enhanced sensitivity of quantum-optical interferometry devices. In particular, we study two coupled nanolasers subjected to phase coherent drivings and coupled by a coherent photon tunneling process. We describe this system by means of a Fokker–Planck equation and show that it exhibits an interesting non-equilibrium phase diagram as a function of the coherent coupling between nanolasers. As we increase that coupling, we find a non-equilibrium phase transition between a phase-locked (PL) and a non-phase-locked (NPL) steady-state, in which phase coherence is destroyed by the photon tunneling process. In the coherent, PL regime, an imbalanced photon number population appears if there is a phase difference between the nanolasers, which appears in the steady-state as a result of the competition between competing local dissipative dynamics and the Josephson photo-current. The latter is amplified for large incoherent pumping rates and it is also enchanced close to the lasing phase transition. We show that the Josephson photocurrent can be used to measure optical phase differences. In the quantum limit, the accuracy of the two nanolaser interferometer grows with the square of the photon number and, thus, it can be enhanced by increasing the rate of incoherent pumping of photons into the nanolasers. [ABSTRACT FROM AUTHOR]

Bose–Bose droplets are self-bound objects emerging from a mixture of two interacting Bose–Einstein condensates when their interactions are appropriately tuned. During droplet formation three continuous symmetries of the system's Hamiltonian are broken: translational symmetry and two U(1) symmetries, allowing for arbitrary choice of phases of the mean-field wavefunctions describing the two components. Breaking of these symmetries must be accompanied by appearance of zero-energy excitations in the energy spectrum of the system recovering the broken symmetries. Normal modes corresponding to these excitations are the zero-energy modes. Here we find analytic expressions for these modes and introduce Hamiltonians generating their time evolution—dynamics of the droplet's centers of mass as well as dynamics of the phases of the two droplet's wavefunctions. When internal types of excitations (quasiparticles) are neglected then the very complex system of a quantum droplet is described using only a few 'global' degrees of freedom—the position of the center of mass of the droplet and two phases of two wave-functions, all these being quantum operators. We believe that our work might be useful in describing in a relatively easy way the low energy collisions of quantum droplets in situations where coherent flow of atoms between the droplets takes place. [ABSTRACT FROM AUTHOR]

We study the thermodynamic properties induced by non-reciprocal interactions between stochastic degrees of freedom in time- and space-continuous systems. We show that, under fairly general conditions, non-reciprocal coupling alone implies a steady energy flow through the system, i.e., non-equilibrium. Projecting out the non-reciprocally coupled degrees of freedom renders non-Markovian, one-variable Langevin descriptions with complex types of memory, for which we find a generalized second law involving information flow. We demonstrate that non-reciprocal linear interactions can be used to engineer non-monotonic memory, which is typical for, e.g., time-delayed feedback control, and is automatically accompanied with a nonzero information flow through the system. Furthermore, already a single non-reciprocally coupled degree of freedom can extract energy from a single heat bath (at isothermal conditions), and can thus be viewed as a minimal version of a time-continuous, autonomous 'Maxwell demon'. We also show that for appropriate parameter settings, the non-reciprocal system has characteristic features of active matter, such as a positive energy input on the level of the fluctuating trajectories without global particle transport. [ABSTRACT FROM AUTHOR]

We study the quantum tunneling of two one-dimensional quasi-condensates made of alkali-metal atoms, considering two different tunneling configurations: side-by-side and head-to-tail. After deriving the quasiparticle excitation spectrum, we discuss the dynamics of the relative phase following a sudden coupling of the independent subsystems. In particular, we calculate the coherence factor of the system, which, due to the nonzero tunneling amplitude, it exhibits dephasing–rephasing oscillations instead of pure dephasing. These oscillations are enhanced by a higher tunneling energy, and by higher system densities. Our predictions provide a benchmark for future experiments at temperatures below T ≲ 5 nK. [ABSTRACT FROM AUTHOR]

The phase sensitivity curve or phase response curve (PRC) quantifies the oscillator’s reaction to stimulation at a specific phase and is a primary characteristic of a self-sustained oscillatory unit. Knowledge of this curve yields a phase dynamics description of the oscillator for arbitrary weak forcing. Similar, though much less studied characteristic, is the amplitude response that can be defined either using an ad hoc approach to amplitude estimation or via the isostable variables. Here, we discuss the problem of the phase and amplitude response inference from observations using test stimulation. Although PRC determination for noise-free neuronal-like oscillators perturbed by narrow pulses is a well-known task, the general case remains a challenging problem. Even more challenging is the inference of the amplitude response. This characteristic is crucial, e.g. for controlling the amplitude of the collective mode in a network of interacting units—a task relevant to neuroscience. Here, we compare the performance of different techniques suitable for inferring the phase and amplitude response, particularly with application to macroscopic oscillators. We suggest improvements to these techniques, e.g. demonstrating how to obtain the PRC in case of stimuli of arbitrary shape. Our main result is a novel technique denoted by IPID-1, based on the direct reconstruction of the Winfree equation and the analogous first-order equation for isostable dynamics. The technique works for signals with or without well-pronounced marker events and pulses of arbitrary shape; in particular, we consider charge-balanced pulses typical in neuroscience applications. Moreover, this technique is superior for noisy and high-dimensional systems. Additionally, we describe an error measure that can be computed solely from data and complements any inference technique.

Synchronization has been reported for a wide range of self-oscillating systems. However, even though it has been predicted theoretically for several decades, the experimental realization of phase self-oscillation, sometimes called phase trapping, in the high driving regime has been studied only recently. We explored in detail the phase dynamics in a synchronized field emission SiC nanoelectromechanical system with intrinsic feedback. A richer variety of phase behavior has been unambiguously identified, implying phase modulation and inertia. This synchronization regime is expected to have implications for the comprehension of the dynamics of interacting self-oscillating networks and for the generation of frequency modulated signals at the nanoscale. [ABSTRACT FROM AUTHOR]

Weconsider competition between layers in adaptive multiplex networks of phase oscillators, where adaptation principles (which cause intra-layer topology evolution) are inspired by real world homophily and homeostasis phenomena. Our model yields the emergence of both scale-free topologies and meso-scale structures in the layers, for an appropriate choice of the control parameters. Wefurther report that the growth of the number of interacting layers leads to a decrease of the global order, due to inter-layer structural competition. However, the increase of the system's scale can effect local synchronization between neighboring (or strongly coupled) nodes. Such unforeseen phenomena is connected with the nature of the competitive mechanism, which implies the rivalry for optimal structure within the whole system, a situation occurring in a variety of natural systems. [ABSTRACT FROM AUTHOR]

Wedescribe an experiment where spin squeezing occurs spontaneously within a standard Ramsey sequence driving a two-component Bose--Einstein condensate (BEC) of87Rb atoms trapped in an elongated magnetic trap. The squeezing is generated by state-dependent collisional interactions, despite the near-identical scattering lengths of the spin states in 87Rb. In our proof-of-principle experiment, we observe a metrological spin squeezing that reaches 1.3 ± 0.4 dB for 5000 atoms, with a contrast of 90 ± 1%. The method may be applied to realize spin-squeezed BEC sources for atom interferometry without the need for cavities, state-dependent potentials or Feshbach resonances. [ABSTRACT FROM AUTHOR]

We discuss polariton graphs as a new platform for simulating the classical XY and Kuramoto models. Polariton condensates can be imprinted into any two-dimensional graph by spatial modulation of the pumping laser. Polariton simulators have the potential to reach the global minimum of the XY Hamiltonian in a bottom-up approach by gradually increasing excitation density to threshold or to study large scale synchronization phenomena and dynamical phase transitions when operating above the threshold.Weconsider the modelling of polariton graphs using the complex Ginzburg–Landau model and derive analytical solutions for a single condensate, the XY model, two-mode model and the Kuramoto model establishing the relationships between them. [ABSTRACT FROM AUTHOR]

The nanomechanical single-electron shuttle is a resonant system in which a suspended metallic island oscillates between and impacts at two electrodes. This setup holds promise for one-by-one electron transport and the establishment of an absolute current standard. While the charge transported per oscillation by the nanoscale island will be quantized in the Coulomb blockade regime, the frequency of such a shuttle depends sensitively on many parameters, leading to drift and noise. Instead of considering the nonlinearities introduced by the impact events as a nuisance, here we propose to exploit the resulting nonlinear dynamics to realize a highly precise oscillation frequency via synchronization of the shuttle self-oscillations to an external signal. We link the established phenomenological description of synchronization based on the Adler equation to the microscopic nonlinear dynamics of the electron shuttle by calculating the effective Adler constant analytically in terms of the microscopic parameters. [ABSTRACT FROM AUTHOR]

We describe a multi-mode quantum memory for propagating microwave photons that combines a solid-state spin ensemble resonantly coupled to a frequency tunable single-mode microwave cavity. We first show that high efficiency mapping of the quantum state transported by a free photon to the spin ensemble is possible both for strong and weak coupling between the cavity mode and the spin ensemble. We also show that even in the weak coupling limit unit efficiency and faithful retrieval can be obtained through time reversal inhomogeneous dephasing based on spin echo techniques. This is possible provided that the cavity containing the spin ensemble and the transmission line are impedance matched. We finally discuss the prospects for an experimental implementation using a rare-earth doped crystal coupled to a superconducting resonator. [ABSTRACT FROM AUTHOR]

We study the dynamics of a nonlinear one-dimensional disordered system from a spectral point of view. The spectral entropy and the Lyapunov exponent are extracted from the short-time dynamics, and are shown to give a pertinent characterization of the different dynamical regimes. The chaotic and self-trapped regimes are governed by log-normal laws whose origin is traced to the exponential shape of the eigenstates of the linear problem. These quantities satisfy scaling laws depending on the initial state and explain the system's behaviour at longer times. [ABSTRACT FROM AUTHOR]

Photoinduced electrocyclic ring opening reactions in conjugated cylcoalkenes are among themost elementary processes in organic chemistry. One prototypical ring opening reaction transforms cyclohexadiene into hexatriene. It is known that a sequence of sub-100 fs internal conversion transitions precedes bond breaking in cyclohexadiene and some of its derivatives. However, these excited state dynamics have never been directly monitored in solution because of insufficient time resolution. Here we aim to uncover the extraordinary photophysics behind related ultrafast internal conversion processes in a derivative of cyclohexadiene, α-terpinene (α-TP), solvated in cyclohexane. Transient absorption anisotropy experiments conducted with 20 fs laser pulses at 267 nm expose non-exponential depopulation kinetics for the ππ* electronic state of α-TP. Our data show that population transfer rapidly accelerates within the first 100 fs after photoexcitation. In addition, recurrences in two-dimensional photon echo (2DPE) line shapes reveal strong vibronic coupling in a normal mode near 523 cm-1, which involves torsions of the C=C bonds and hydrogen out-of-plane (HOOP) wagging on a vinyl group. With the support of several experiments, we hypothesize that the excited state wavepacket in α-TP undergoes several recurrences in the C=C stretching coordinate before displacement along the C=C torsion/vinyl HOOP coordinate finally sets it free from the Franck-Condon region of the potential energy surface. The unconfined wavepacket departs the ππ* electronic state by way of a conical intersection with a lower energy excited state. The present observations are made possible by recent improvements to both the time resolution and detection sensitivity of our experimental setup. This work demonstrates that it is now possible to acquire 2DPE signals in the deep ultraviolet, which are comparable with high-quality measurements in the visible spectral region. These technical developments open the door to studies of many beautiful models for elementary chemical dynamics. [ABSTRACT FROM AUTHOR]

Transient nanoplasmas in laser-excited metal clusters open the route to probing ultrafast collisional and collective laser-plasma processes in a wide and well-tunable range of densities and temperatures. The transition from a fully degenerate to a nearly classical plasma can occur within a few femtoseconds, accompanied by fundamental changes in the relaxation processes driven by electron-electron collisions (EECs). To investigate the resulting implications for laser-metal-cluster interactions, we developed an extended semiclassical Vlasov-Uehling-Uhlenbeck approach where the collision term resolves timedependent Pauli blocking and local screening effects for arbitrary levels of degeneracy. Our simulation results for resonant dual-pulse excitations of Na55 reveal an unexpected synergy effect of EECs and collective laser-plasma processes, i.e. a strongly enhanced electron acceleration via plasmon-assisted rescattering in the presence of EECs. [ABSTRACT FROM AUTHOR]

We numerically study the classical and quantum dynamics of an atomic bright soliton in a highly elongated one-dimensional harmonic trap with a Gaussian barrier. In the regime of the recent experiment by Dyke et al the system realizes a coherent nonlinear soliton beam-splitter and interferometer whose accuracy we analyze. In the case of tighter radial trap confinement and enhanced quantum fluctuations, a split soliton can represent a spin-squeezed, or alternatively, a fragmented condensate with reduced phase coherence that can be measured by interfering the split soliton by the barrier.We also find large quantum mechanical uncertainties in the soliton's position and momentum due to nonlinear interaction with the barrier. [ABSTRACT FROM AUTHOR]

We numerically study the dynamics and frequency response of the recently proposed Ising machine based on the polarization degrees of freedom of an injection-locked laser network (Utsunomiya et al 2011 Opt. Express 19 18091). We simulate various anti-ferromagnetic Ising problems, including the ones with symmetric Ising and Zeeman coefficients, which enable us to study the problem size up to M = 1000. Transient time, to reach a steady-state polarization configuration after a given Ising problem is mapped onto the system, is inversely proportional to the locking bandwidth and does not scale exponentially with the problem size. In the Fourier analysis with first-order linearization approximation, we find that the cut-off frequency of a system's response is almost identical to the locking bandwidth, which supports the time-domain analysis. It is also shown that the Zeeman term, which is created by the horizontally polarized injection signal from the master laser, serves as an initial driving force on the system and contributes to the transient time in addition to the inverse locking bandwidth. [ABSTRACT FROM AUTHOR]

We investigate the effect of general time transformations on the phase synchronization (PS) phenomenon and the mutual information rate (MIR) between pairs of nodes in dynamical networks. We demonstrate two important results concerning the invariance of both PS and the MIR. Under time transformations PS can neither be introduced nor destroyed and the MIR cannot be raised from zero. On the other hand, for proper time transformations the timing between the cycles of the coupled oscillators can be largely improved. Finally, we discuss the relevance of our findings for communication in dynamical networks. [ABSTRACT FROM AUTHOR]

We employ a nonequilibrium energy balance and carrier rate equation model based on microscopic semiconductor theory to describe the quantum-dot (QD) laser dynamics under optical injection and time-delayed feedback. The model goes beyond typical phenomenological approximations of rate equations, such as the α -factor, yet allows for a thorough numerical bifurcation analysis, which would not be possible with the computationally demanding microscopic equations. We find that with QD lasers, independent amplitude and phase dynamics may lead to less complicated scenarios under optical perturbations than predicted by conventional models using the α -factor to describe the carrier-induced refractive index change. For instance, in the short external cavity feedback regime, higher critical feedback strength is actually required to induce instabilities. Generally, the α -factor should only be used when the carrier distribution can follow the QD laser dynamics adiabatically.

Phase plays a crucial role in many quantum effects including interference. Here we lay the foundations for the study of phase in probabilistic theories more generally. Phase is normally defined in terms of complex numbers that appear when representing quantum states as complex vectors. Here we give an operational definition whereby phase is instead defined in terms of measurement statistics. Our definition is phrased in terms of the operational framework known as generalized probabilistic theories or the convex framework . The definition makes it possible to ask whether other theories in this framework can also have phase. We apply our definition to investigate phase and interference in several example theories: classical probability theory, a version of Spekkens' toy model, quantum theory and box-world. We find that phase is ubiquitous; any non-classical theory can be said to have non-trivial phase dynamics.

We report on the dynamics of a Bose–Einstein condensate in one and two dimensions driven by the time-dependent harmonic trapping potential. Without the inter-particle interaction, the condensate exhibits the coherent behavior with the time-oscillating density distribution. When the inter-particle interaction is taken into consideration, the phase fluctuations, the multi-peak structure of the density distribution, and the coherence revival phenomenon, apart from the well-studied density oscillation behavior, can be observed in the condensate. Furthermore, it is demonstrated that due to the dimensional restriction these effects are more stable in the two and three-dimensional system, if compared to the one-dimensional case. [ABSTRACT FROM AUTHOR]

Feshbach molecules forming a Bose–Einstein condensate (BEC) behave as non-ideal bosonic particles due to their underlying fermionic structure. We study the observable consequences of the fermion exchange interactions in the interference of molecular BECs for entangled-enhanced precision measurements. Our many-body treatment of the molecular condensate is based on an ansatz of composite two-fermion bosons which accounts for all possible fermion exchange correlations present in the system. The Pauli principle acts prohibitively on the particle fluctuations during the interference process leading to a loss of precision in phase estimations. However, we find that, in the regime where molecular dissociations do not jeopardize the interference dynamics, measurements of the phase can still be performed with a precision beyond the classical limit comparable to atomic interferometers. We also show that the effects of Pauli principle increases with the noise of the particle detectors such that molecular interferometers would require more efficient detectors. [ABSTRACT FROM AUTHOR]

Implementing a positive correlation between the natural frequencies of nodes and their connectivity on a single star graph leads to a pronounced explosive transition to synchronization, additionally presenting hysteresis behavior. From the viewpoint of network connectivity, a star has been considered as a building motif to generate a big graph by graph operations. On the other hand, we propose to construct complex synchronization dynamics by applying the Cartesian product of two Kuramoto models on two star networks. On the product model, the lower dimensional equations describing the ensemble dynamics in terms of collective order parameters are fully solved by the Watanabe–Strogatz method. Different graph parameter choices lead to three different interacting scenarios of the hysteresis areas of two individual factor graphs, which further change the basins of attraction of multiple fixed points. Furthermore, we obtain coupling regimes where cluster synchronization states are often present on the product graph and the number of clusters is fully controlled. More specifically, oscillators on one star graph are synchronized while those on the other star are not synchronized, which induces clustered state on the product model. The numerical results agree perfectly with the theoretic predictions. [ABSTRACT FROM AUTHOR]

We analyse the properties of the synchronisation transition in a many-body system consisting of quantum van der Pol oscillators with all-to-all coupling using a self-consistent mean-field method. We find that the synchronised state, which the system can access for oscillator couplings above a critical value, is characterised not just by a lower phase uncertainty than the corresponding unsynchronised state, but also a higher number uncertainty. Just below the critical coupling the system can evolve to the unsynchronised steady state via a long-lived transient synchronised state. We investigate the way in which this transient state eventually decays and show that the critical scaling of its lifetime is consistent with a simple classical model. [ABSTRACT FROM AUTHOR]

Power grids sustain modern society by supplying electricity and thus their stability is a crucial factor for our civilization. The dynamic stability of a power grid is usually quantified by the probability of its nodes’ recovery to phase synchronization of the alternating current it carries, in response to external perturbation. Intuitively, the stability of nodes in power grids is supposed to become more robust as the coupling strength between the nodes increases. However, we find a counterintuitive range of coupling strength values where the synchronization stability suddenly droops as the coupling strength increases, on a number of simple graph structures. Since power grids are designed to fulfill both local and long-range power demands, such simple graph structures or graphlets for local power transmission are indeed relevant in reality. We show that the observed nonmonotonic behavior is a consequence of transitions in multistability, which are related to changes in stability of the unsynchronized states. Therefore, our findings suggest that a comprehensive understanding of changes in multistability are necessary to prevent the unexpected catastrophic instability in the building blocks of power grids. [ABSTRACT FROM AUTHOR]

Methods for reconstructing the topology of complex networks from time-resolved observations of node dynamics are gaining relevance across scientific disciplines. Of biggest practical interest are methods that make no assumptions about the properties of the dynamics, and can cope with noisy, short and incomplete trajectories. Ideal reconstruction in such scenario requires an exhaustive approach of simulating the dynamics for all possible network configurations and matching the simulated against the actual trajectories, which of course is computationally too costly for any realistic application. Relying on insights from equation discovery and machine learning, we here introduce decoupling approximation of dynamical networks and propose a new reconstruction method based on it. Decoupling approximation consists of matching the simulated against the actual trajectories for each node individually rather than for the entire network at once. Despite drastic reduction of the computational cost that this approximation entails, we find our method’s performance to be very close to that of the ideal method. In particular, we not only make no assumptions about the properties of the trajectories, but provide strong evidence that our methods’ performance is largely independent of the dynamical regime at hand. Of crucial relevance for practical applications, we also find our method to be extremely robust to both length and resolution of the trajectories and relatively insensitive to noise. [ABSTRACT FROM AUTHOR]

Inferring direct interactions in complex networked systems from time series data constitutes a challenging open problem of current research. Major obstacles include the often limited number of time points accessible, unknown or inaccurate dynamical systems models in many practical applications, the impossibility to infer topological information from invariant collective dynamics such as synchronized states, and the required computational effort. Here, we propose and analyze a mathematical scheme that transforms observed transient dynamics towards invariant states in to accelerated reference frames to reveal network interactions. The transformation yields simple linear constraints relating a number of short observed time series (of only a few data points) of the dynamics to estimates the absence, presence and strength of direct physical interactions in a computationally efficient way. As we illustrate numerically, the scheme applies across transient dynamics towards periodic and chaotic, phase-locked and other synchronized states. Reconstruction robustly reveals the entire connectivity of network dynamical systems with increased reconstruction quality for large and for sparse networks. [ABSTRACT FROM AUTHOR]

We present here an adaptive control scheme with a feedback delay to achieve elimination of synchronization in a large population of coupled and synchronized oscillators. We validate the feasibility of this scheme not only in the coupled Kuramoto’s oscillators with a unimodal or bimodal distribution of natural frequency, but also in two representative models of neuronal networks, namely, the FitzHugh–Nagumo spiking oscillators and the Hindmarsh–Rose bursting oscillators. More significantly, we analytically illustrate the feasibility of the proposed scheme with a feedback delay and reveal how the exact topological form of the bimodal natural frequency distribution influences the scheme performance. We anticipate that our developed scheme will deepen the understanding and refinement of those controllers, e.g. techniques of deep brain stimulation, which have been implemented in remedying some synchronization-induced mental disorders including Parkinson disease and epilepsy. [ABSTRACT FROM AUTHOR]

We present a comprehensive analysis of the form and interaction of dipolar bright solitons across the full parameter space afforded by dipolar Bose–Einstein condensates, revealing the rich behavior introduced by the non-local nonlinearity. Working within an effective one-dimensional description, we map out the existence of the soliton solutions and show three collisional regimes: free collisions, bound state formation and soliton fusion. Finally, we examine the solitons in their full three-dimensional form through a variational approach; along with regimes of instability to collapse and runaway expansion, we identify regimes of stability which are accessible to current experiments. [ABSTRACT FROM AUTHOR]

This collection of papers describes research that goes into detail on some of the more important issues in the physics of stimulated Brillouin scattering. This perspective describes the earliest years of the physics of stimulated Brillouin scattering, along with key developments that have led to this technically and physically rich field of today’s nonlinear optics. Stimulated Brillouin has a profound effect in optical fiber communications, initially discovered by its limit on the transmitted power. By controlling SBS in fibers and making use of its phase conjugation properties in both fibers and bulk media, a wide range of applications have been enabled. Today ring Brillouin lasers in fibers, whispering gallery modes and in photonic integrated circuits provide optical delay lines and switches, pulse shapers and components for increasingly complex and important optical systems. [ABSTRACT FROM AUTHOR]

Artificial gauge fields for neutral particles such as photons, recently attracted a lot of attention in various fields ranging from photonic crystals to ultracold atoms in optical lattices to optomechanical arrays. Here we point out that, among all implementations of gauge fields, the optomechanical setting allows for the most natural extension where the gauge field becomes dynamical. The mechanical oscillation phases determine the effective artificial magnetic field for the photons, and once these phases are allowed to evolve, they respond to the flow of photons in the structure. We discuss a simple three-site model where we identify four different regimes of the gauge-field dynamics. Furthermore, we extend the discussion to a two-dimensional lattice. Our proposed scheme could for instance be implemented using optomechanical crystals. [ABSTRACT FROM AUTHOR]

We consider superfluidity and quantum vorticity in rotating spacetimes. The system is described by a complex scalar satisfying a nonlinear Klein–Gordon equation. Rotation terms are identified and found to lead to the transfer of angular momentum of the spacetime to the scalar field. The scalar field responds by rotating, physically behaving as a superfluid, through the creation of quantized vortices. We demonstrate vortex nucleation through numerical simulation. [ABSTRACT FROM AUTHOR]

Despite the vast progress and achievements in systems biology and integrative physiology in the last decades, there is still a significant gap in understanding the mechanisms through which (i) genomic, proteomic and metabolic factors and signaling pathways impact vertical processes across cells, tissues and organs leading to the expression of different disease phenotypes and influence the functional and clinical associations between diseases, and (ii) how diverse physiological systems and organs coordinate their functions over a broad range of space and time scales and horizontally integrate to generate distinct physiologic states at the organism level. Two emerging fields, network medicine and network physiology, aim to address these fundamental questions. Novel concepts and approaches derived from recent advances in network theory, coupled dynamical systems, statistical and computational physics show promise to provide new insights into the complexity of physiological structure and function in health and disease, bridging the genetic and sub-cellular level with inter-cellular interactions and communications among integrated organ systems and sub-systems. These advances form first building blocks in the methodological formalism and theoretical framework necessary to address fundamental problems and challenges in physiology and medicine. This ‘focus on’ issue contains 26 articles representing state-of-the-art contributions covering diverse systems from the sub-cellular to the organism level where physicists have key role in laying the foundations of these new fields. [ABSTRACT FROM AUTHOR]

We present two novel matter-wave Sagnac interferometers based on ring-shaped time-averaged adiabatic potentials, where the atoms are put into a superposition of two different spin states and manipulated independently using elliptically polarized rf-fields. In the first interferometer the atoms are accelerated by spin-state-dependent forces and then travel around the ring in a matter-wave guide. In the second one the atoms are fully trapped during the entire interferometric sequence and are moved around the ring in two spin-state-dependent ‘buckets’. Corrections to the ideal Sagnac phase are investigated for both cases. We experimentally demonstrate the key atom-optical elements of the interferometer such as the independent manipulation of two different spin states in the ring-shaped potentials under identical experimental conditions. [ABSTRACT FROM AUTHOR]

Spiral waves in cardiac tissue can pin to tissue heterogeneities and form stable pinned waves. These waves can be unpinned by electric stimuli applied close to the pinning center during the vulnerable window of the spiral. Using a phase transition curve (PTC), we quantify the response of a pinned wave in a cardiac monolayer to secondary excitations generated electric field pulses. The PTC can be used to construct a one-dimensional map that faithfully predicts the pinned wave’s response to periodic field stimuli. Based on this 1D map, we predict that pacing at a frequency greater than the spiral frequency, over drive pacing, leads to phase locking of the spiral to the stimulus, which hinders unpinning. In contrast, under drive pacing can lead to scanning of the phase window of the spiral, which facilitates unpinning. The predicted mechanisms of phase scanning and phase locking are experimentally tested and confirmed in the same monolayers that were used to obtain the PTC. Our results have the potential to help choose optimal parameters for low energy antifibrillation pacing schemes. [ABSTRACT FROM AUTHOR]

We demonstrate the feasibility of generation of quasi-stable counter-propagating solitonic structures in an atomic Bose–Einstein condensate confined in a realistic toroidal geometry, and identify optimal parameter regimes for their experimental observation. Using density engineering we numerically identify distinct regimes of motion of the emerging macroscopic excitations, including both solitonic motion along the azimuthal ring direction, such that structures remain visible after multiple collisions even in the presence of thermal fluctuations, and snaking instabilities leading to the decay of the excitations into vortical structures. Our analysis, which considers both mean field effects and fluctuations, is based on the ring trap geometry of Murray et al (2013 Phys. Rev. A 88 053615). [ABSTRACT FROM AUTHOR]

We study how quantum and thermal noise affects synchronization of two optomechanical limit-cycle oscillators. Classically, in the absence of noise, optomechanical systems tend to synchronize either in-phase or anti-phase. Taking into account the fundamental quantum noise, we find a regime where fluctuations drive transitions between these classical synchronization states. We investigate how this ‘mixed’ synchronization regime emerges from the noiseless system by studying the classical-to-quantum crossover and we show how the time scales of the transitions vary with the effective noise strength. In addition, we compare the effects of thermal noise to the effects of quantum noise. [ABSTRACT FROM AUTHOR]

A sustainable and reliable energy supply constitutes a fundamental prerequisite for the future of our society. The change to renewable sources comes with several systemic changes and includes, among others, smaller and more distributed producers as well as stronger and less predictable fluctuations. Parallel developments such as the transition from conventional producers and consumers to prosumers and the increasing number of electric vehicles add further complications. These changes require to extend and upgrade currently existing power grids. Yet precisely how to achieve an effective, robustly operating (electric) energy system is far from being understood. This focus issue aims to contribute to a number of these upcoming challenges from the perspective of self-organization and the collective nonlinear dynamics of power grids, interacting economic factors as well as technical restrictions and opportunities for distributed systems. [ABSTRACT FROM AUTHOR]

Activity pattern modalities of neuronal ensembles are determined by node properties as well as network structure. For many purposes, it is of interest to be able to relate activity patterns to either node properties or to network properties (or to a combination of both). When in physiological neural networks we observe bursting on a coarse-grained time and space scale, a proper decision on whether bursts are the consequence of individual neurons with an inherent bursting property or whether we are dealing with a genuine network effect has generally not been possible because of the noise in these systems. Here, by linking different orders of time and space scales, we provide a simple coarse-grained criterion for deciding this question. [ABSTRACT FROM AUTHOR]

We analyze the coherent dynamics of a fluxonium device (Manucharyan et al 2009 Science 326 113) formed by a superconducting ring of Josephson junctions in which strong quantum phase fluctuations are localized exclusively on a single weak element. In such a system, quantum phase tunnelling by occurring at the weak element couples the states of the ring with supercurrents circulating in opposite directions, while the rest of the ring provides an intrinsic electromagnetic environment of the qubit. Taking into account the capacitive coupling between nearest neighbors and the capacitance to the ground, we show that the homogeneous part of the ring can sustain electrodynamic modes which couple to the two levels of the flux qubit. In particular, when the number of Josephson junctions is increased, several low-energy modes can have frequencies lower than the qubit frequency. This gives rise to a quasiperiodic dynamics, which manifests itself as a decay of oscillations between the two counterpropagating current states at short times, followed by oscillation-like revivals at later times. We analyze how the system approaches such a dynamics as the ring’s length is increased and discuss possible experimental implications of this non-adiabatic regime. [ABSTRACT FROM AUTHOR]

We consider a correlated Bose gas tightly confined into a ring shaped lattice, in the presence of an artificial gauge potential inducing a persistent current through it. A weak link painted on the ring acts as a source of coherent back-scattering for the propagating gas, interfering with the forward scattered current. This system defines an atomic counterpart of the rf-SQUID: the atomtronics quantum interference device. The goal of the present study is to corroborate the emergence of an effective two-level system in such a setup and to assess its quality, in terms of its inner resolution and its separation from the rest of the many-body spectrum, across the different physical regimes. In order to achieve this aim, we examine the dependence of the qubit energy gap on the bosonic density, the interaction strength, and the barrier depth, and we show how the superposition between current states appears in the momentum distribution (time-of-flight) images. A mesoscopic ring lattice with intermediate-to-strong interactions and weak barrier depth is found to be a favorable candidate for setting up, manipulating and probing a qubit in the next generation of atomic experiments. [ABSTRACT FROM AUTHOR]

Networks of interacting oscillators abound in nature, and one of the prevailing challenges in science is how to characterize and reconstruct them from measured data. We present a method of reconstruction based on dynamical Bayesian inference that is capable of detecting the effective phase connectivity within networks of time-evolving coupled phase oscillators subject to noise. It not only reconstructs pairwise, but also encompasses couplings of higher degree, including triplets and quadruplets of interacting oscillators. Thus inference of a multivariate network enables one to reconstruct the coupling functions that specify possible causal interactions, together with the functional mechanisms that underlie them. The characteristic features of the method are illustrated by the analysis of a numerically generated example: a network of noisy phase oscillators with time-dependent coupling parameters. To demonstrate its potential, the method is also applied to neuronal coupling functions from single- and multi-channel electroencephalograph recordings. The cross-frequency δ, α to α coupling function, and the θ, α, γ to γ triplet are computed, and their coupling strengths, forms of coupling function, and predominant coupling components, are analysed. The results demonstrate the applicability of the method to multivariate networks of oscillators, quite generally. [ABSTRACT FROM AUTHOR]