Search

The authors show that neural networks exhibiting noise-induced rhythms, also known as quasi-cycle oscillations, can synchronize through out-of-phase locking depending on the noise intensity and the size of the coupling delay

We show that the analog of the geometric phase for non-Hermitian coupled waveguides with $\mathcal{PT}$ symmetry and at least one periodically varying parameter can be purely imaginary, is hence no longer a true phase and instead a real multiplier, and will consequently result in the amplification of Floquet sidebands in the system. The sideband peaks seen in the spectrum of the system's eigenstates after evolution along the waveguides can be directly mapped to the spectrum of the derivative of the geometric function. The sidebands are magnified (becoming virtually unstable) as the exceptional point of the system is approached, and nonadiabatic effects begin to appear. Because the system cannot evolve adiabatically in the vicinity of the exceptional point, $\mathcal{PT}$ symmetry will be observed breaking earlier than theoretically predicted.

We study theoretically the non linear polarization dynamics of Vertical-Cavity Surface-Emitting Lasers in the presence of an external cavity providing delayed optical feedback and cross polarization re-injection. We show that far from the laser threshold, the dynamics remains confined close to the equatorial plane of a Stokes sphere of a given radius and we reduce the dynamics to a dynamical system composed of two phases: the orientation phase of the quasi-linear polarization and the optical phase of the field. We explore the complex modal structure given by the double feedback configuration and recovers as particular cases the Lang-Kobayashi modes and the modes founds by Giudici et al. [1]. We also re-interpret the square waves switching dynamics as phase kinks.

We study the nonlinear phase equation for propagating patterns. We investigate the transition from a propagating localized pattern to a space-filling spatiotemporally disordered pattern and discuss in detail to what extent there are propagating localized states that breathe in time periodically, quasiperiodically, and chaotically. Differences and similarities to the phenomena occurring for the quintic complex Ginzburg-Landau equation are elucidated. We also discuss for which experimentally accessible systems one could observe the phenomena described.

Even though synchronization in autonomous systems has been observed for over three centuries, reports of systematic experimental studies on synchronized oscillators are limited. Here, we report on observations of internal synchronization in coupled silicon micromechanical oscillators associated with a reduction in the relative phase random walk that is modulated by the magnitude of the reactive coupling force between the oscillators. Additionally, for the first time, a significant improvement in the frequency stability of synchronized micromechanical oscillators is reported. The concept presented here is scalable and could be suitably engineered to establish the basis for a new class of highly precise miniaturized clocks and frequency references.

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

We propose a natural two-speed model for the phase dynamics of Si(111) 7x7 phase transition to high-temperature unreconstructed phase. We formulate the phase dynamics by using phase-field method and adaptive mesh refinement. Our simulated results show that a 7x7 island decays with its shape kept unchanged, and its area decay rate is shown to be a constant increasing with its initial area. Low-energy electron microscopy experiments concerned are explained, which confirms that the dimer chains and corner holes are broken first in the transition, and then the stacking fault is remedied slowly. This phase-field method is a reliable approach to phase dynamics of surface phase transitions.

In a directional viscous fingering experiment, a phase diffusion behavior of the regular array of cells is demonstrated. At constant wave number, the evolution of the phase diffusion coefficient D with the parameter of the instability \ensuremath{\epsilon} is reported. This coefficient D is found to decrease at low \ensuremath{\epsilon} values in agreement with the presence of an Eckhaus instability, but to increase strongly at large \ensuremath{\epsilon} values. This unusual increase of D is also present in the analytical and numerical study of two coupled amplitude equations for the modes k and 2k. The phase diffusion coefficient is found to diverge at the threshold of the parity-breaking bifurcation.

Based on the complex Ginzburg-Landau equation (CGLE), a new mapping model of oscillatory media is proposed. The present dynamics is fully determined by an effective phase field renormalized by amplitude. The model exhibits phase turbulence, amplitude turbulence, and a frozen state reported in the CGLE. In addition, we find a state in which the phase and amplitude have spiral structures with opposite rotational directions. This state is found to be observed also in the CGLE. Thus, one concludes that the behaviors observed in the CGLE can be described by only the phase dynamics appropriately constructed.

The relative phase between two uncoupled Bose-Einstein condensates tends to attain a specific value when the phase is measured. This can be done by observing their decay products in interference. We discuss exactly solvable models for this process in cases where competing observation channels drive the phases to different sets of values. We treat the case of two modes which both emit into the input ports of two beam splitters and of a linear or circular chain of modes. In these latter cases, the transitivity of the relative phase becomes an issue.

Temporal cavity solitons (CSs) enable the generation of coherent Kerr frequency combs with a broad bandwidth. Here we derive analytically and numerically the relationship between the carrier-envelope-phase (CEP) slip of CSs and the pump phase detuning. To preserve the stability of CSs, CEP slips always equal the pump phase detuning. Since the CEP slip for solitons has a contribution from the Kerr effect, the locking between the CEP slip and pump phase detuning results in a universal constraint on the peak power for CSs. The CEP dynamics is also found to affect the stability of CSs. When the CEP slip fails to follow the pump phase detuning, CSs become unstable, exhibiting periodic or chaotic breathing. Our results can be important for the self-referencing of Kerr frequency combs.

We derive a new nonlinear criterion for the occurrence of fast relaxation (crash) events at the edge of high-confinement-mode plasmas. These fast relaxation events called ELMs (edge-localized modes) evolve from ideal magnetohydrodynamics (MHD) instabilities, but the crash is not due only to linear physics. We show that for an ELM crash to occur, the coherence time of the relative phase between potential and pressure perturbations must be long enough to allow growth to large amplitude. This phase coherence time is determined by both linear and nonlinear dynamics. An ELM crash requires that the instability growth rate exceed a critical value, i.e., γ>γc, where γc is set by 1/τc and τc is the phase coherence time. For 0

We study the phase and amplitude distribution of superfluid (SF) order parameters for spin-orbit-coupled two species bosons in a two-dimensional finite-size square lattice using inhomogeneous mean-field analysis. We demonstrate how phase distribution of the SF order parameter evolves as we tune the spin-orbit coupling $\ensuremath{\gamma}$ and $t$, the spin-independent hopping in the strong-coupling limit. For $t\ensuremath{\gg}\ensuremath{\gamma}$, we find the homogeneous superfluid phase where the phase of the SF order parameter is uniform. As we increase $\ensuremath{\gamma}$, spatial inhomogeneity in the phases of the SF order parameter grows leading to a twisted superfluid phase. For $t\ensuremath{\sim}\ensuremath{\gamma}$, competing orderings in the phase distribution are observed. At large $\ensuremath{\gamma}$ limit, a ferromagnetic stripe ordering appears along the diagonal. We explain that this is due to the frustration bought in by the spin-orbit interaction. Isolated vortex formation is also shown to appear. The effect of the detuning field $\ensuremath{\delta}$ on the distribution of phases and amplitudes of the order parameter has also been studied. We also investigate the possible collective modes for this finite-size system. In a deep superfluid regime we derive the Euler-Lagrange equation of motion for the phases and the dynamics of lowest normal modes are discussed.

We have studied the electrical transport properties of superconducting clusters, periodic arrays of Josephson-coupled superconducting islands containing only a few cells. In such small samples, variations in the coupling between adjacent islands are not averaged out and produce asymmetries in the magnetoresistance as a function of bias current and applied magnetic field. By comparing experimental results with computer simulations of the Josephson phase dynamics in the clusters, we are able to understand the origin of the observed asymmetries and obtain a quantitative estimate of the coupling disorder in our arrays.

We study the phase dynamics of a single-mode ring laser described by the complex Maxwell-Bloch equations. We identify three reference-frame frequencies and determine the properties of the field dynamics observed in these frames. In one of these reference frames, the phase jumps are always equal to π, irrespective of the detuning, while in another reference frame quasiperiodic field portraits reduce to periodic field portraits. We also apply the recent theory of Ning and Haken [Phys. Rev. Lett. 68, 2109 (1992)] to prove that the laser phase can be decomposed into a geometrical component that is frame invariant and a dynamical component that is frame dependent

We investigate the temporal evolution of the instantaneous frequency of ultrashort-pulse four-wave mixing in GaAs/Ga[sub [ital x]]Al[sub 1[minus][ital x]]As quantum-well structures. We find that the coherent light emitted by excitons exhibits a complex phase behavior which depends critically on the density of excitons and the central frequency of the exciting pulses. Depending on the excitation conditions, we observe nonlinear shifts of the instantaneous frequency within one ultrashort pulsed emission or quantum beats. In the latter case we determine that the beat [pi]-phase shift is very fast, only 40% above the fundamental quantum limit. We also present elaborate numerical simulations of the experiments based on a six-band generalization of the semiconductor Bloch equations. This formalism takes into account Coulomb many-body interactions and Pauli exclusion. It reproduces the salient features of the experimental data. It fails to account for important details revealed by the very sensitive phase measurements. The discrepancies can be traced back to two approximations in the theory: the statical treatment of screening, and the Lorentzian description of dephasing. In both cases, this indicates the need for theoretical refinements requiring a microscopic description of Coulomb scattering and dephasing processes in a non-Markovian theory.

Theoretical treatment is given to the possibility of the existence of propagating confined states in the nonlinear phase equation by generalizing stationary confined states. The nonlinear phase equation is set forth for the case of propagating patterns with long wavelengths and low-frequency modulation. A large range of parameter values is shown to exist for propagating confined states which have spatially localized regions which travel on a background with unique wavelengths. The theoretical phenomena are shown to correspond to such physical systems as spirals in Taylor instabilities, traveling waves in convective systems, and slot-convection phenomena for binary fluid mixtures.

The phase dynamics of a semiconductor laser with optical feedback is studied by construction of the Hilbert phase from its experimentally measured intensity time series. The Hurst exponent is evaluated for the phase fluctuations and grows from 0.5 to approximately 0.7 (indicating fractional Brownian motion) as the feedback strength is increased. A comparison with numerical computations based on a delay-differential equation model shows excellent agreement and reveals the relative roles of spontaneous emission noise and deterministic dynamics for different feedback strengths.

Confined states in phase dynamics\char21{}the coexistence of states with different wavelengths\char21{}are further studied. In particular, a stable and accurate numerical code is developed to study the dynamic equation of motion for two sets of boundary conditions\char21{}a pinned phase and an unpinned phase. With a pinned phase, stable confined states are found to exist for a wide range of parameter values. With an unpinned phase, the localized states are at best neutrally stable. Also, analytic solutions are found for the stationary confined states.

The basic features characterizing the dynamical evolution of the phase of a detuned-laser field under an unstable regime are physically interpreted in terms of dispersive and dynamical effects. A general method for obtaining any attractor projection containing the phase information is established, which provides evidence for the heteroclinic character of the attractor in the presence of cavity detuning for any emission regime.

We make a geometric study of the phases acquired by a general, pure bipartite two-level system after a cyclic unitary evolution. The geometric representation of the two particle Hilbert space makes use of Hopf fibrations. It allows for a simple description of the dynamics of the entangled state's phase during the whole evolution. The global phase after a cyclic evolution is always an entire multiple of {pi} for all bipartite states, a result that does not depend on the degree of entanglement. There are three different types of phases combining themselves so as to result in the n{pi} global phase. They can be identified as dynamical, geometrical, and topological. Each one of them can be easily identified using the presented geometric description. The interplay between them depends on the initial state and on its trajectory, and the results obtained are shown to be in connection to those on mixed state phases.

The phenomenon of phase multistability in the synchronization of two coupled oscillatory systems typically arises when the systems individually display complex wave forms associated, for instance, with the presence of subharmonic components. Alternatively, phase multistability can be caused by variations of the phase velocity along the orbit of the individual oscillator. Focusing on the mechanisms underlying the appearance of phase multistability, the paper examines a variety of phase-locked patterns in the bursting behavior of a model of coupled pancreatic cells. In particular, we show how the number of spikes per train and the proximity of a neighboring equilibrium point can influence the formation of coexisting regimes.

We study a simple model of a massive inflaton field $\phi$ coupled to another scalar filed $\chi$ with interaction term $g^2\phi^2\chi^2$. We use the theory developed by Kofman {\em et al.} (Phys. Rev. D {\bf 56} (1997) 3258 [arXiv:hep-ph/9704452])for the first stage of preheating to give a full description of the dynamics of the $\chi$ field modes, including the behaviour of the phase, in terms of the iteration of a simple family of circle maps. The parameters of this family of maps are a function of time when expansion of the universe is taken into account. With this more detailed description, we obtain a systematic study of the efficiency of particle production as a function of the inflaton field and coupling parameters, and we find that for $g \lesssim 3 \times 10^{-4}$ the broad resonance ceases during the first stage of preheating., Comment: 14 pages, 12 figures, accepted for publication in Phys. Rev. D. Correct Figure 9, results unchanged. Added references and corrected misprints/misspellings

We show that the classical dynamics underlying the mean-field description of homogeneous mixtures of spinor $F=1$ Bose-Einstein condensates in an external magnetic field is integrable as a consequence of number conservation and axial symmetry in spin space. The population dynamics depends only on the quadratic term of the Zeeman energy and on the strength of the spin-dependent term of the atom-atom interaction. We determine the equilibrium populations as function of the ratio of these two quantities and the miscibility of the hyperfine components in the ground state spinors are thoroughly discussed. Outside the equilibrium, the populations are always a periodic function of time where the periodic motion can be a libration or a rotation. Our studies also indicate the absence of metastability.

Deterministic diffusions of superconducting phases in extremely underdamped SQUID's are studied. It is found that, by controlling the total energy, two types of diffusion, i.e., anomalous and normal ones, appear. In the anomalous diffusion, the orbit in the phase space is trapped mainly into the jump-related hierarchy structure so that the mean-square displacement behaves as t γ with 1< y

We study the dynamics of a multimode laser diode with delayed optical feedback operating in the low-frequency fluctuations regime. We show that a multimode extension of the Lang-Kobayashi equations that takes into account spontaneous emission noise predicts two qualitatively different behaviors of the laser on the picosecond time scale. Individual modes of the laser can emit pulses in-phase or oscillate out-of-phase, depending on the operating parameters. The corresponding statistical distributions are in good agreement with two recent experiments.

We discuss the long-wavelength, low-frequency excitations of non- equilibrium systems with a helical structure as observed in spiral vortex flow in the Taylor instability in long cylinders. We find that a single-phase equation can give rise to a propagating mode, a situation unknown from hydrodynamics in local thermodynamic equilibrium.

The growth of statistical domains in quenched Ising-like p-state clock models with p = 3 or more is investigated theoretically, reformulating the analysis of Ohta et al. (1982) in terms of a phase variable and studying the dynamics of defects introduced into the phase field when the phase variable becomes multivalued. The resulting defect/phase domain-growth equation is applied to the interpretation of Monte Carlo simulations in two dimensions (Kaski and Gunton, 1983; Grest and Srolovitz, 1984), and problems encountered in the analysis of related Potts models are discussed. In the two-dimensional case, the problem is essentially that of a purely dissipative Coulomb gas, with a sq rt t growth law complicated by vertex-pinning effects at small t.

Recently two groups1–3 have described the observation of confined states in an annulus near the onset of convection in binary fluid mixtures. These confined states are characterized by the fact that for part of the annulus a convective pattern is visible — that is the envelope of the convective pattern assumes a finite value — whereas the rest of the container is in the heat conduction state. These observations are now under intense investigation theoretically4–6 and experimentally2,3.

We carry out a thorough analysis on a class of cosmological spacetimes which admit three space-like Killing vectors of Bianchi class B and contain electromagnetic fields. Using dynamical system analysis, we show that a family of vacuum plane-wave solutions of the Einstein-Maxwell equations is the stable attractor for expanding universes. Phase dynamics are investigated in detail for particular symmetric models. We integrate the system exactly for some special cases to confirm the qualitative features. Some of the obtained solutions have not been presented previously to the best of our knowledge. Finally, based on those solutions, we discuss the relation between those homogeneous models and perturbations of open FLRW universes. We argue that the vacuum plane-wave modes correspond to a certain long-wavelength limit of electromagnetic perturbations., Revised for publication. 25 pages

We analyze the phase properties of a strong cavity field interacting with an ensemble of initially excited N two-level atoms. Using the Pegg-Barnett phase formalism [Phys. Rev. A 39, 1665 (1989)], we calculate the phase probability distribution as well as the phase variance. The phase probability density exhibits a (N+1)-peak structure at the initial stages of the evolution. The phase variance is used to illustrate the progressive randomization of the phase on the long-time evolution. The difference in the phase dynamics for the N even and the N odd case is pointed out.

The phase difference in coupled chaotic oscillators exhibits a small noiselike fast fluctuation in long-term phase dynamics. The fast fluctuation can cause an error in the measurement of the period of the temporary phase locking state. We discuss why we should filter out the fast fluctuation on determination of periodic phase synchronization.

We measure the velocities of the mean flows that are driven by curved rolls in a pattern formation system. Curved rolls in Faraday waves are generated in experimental cells consisting of channels with varying widths. The mean flow magnitudes are found to scale linearly with roll curvatures and squares of wave amplitudes, agreeing with the prediction from the analysis of phase dynamics expansion. The effects of the mean flows on reducing roll curvatures are also seen.

We study the correlated evolutions of two Rydberg atoms, interacting via a van der Waals (vdW) potential ${V}_{6}$ and driven by a laser field of detunings ${\mathrm{\ensuremath{\Delta}}}_{1}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}$. The two atoms may exhibit the in-phase dynamics with identical Rydberg populations or the antiphase dynamics with complementary Rydberg populations, depending on their initial states. For a moderate vdW potential far from the blockade regime, the in-phase or antiphase dynamics can be attained along two intersecting lines in the parameter space of ${\mathrm{\ensuremath{\Delta}}}_{1}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}$ with an exact or approximate figure of merit, respectively. Note, in particular, that the exact in-phase dynamics is trivial because it requires identical detunings while the approximate in-phase, exact antiphase, and approximate antiphase dynamics are nontrivial because they require distinct detunings. The specific requirements on ${\mathrm{\ensuremath{\Delta}}}_{1}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}$ for both in-phase and antiphase dynamics can be understood by considering the balanced transitions from two initially populated states to two initially empty states in the double-atom state basis.

We derive a unified amplitude-phase decomposition for both noisy limit cycles and quasicycles; in the latter case, the oscillatory motion has no deterministic counterpart. We extend a previous amplitude-phase decomposition approach using the stochastic averaging method (SAM) for quasicycles by taking into account nonlinear terms up to order 3. We further take into account the case of coupled networks where each isolated network can be in a quasi- or noisy limit-cycle regime. The method is illustrated on two models which exhibit a deterministic supercritical Hopf bifurcation: the Stochastic Wilson-Cowan model of neural rhythms, and the Stochastic Stuart-Landau model in physics. At the level of a single oscillatory module, the amplitude process of each of these models decouples from the phase process to the lowest order, allowing a Fokker-Planck estimate of the amplitude probability density. The peak of this density captures well the transition between the two regimes. The model describes accurately the effect of Gaussian white noise as well as of correlated noise. Bursting epochs in the limit-cycle regime are in fact favored by noise with shorter correlation time or stronger intensity. Quasicycle and noisy limit-cycle dynamics are associated with, respectively, Rayleigh-type and Gaussian-like amplitude densities. This provides an additional tool to distinguish quasicycle from limit-cycle origins of bursty rhythms. The case of multiple oscillatory modules with excitatory all-to-all delayed coupling results in a system of stochastic coupled amplitude-phase equations that keeps all the biophysical parameters of the initial networks and again works across the Hopf bifurcation. The theory is illustrated for small heterogeneous networks of oscillatory modules. Numerical simulations of the amplitude-phase dynamics obtained through the SAM are in good agreement with those of the original oscillatory networks. In the deterministic and nearly identical oscillators limits, the stochastic Stuart-Landau model leads to the stochastic Kuramoto model of interacting phases. The approach can be tailored to networks with different frequency, topology, and stochastic inputs, thus providing a general and flexible framework to analyze noisy oscillations continuously across the underlying deterministic bifurcation.

We report the discovery of a codimension-two phenomenon in the phase diagram of a second-order self-sustained nonlinear oscillator subject to a constant external periodic forcing, around which three regimes associated with the synchronization phenomenon exist, namely phase-locking, frequency-locking without phase-locking, and frequency-unlocking states. The triple point of synchronization arises when a saddle-node homoclinic cycle collides with the zero-amplitude state of the forced oscillator. A line on the phase diagram where limit-cycle solutions contain a phase singularity departs from the triple point, giving rise to a codimension-one transition between the regimes of frequency unlocking and frequency locking without phase locking. At the parameter values where the critical transition occurs, the forced oscillator exhibits a separatrix with a $\ensuremath{\pi}$ phase jump, i.e., a particular trajectory in phase space that separates two distinct behaviors of the phase dynamics. Close to the triple point, noise induces excitable pulses where the two variants of type-I excitability, i.e., pulses with and without $2\ensuremath{\pi}$ phase slips, appear stochastically. The impacts of weak noise and some other dynamical aspects associated with the transition induced by the singular phenomenon are also discussed.

Networks of coupled oscillators show a wealth of fascinating dynamics and are capable of storing and processing information. In biological and social networks, the coupling is often asymmetric. We use the chirality of rotating spiral waves to introduce this asymmetry in an excitable reaction-diffusion model. The individual vortices are pinned to unexcitable disks and arranged at a constant spacing $L$ along straight lines or simple geometric patterns. In the case of periodic boundaries or pinning disks arranged along the edge of a closed shape, small $L$ values lead to synchronization via repeated wave collisions. The rate of synchronization as a function of $L$ shows a single maximum and is determined by the dispersion behavior of a continuous wave train traveling along the system boundary. For finite systems, spirals are affected by their upstream neighbor, and a single dominant spiral exists along each chain. Specific initial conditions can decouple neighboring vortices even for small $L$ values. We also present a time-delay differential equation that reproduces the phase dynamics in periodic systems.

We propose a two-phase reheating scenario where the initial preheating dynamics is described by an effective dynamics followed by the standard perturbative reheating. Some of the important universal results of lattice simulation during preheating have been considered as crucial inputs in our two-phase dynamics. In this framework, detailed phenomenological constraints have been obtained on the inflaton couplings with reheating fields, and dark matter parameters in terms of CMB constrained inflationary scalar spectral index. It is observed that the conventional reheating scenario generically predicts the maximum reheating temperature $T_{re}^{max} \simeq 10^{15}$ GeV, corresponding to an almost instantaneous transition from the end of inflation to radiation domination. This fact will naturally lead to the problem of non-perturbative inflaton decay, which is in direct conflict with the perturbative reheating itself. Taking into account this by incorporating effective non-perturbative dynamics as the initial phase, our model of two-phase reheating scenarios also predicts model-independent maximum reheating temperature, which does not correspond to the instantaneous process. Further, $T_{re}^{max}$ is predicted to lie within $(10^{13}, 10^{10})$ GeV if CMB constraints on inflaton couplings with different reheating field are taken into account. We have further studied in detail the dark matter phenomenology in a model-independent manner and show how dark matter parameter space can be constrained through CMB parameters via the inflaton spectral index. Considering dark matter production during reheating via the Freeze-in mechanism, its parameter space has been observed to be highly constrained by our two-phase reheating than the constraints predicted by the conventional reheating scenarios, which are believed to theoretically incomplete., 63 pages, 29 figures, An expanded version of this paper arxiv number: 1709.00251

We show that self-organization occurs in the phase dynamics of soliton modelocking in paramet- ric frequency combs. Reduction of the Lugiato-Lefever equation (LLE) to a simpler set of phase equations reveals that this self-organization arises via mechanisms akin to those in the Kuramoto model for synchronization of coupled oscillators. In addition, our simulations show that the phase equations evolve to a broadband phase-locked state, analogous to the soliton formation process in the LLE. Our simplified equations intuitively explain the origin of the pump phase offset in soliton- modelocked parametric frequency combs. They also predict that the phase of the intracavity field undergoes an anti-symmetrization that precedes phase synchronization, and they clarify the role of chaotic states in soliton formation in parametric combs.

We present a theoretical analysis of spatial correlations in a one-dimensional driven-dissipative non-equilibrium condensate. Starting from a stochastic generalized Gross-Pitaevskii equation, we derive a noisy Kuramoto-Sivashinsky equation for the phase dynamics. For sufficiently strong interactions, the coherence decays exponentially in close analogy to the equilibrium Bose gas. When interactions are small on a scale set by the nonequilibrium condition, we find through numerical simulations a crossover between a Gaussian and exponential decay with peculiar scaling of the coherence length on the fluid density and noise strength., Comment: 5 pages, 2 figures, supplemental material

Studies have been made on the phase transition phenomena of an oscillator network model based on a standard Hebb learning rule like the Hopfield model. The relative phase informations---the in-phase and anti-phase, can be embedded in the network. By self-consistent signal-to-noise analysis (SCSNA), it was found that the storage capacity is given by $\alpha_c = 0.042$, which is better than that of Cook's model. However, the retrieval quality is worse. In addition, an investigation was made into an acceleration effect caused by asymmetry of the phase dynamics. Finally, it was numerically shown that the storage capacity can be improved by modifying the shape of the coupling function., Comment: 10 pages, 6 figures

The phase dynamics of a one-dimensional cellular pattern is studied on a regular array of liquid columns formed below an overflowing horizontal cylinder. When a uniform wavelength dilation is imposed by static boundaries, an oscillatory secondary bifurcation is observed ~‘‘optical mode’’!. The case of a moving boundary ~sinusoidal motion! allows us to observe three dynamical states: phase diffusion, phase diffusion coupled with the oscillatory state, and propagation of dilation waves. The dependence of the phase diffusion coefficient D upon the pattern wavelength is investigated for different flow rates: D is nearly constant until the appearance of the oscillations and jumps to a larger value when the optical mode is excited. This unusual behavior is recovered by an analytical treatment of Coullet-Ioss equations. @S1063-651X~98!12002-0#

We report on the study of the phase dynamics of high-critical-temperature superconductor Josephson junctions. We realized YBa${}_{2}$Cu${}_{3}$O${}_{7\ensuremath{-}x}$ grain boundary biepitaxial junctions in the submicron scale using low-loss substrates and analyzed their dissipation by comparing the transport measurements with Monte Carlo simulations. The behavior of the junctions can be fitted using a model based on two quality factors, which results in a frequency-dependent damping. Moreover, our devices can be designed to have Josephson energy of the order of the Coulomb energy. In this unusual energy range, phase delocalization strongly influences the device's dynamics, promoting the transition to a quantum phase diffusion regime. We study the signatures of such a transition by combining the outcomes of Monte Carlo simulations with the analysis of the device's parameters, the critical current, and the temperature behavior of the low-voltage resistance ${R}_{0}$.

We numerically investigate a coupled map lattice model which is a generalization of the critical height sandpile automaton. In the case of periodic boundary conditions we find in dependence on a threshold parameter strong evidence for a second order phase transition between states of different spatial order. In the disordered phase the spatial structure is irregular with long range linearly decaying correlations. In the ordered phase dynamics is dominated by a few coexisting periodic attractors whose basins of attraction become infinitely small at the critical point. At this point transient lengths diverge and the transients are chaotic. With open boundary conditions the system exhibits self-organized criticality, i.e., adjusts itself to the vicinity of this critical point.

Measuring the phase dynamics of the beat note in the output of a HeNe Zeeman laser, we (i) unravel the interplay of phase locking and correlated spontaneous emission, (ii) observe the phase-diffusion noise reduced to $\frac{1}{14}$ of the Schawlow-Townes quantum level (the largest reduction of quantum noise reported so far), and (iii) show that balanced pumping of the two upper laser levels would achieve correlation of the laser phase noise with no locking at all. The resulting reduction in the phase noise of the beat note allows interferometric measurements of vastly enhanced sensitivity.

We perform a precise numerical study of phase dynamics in high-temperature superconductors under electromagnetic radiation. We observe the charging of superconducting layers in the bias current interval corresponding to the Shapiro step. A remarkable change in the longitudinal plasma wavelength at parametric resonance is shown. Double resonance of the Josephson oscillations with radiation and plasma frequencies leads to additional parametric resonances and the non-Bessel Shapiro step.

We consider a voltage-biased nanoelectromechanical Josephson junction, where a suspended nanowire forms a superconducting weak-link, in an inhomogeneous magnetic field. We show that a nonlinear coupling between the Josephson current and the magnetic field generates a Laplace force that induces a whirling motion of the nanowire. By performing an analytical and a numerical analysis, we demonstrate that at resonance, the amplitude-phase dynamics of the whirling movement present different regimes depending on the degree of inhomogeneity of the magnetic field: time independent, periodic and chaotic. Transitions between these regimes are also discussed., 7 pages, 5 figures

Recently, we demonstrated that the liquid-solid interface of the isotropic model of lamellar eutectic growth may undergo a parity-breaking transition from a symmetric to a tilted state. We found that the bifurcation to the asymmetric state is supercritical. Now we have solved the full boundary integral equation of the system assuming anisotropic surface tension. We observe that generically the supercritical bifurcation becomes imperfect, as could be expected from a simple phenomenological picture. In order to study whether finite domains of tilted states can exist under these circumstances, we consider a simple model for the coupling between tilt angle and phase dynamics that exhibits an imperfect bifurcation. We find that if the anisotropy is not too strong, the coupling leads to a picture that retains many of the qualitative features of the phenomenological approach given by Coullet, Goldstein, and Gunaratne [Phys. Rev. Lett. 63, 1954 (1989)] for subcritical bifurcations. Furthermore, we offer a natural explanation for the experimental finding that on creation of a tilted state lamellae of a given grain preferentially tilt in one direction, not in the opposite one.

We investigate classical thermal activation (TA) and macroscopic quantum tunneling (MQT) for a YBa2Cu3O7−δ (YBCO) Josephson junction coupled to an LC circuit theoretically. Due to the coupling between the junction and the LC circuit, the macroscopic phase dynamics can be described as the escape process of a fictitious particle with an anisotropic mass moving in a two-dimensional potential. We analytically calculate the escape rate including both the TA and MQT regime by taking into account the peculiar dynamical nature of the system. In addtion to large suppression of the MQT rate at zero temperature, we study details of the temperature dependence of the escape rate across a crossover region. These results are in an excellent agreement with recent experimental data for the MQT and TA rate in a YBCO biepitaxial Josephson junction. Therefore the coupling to the LC circuit is essential in understanding the macroscopic quantum dynamics and the qubit operation based on the YBCO biepitaxial Josephson junctions.