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Giant fractional Shapiro steps have been observed in Josephson junction arrays as resulting from magnetic flux quantization in the two-dimensional array. We demonstrate experimentally the appearance of giant fractional Shapiro steps in anisotropic Josephson junction arrays as unambiguous evidence of a skewed current phase relationship. Introducing anisotropy in the array results in a giant collective high frequency response that reflects the properties of a single junction, as evidenced by the observation of a Fraunhofer like magnetic field dependence of the total critical current of the system. The observed phase dynamics can be perfectly captured within an extended resistively shunted Josephson junction model. These results directly indicate the potential of Josephson junction arrays to explore the current phase relation in a very broad frequency range (down to 50 MHz) and in a wide variety of novel link materials exhibiting non-conventional current phase relationships. Giant fractional Shapiro steps have been observed in Josephson junction arrays as resulting from magnetic flux quantization in the two-dimensional array. Here, the authors demonstrate the observation of giant fractional Shapiro steps in an anisotropic Josephson junction array, as unambiguous evidence of a skewed current phase relationship.

Although Mn-Ga alloys are discussed as novel permanent magnetic materials, there are several drawbacks, including the high price of Ga and the yet too small saturation magnetization to name a few. We used several guidelines to motivate the replacement of Ga by Sn to tackle these issues and explored the phase formation, structural and magnetic properties of a Mn 2.6 Ga 1− x Sn x alloy series. The structure of Sn-rich samples is dominated by the corresponding hexagonal and orthorhombic phases, while the structure of Ga-rich samples shows additional contributions from the tetragonal DO 22 structure. However, formation of the tetragonal phase happens only upon an appropriate annealing procedure. In contrast to the discussion in the literature, our experiments do not hint on the tetragonal DO 22 structure being metastable, but rather indicate the DO 22 structure being an equilibrium phase. In general, the experimentally found phase fractions impact on the magnetic properties and hard magnetic properties are downgraded very rapidly even if only a small amount of Ga is substituted by Sn. This indicates that the DO 22 phase found only in the Ga-rich samples is indeed the one which is most relevant for realization of high magnetic anisotropy.

The problem of interval estimation of the time delay of the coupling between oscillatory systems from observed time series is considered. It is shown that the known asymptotic estimates based on the empirical model in the form of a system of first-order phase oscillators and the maximum likelihood formalism can lead to false inferences of the value of the time delay in two typical situations: 1) nonlinear low-dimensional systems whose phases are well-determined but, as a result of significant amplitude fluctuations, the phase approximation is insufficient for describing the dynamics and 2) systems whose phases are defined not quite well because of too large amplitude fluctuations. A method for empirical diagnostics of problematic situations and its modification (coarse estimation) providing a low probability of false inferences in these situation are proposed. The efficiency of the diagnostic criterion and coarse estimation suggested is demonstrated on reference systems with different dynamic properties (linear stochastic oscillators, van der Pol oscillators, and Ressler and Lorenz chaotic systems).

Josephson junctions with weak-links of exotic materials allow the elucidation of the Josephson effect in previously unexplored regimes. Further, such devices offer a direct probe of novel material properties, for example in the search for Majorana fermions. In this work, we report on DC and AC Josephson effect of high-mobility, hexagonal boron nitride (h-BN) encapsulated graphene Josephson junctions. On the application of RF radiation, we measure phase-locked Shapiro steps. An unexpected bistability between $\pm 1$ steps is observed with switching times on the order of seconds. A critical scaling of a bistable state is measured directly from the switching time, allowing for direct comparison to numerical simulations. We show such intermittent chaotic behavior is a consequence of the nonlinear dynamics of the junction and has a sensitive dependence on the current-phase relation. This work draws connections between nonlinear phenomena in dynamical systems and their implications for ongoing condensed matter experiments exploring topology and exotic physics.

We investigate nonlinear phase dynamics of an ideal kink mode, induced by E × B flow. Here the phase is the cross phase (θ c) between perturbed stream function of velocity ( ϕ ˜ ) and magnetic field ( ψ ˜ ), i.e. θ c = θ ϕ − θ ψ . A dimensionless parameter, analogous to the Richardson number, R i = 16 γ kink 2 / ω ˆ E 2 (γ kink: the normalized growth rate of the pure kink mode; ω ˆ E : normalized E × B shearing rate) is defined to measure the competition between phase pinning by the current density and phase detuning by the flow shear. When R i > 1, θ c is locked to a fixed value, corresponding to the conventional eigenmode solution. When R i ≤ 1, θ c enters a phase slipping or oscillating state, corresponding to a nonmodal solution. The nonlinear phase dynamics method provides a more intuitive explanation of the complex dynamical behavior of the kink mode in the presence of E × B shear flow.

The phase dynamics of a SQUID consisting of Josephson junctions with topologically nontrivial barriers has been studied. Its comparative analysis with the dynamics of a conventional SQUID has been performed. The current–voltage characteristics have been calculated. The dependence of the return current on the magnetic field has been found. It has been shown that the branch of the current–voltage characteristic corresponding to the resonance frequency in the case of the SQUID with nontrivial barriers is displaced by \(\sqrt 2 \) over voltage. This effect can be used for the detection of Majorana fermions.

In this work, a Lattice-Boltzmann-Method (LBM) model for simulating hysteresis in a proton exchange membrane (PEMFC) electrode is presented. One of the main challenges hindering study of the cathode catalyst layer (CCL) in PEMFCs is the lack of understanding of two-phase transport and how it affects electrochemical performance. Researchers have typically used high level approximations that oversimplify the microstructure of the CCL—these are known as macrohomogenous models. However, as the field has progressed, the flaws in these idealizations are being revealed, especially in areas of improving our understanding of flooding as well as catalyst layer hysteresis. Previously, the microstructure details needed to build an accurate mesoscale model have eluded researchers; however, with advances in tomography and focused-ion-beam scanning-electron-microscopy (FIB-SEM), creating these representations has become possible. Using LBM with these representations, the difficult problem of catalyst layer capillary hysteresis can be examined. In two-phase capillary hysteresis, both the equilibrium saturation position as well as absolute value depends on the wetting history. Based on the models, it is ascertained that at lower capillary numbers, the liquid begins to undergo capillary fingering – only above a capillary pressure of 5 MPa, a regime change into stable displacement is observed. As capillary fingering does not lead to uniform removal of liquid, the prediction is that because high capillary pressures are needed to change to the regime of stable displacement, wicking will not be an effective means of water removal. Figure 1

Phase identification is an arduous task during high-throughput processing experiments, which can be exacerbated by the need to reconcile results from multiple measurement techniques to form a holistic understanding of phase dynamics. Here, we demonstrate AutoPhase, a machine learning algorithm, which can identify the presence of the different phases in spectral and diffraction data. The algorithm uses training data to determine the characteristic features of each phase present and then uses these features to evaluate new spectral and diffraction data. AutoPhase was used to identify oxide phase growth during a high-throughput oxidation study of NiAl bond coats that used x-ray diffraction, Raman, and fluorescence spectroscopic techniques. The algorithm had a minimum overall accuracy of 88.9% for unprocessed data and 98.4% for postprocessed data. Although the features selected by AutoPhase for phase attribution were distinct from those of topical experts, these results show that AutoPhase can substantially increase the throughput high-throughput data analysis.

The phase dynamics of two parallel connected stacks of intrinsic Josephson junctions (JJs) in high temperature superconductors is numerically investigated. The calculations are based on the system of nonlinear differential equations obtained within the CCJJ + DC model, which allows one to determine the general current-voltage characteristic of the system, as well as each individual stack. The processes with increasing and decreasing base currents are studied. The features in the behavior of the current in each stack of the system due to the switching between the states with rotating and oscillating phases are analyzed.

A two-dimensional D-shaped cylinder and heaving foil were mounted in tandem and used to simulate the main body and tail, respectively, of a natural swimmer. Thrust/drag measurements of the force on the foil and particle image velocimetry measurements of the flow downstream of the swimming system were conducted at a Reynolds number of about $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}10^4$ in a water channel with a constant free stream current speed. Two main sets of measurements were conducted: one set with the swimming system locked at a fixed streamwise location in the water channel as the heave frequency of the foil was varied; the other set with the system freely swimming to a desired set-point position from different upstream and downstream locations. When the freely swimming system reached and maintained its set-point position, so that its swimming speed matched that of the current, the oscillation frequency of the heaving foil corresponded to a Strouhal number of 0.36. Phase portraits of the measured thrust/drag forces reveal limit cycle oscillations for all swimming cases studied, which suggests that self-regulation drives the selection of this Strouhal number. No coupling was observed between the vortices shed by the D-shaped cylinder and the self-selected frequency of the heaving foil during free swimming. An examination of the ratio of the phase-locking indices for the input heaving motion of the foil and the coupled fluidic thrust/drag response reveals that it approaches a value of 0.5 over time when the freely swimming system is released from rest and allowed to achieve steady-state cruising. The jet produced by the freely swimming foil was inclined at an angle of approximately $4^\circ $ with respect to the direction of the mean flow.

We formulate a theory for the collective phase description of globally coupled noisy limit-cycle oscillators exhibiting macroscopic rhythms. Collective phase equations describing such macroscopic rhythms are derived by means of a two-step phase reduction. The collective phase sensitivity and collective phase coupling functions, which quantitatively characterize the macroscopic rhythms, are illustrated using three representative models of limit-cycle oscillators. As an important result of the theory, we demonstrate noise-induced anti-phase synchronization between macroscopic rhythms by direct numerical simulations of the three models., Comment: 19 pages, 11 figures

A minimal model of nonlinear phase dynamics in drift waves is shown to support phase bore solutions. Coupled nonlinear equations for amplitude, phase, and zonal flow are derived for the Hasegawa-Mima system and specialized to the case of spatiotemporally constant amplitude. In that limit, phase curvature (finite second derivative of the phase with respect to the radius) alone generates propagating shear flows. The phase field evolves nonlinearly by a competition between phase steepening and dispersion. The analytical solution of the model reveals that the phase bore solutions so obtained realize the concept of a phase slip in a concrete dynamical model of drift wave dynamics. The implications for phase turbulence are discussed.

A Ginzburg–Landau theory for multi-band mesoscopic Josephson junctions has been developed. The theory, obtained by generalizing the de Gennes matching-matrix method for the interface order parameters, allows the study of the phase dynamics of various types of mesoscopic Josephson junctions. As a relevant application, we studied mesoscopic double-band junctions also in the presence of a superconducting nanobridge interstitial layer. The results are in agreement with a microscopic treatment of the same system. Furthermore, thermal stability of the nanobridge junction is discussed in connection with recent experiments on iron-based grain-boundary junctions.

Phase dynamics of disordered Josephson junction ladders (JJLs) driven by external currents which are spatially and temporally modulated is studied using a numerical simulation based on a random field XY model. This model is considered theoretically as an effective model of JJLs with structural disorder in a magnetic field. The spatiotemporal modulation of external currents causes peculiar dynamical effects of phases in the system under certain conditions, such as the directed motion of phases and the mode-locking in the absence of dc currents. We clarify the details of effects of the spatiotemporal modulation on the phase dynamics.

The detailed investigation of the phase dynamics and the I–V curves in the system of coupled Josephson junctions have been carried out. The superconducting, quasiparticle, diffusion, and displacement currents have been calculated as functions of the total current through the system. The role of the diffusion current in the formation of the I–V curves has been studied and the influence of this quantity on the I–V curve branching and the magnitude of the return current has been revealed. The calculation results agree qualitatively with the experimental data.

Based on the model system undergoing phase separation and chemical reactions, we investigate the dynamics of propagating dissipative waves under external forcing which is periodic both in space and time. A phase diagram for the entrained and non-entrained states under the external forcing is obtained numerically. Theoretical analysis in terms of phase description of the traveling waves is carried out to show that the transition between the entrained and the non-entrained states by changing the external frequency occurs either through a saddle-node bifurcation or through a Hopf bifurcation and that these two bifurcation lines are connected at a Bogdanov-Takens bifurcation point.

Spiral turbulence observed in Couette-Taylor system has been characterized using the phase diffusion equation suggested by Hegseth et al. [Phys. Rev. Lett. 62, 257 (1989)]. From space-time diagrams, we have measured the diffusion coefficient, the diffusion velocity, and the turbulent spiral pitch.

Based on a developed and experimentally tested model, self-oscillatory lasing regimes have been studied for a Class A four-frequency gas ring laser with linear coupling of elliptically polarized counter-propagating waves. In the self-oscillatory regime, switching of the intensities, polarization states, and phase differences of the counter-propagating waves is observed, and also a polarization-phase dynamics effect involving displacement of the intensity switching point (with respect to detuning), due to the phase shift as a result of an ellipticity different from zero.

The statistics of the instantaneous phase of oscillations in dynamic systems with a noisy limit cycle is compared to the statistics of the instantaneous phase of oscillations in dynamic systems with a spiral chaotic attractor. Simulation of the phase dynamics of chaotic self-sustained oscillations by a Wiener process is considered. The results provided by various methods of determination of the instantaneous phase are analyzed.

In the quasi-one-dimensional mixed-stack organic charge-transfer complex, TTF-CA, photoirradiation is known to trigger transitions between the neutral and ionic phases. Here we use a one-dimensional extended Peierls–Hubbard model with alternating potentials and calculate the mean-field dynamics of charge density coupled with that of lattice displacements. We show qualitative differences between the photoinduced ionic-to-neutral and neutral-to-ionic transitions, which are consistent with recent experimental findings. That is, the ionic-to-neutral transition proceeds cooperatively, characterized by threshold behavior, while the neutral-to-ionic transition proceeds uncooperatively, characterized by linear behavior. The threshold absorption in the former depends on the strength or the duration of the pulse. The coherence during the transition dynamics is also different between the two transitions. In the ionic-to-neutral transition, a clear interference effect is observed as a function of the interval when the pulse is spilt into two.

Soap froths as archetypal disordered cellular structures, exhibiting spatial and temporal evolution, have been predominantly studied in terms of their topological properties. Recently, constrained geometries in froth have attracted attention, since these arise both from existing or natural structure or, more usually, can be artificially configured. Using a direct simulation method, which retains detailed information on bubble (cell) mechanisms, we have investigated dynamics in 2D froths with various initial structures corresponding to controlled disorder. In particular, we examine the special case of a defect ring surrounding a central inclusion in a uniform froth, for different number of defects and ring radius. This geometry permits comparison with shell theory, as well as insight on dynamics of a virtual phase (as defined for persistence and non-equilibrium processes in general). It appears that defect location and pattern of inclusion in the virtual phase cause considerable variation in the evolutionary behaviour, leading to non-universal exponents for the phase dynamics. This is probably explained by the fact that the froth is still in the transient period over simulation time scales, rather than achieving the final stage of persistence. However, distinctive patterns of response can be identified for the different froth regions, despite system size limitations, with topological and other properties indicating that a quasi-equilibrium results.

We construct a theory of dynamical behavior in intrinsic Josephson junction stacks with multigap superconducting layers. The theory predicts the existence of two kinds of phase modes, one of which is the Josephson-plasma mode and other of which is the Leggett’s mode. We discuss a cooperative phenomena induced by inter-band Josephson coupling in addition to capacitive and inductive couplings between the superconducting layers.

We derived the I-V characteristics of short nanowire in the circuit with and without resistive and inductive shunt. For that we used numerical calculations in the framework of time-dependent Ginzburg-Landau equations with different relaxation times for the amplitude and phase dynamics. We also derived dependence of the I-V characteristics on flux in superconducting quantum interference device (SQUID) made of such two weak links., 5.4 pages and 7 figures

The simplified models of neural networks based on biophysical Hodgkin–Huxley neurons are studied with a focus on coherent-phase dynamics. In our approach, each neuron is considered as a nonlinear oscillator, and collective dynamics of a mesoscopic network of neural oscillators are studied using the methods of nonlinear dynamics. We explore the mechanisms for synchrony, clustering and their breakup in the synaptic parameter space and discuss implications to temporal aspects of neural-information processing.

A time dependent thermal model for a superconducting constriction based weak-link (WL) is discussed for investigating the deterministic dynamics of its temperature and phase. A new dynamic regime is found where a non-zero voltage exists across the WL and its temperature stabilizes between the bath temperature and superconductor's critical temperature. This regime exists over a limited bias current range and gives rise to a new hysteretic regime in current-voltage characteristics. We also discuss the effect of fluctuations on the current-voltage characteristics and experimental implications of this dynamic regime., Comment: 7 pages, 4 figures; revised on 25 Nov 2014

We investigate the phase dynamics of moderately damped NbN/AlN/NbN Josephson junctions and we present experimental results on detailed aspects of phase diffusion processes. We measure both single escape and multiple escape and retrapping events obtaining a crossover temperature T* from Kramers to phase diffusion switching. We observe a clear dependence of the crossover temperature T* by the bias current ramp rate, while the damping factor Q remains the same. The measured effect is in strong agreement with theoretical predictions reported by Fenton and Warburton. © 2014 AIP Publishing LLC.

We consider a $\ensuremath{\varphi}$ Josephson junction, which has a bistable zero-voltage state with the stationary phases $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$. In the nonzero voltage state the phase ``moves'' viscously along a tilted periodic double-well potential. When the tilting is reduced quasistatically, the phase is retrapped in one of the potential wells. We study the viscous phase dynamics to determine in which well ($\ensuremath{-}\ensuremath{\varphi}$ or $+\ensuremath{\varphi}$) the phase is retrapped for a given damping, when the junction returns from the finite-voltage state back to the zero-voltage state. In the limit of low damping, the $\ensuremath{\varphi}$ Josephson junction exhibits a butterfly effect---extreme sensitivity of the destination well on damping. This leads to an impossibility to predict the destination well.

The moderately damped regime (MDR) in a Josephson junction (JJ) is quite distinct from the well-known case of underdamped systems and quite common in devices characterized by low critical currents. Measurements of switching current distribution (SCD) are a direct way of discriminating the phase dynamics and the transport also in nontrivial cases of moderate damping. MDR is going to be more and more common with advances in nanopatterning superconductors and in materials science finalized to build hybrid devices. We report on measurements of SCDs, both in the thermal and quantum regime, on moderately damped NbN/MgO/NbN JJs. A transition from the Thermal Activation (TA) regime to Macroscopic Quantum Tunnelling (MQT) occurs at about 90 mK, while above 1.6 K a phase diffusive dynamics is clearly observed. The combined analysis of these regimes through numerical simulations allowed us to extract the fundamental parameters, which completely characterize the phase dynamics of such moderately damped JJs.

The idea of phase dynamics originally considered for regular non-equilibrium patterns is applied to irregular patterns. In the dissipation-dominated regime, a slow modulation of irregular pattern is shown to decay in time according to the diffusion law. Possible relevance of this result for the ultra-slow diffusion modes observed in glass-forming systems is discussed. In this connection we speculate about a possibility of appearance of some sorts of soft structures resembling quasi-periodic microcrystalline states in glass-forming systems.

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.

The discovery of High Critical Temperature Superconductors (HTS) generated great activity to develop dc Superconductive Quantum Interference Devices (SQUIDs), with operating temperatures up to the boiling point of liquid nitrogen, 77. K.It was immediately apparent that small-scale devices, like SQUIDs, would require the development of thin-film techniques and novel Josephson junction's fabrication technologies. At present, grain-boundary junctions are the most widely used in SQUIDs. However, their properties are strongly affected by the d-wave symmetry of the order parameter. As a consequence the static and dynamic properties of HTS SQUIDs can be profoundly modified. The d-wave symmetry also offers the possibility to design π-SQUIDs showing a complementary behavior in magnetic field, compared to conventional ones, as well as dc SQUIDs with a double well potential. In this chapter the new Josephson phenomenology of HTS SQUIDs is derived, compared with experimental data available in literature, and discussed in view of future novel applications. © 2011 Woodhead Publishing Limited All rights reserved.

Physico-chemical systems driven away from thermal equilibrium usually undergo various types of instabilities leading to the formation of spatio-temporal patterns on macroscopic time and space scales. In two-dimensional geometries, patterns of different symmetries may be simultaneously stable. We study here the phase stability of hexagonal planforms in the framework of amplitude equations and reduced dynamical models close to the instability points.

Arrays of coupled oscillators can be used for power-combining at microwave and millimeter-wave frequencies, and have been successfully demonstrated with a variety of devices. Such arrays have also recently been mode-locked for pulse generation, and can be configured for phase-shifterless beam scanning. The nonlinear theory of coupled oscillator phase dynamics depends crucially on the parameters describing the coupled between oscillators. Methods for experimental characterization of these parameters are described here, and simple models which reproduce the measurements quite well are developed. The models apply to radiative coupling and the effects of external reflectors which are sometimes used for stabilization. The theory is verified with a two-oscillator system. >

We have proposed and investigated a model of drying colloidal suspension drop placed onto a horizontal substrate in which the sol to gel phase transition occurs. The temporal evolution of volume fraction of the solute and the gel phase dynamics were obtained from numerical simulations. Our model takes into account the fact that some physical quantities are dependent on volume fraction of the colloidal particles., Submitted to IJMPB

We consider a three-component model of an active medium where local oscillations are coupled to a slowly propagating field. Using the Kuramoto approximation of phase dynamics, we show that this uniform medium can support steady autonomous pacemakers. These were patterns spontaneously emerge from the background of uniform bulk oscillations and are stable with respect to small perturbations.

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.

By means of an electron hole rate equation model we explain the phase dynamics of a quantum dot semiconductor optical amplifier and the appearance of different decay times observed in pump and probe experiments. The ultrafast hole relaxation leads to a first ultrafast recovery of the gain, followed by electron relaxation and, in the nanosecond timescale, radiative and non-radiative recombinations. The phase dynamics is slower and is affected by thermal redistribution of carriers within the dot. We explain the ultrafast response of quantum dot amplifiers as an effect of hole escape and recombination without the need to assume Auger processes.

We present results from our time dependent model on electro-magnetically induced transparency in a standard Λ configuration. We show that sudden phase jumps in either field leads to transient enhanced absorption for the probe field.

Coherent terahertz (THz) radiations based on intrinsic Josephson junctions (IJJs) from a Bi2Sr2CaCu2O[Formula: see text] (BSCCO) mesa under a bias voltage were observed in 2007. Later on, a novel [Formula: see text] phase kink state was proposed which can explain the key experimental results. However, how to drive the system into the [Formula: see text] phase kink state efficiently still remains an open problem. In this work, we propose several ways to synchronize the system to the [Formula: see text] phase kink state. We start from random and typical regular initial phase configurations. It is found that starting from some initial phase configurations, the system can be driven efficiently into the [Formula: see text] phase kink state. The time spent before entering the [Formula: see text] phase kink states for these initial phase configurations is shorter when the initial phase configuration is further away from the uniform phase configuration.

SUMMARY Since thr recent experimental observation of Dose-Einstein condensation in dilutc atomic gases, much interest has been raised about the coherence properties of the condensates Considerable attention has ben devoted to the matter uf the relativr phasp bctween two condensates: hm this phase manifests itself in an interference experiment [I], haw it cm be estnbliihed by measurement, and how it evolves in prespnee of atomic interactionsl2). Rerrritl) it was predicted that the relative phase betwm two condensates should display collopscs and revivals in time due to atomir inierxtioiis. For condcnsates with a rclatwely small number of atoms. of the ordcr of some hundreds, the revirds of thr 7ihar;e cm occur on the 10.'~ time Scale and niight in principle be observed. Howerer up to non a theoretical analysis of irifluence of partrcie lams 011 Lhr pha? dpnmirr B~F missing. Such loss proccs~s. due for example to collisions of rondmsed atonic With the buckgiuund gas or to three-bod! colliaionr. arp nnaruidiiblu in a real experiment and might spoil the cnherenrr prevmring the ubrurvtion of the revivals. IVe dewlop B model to dearrihe thP phase dynamici of the condensates m presence r the asaurnption that the fraction of lost parLicles in II, wc obtain analytical results for thP time depcrldcnce abservables for two nm overlapping and mutually non sueb as tlir nwm beating intensity of the condensates .epresented by the quantity (0'6) (a.herp o (a') and b (6') are the creation iannihilat,ion) operator^ of a particle in the condmsatr A ui B respectively). and the relacive phase probability distrihul ion. We find that. besides the collapses and revirals due to thr Hakiltonian evolution, the rrlvtive phase dependent observable (0'6) expericncps im esponmttal deea)- in time with a rate X given hr the mean total tiumber of luss ewnts per unit oft derohereuce betaren tw condensatcs, is therefore apprommatel inverse lifetiiiiu of a particle in the condensates (whew :T is the total number of atomr). Neverthclcs \ye show that losses do nnt prevent the ObsQrvatiOn of the rrlatise phase rsyivals in condensates with small number of atoms. Finally; se giw a suggestive interimtation of the dramatic cffect of the losses on the rflatii-e phase based on the h1oel.e Carlo wa\p function approach the condensates relative phase in a single !dome Carlo reaiization is shifted br a random amount on tbe order of 7 cosarquently to each mch loss event occurring in the condensates. A few loss prorcsses in a given time interd are then sufficient to smear out the relative phase completely when the average over the stochastic realizacion is taker

Two parallel stacks of coupled Josephson junctions (JJs) are investigated to clarify the physics of transitions between the rotating and oscillating states and their effect on the IV-characteristics of the system. The detailed study of phase dynamics and bias dependence of the superconducting and diffusion currents allows one to explain all features of simulated IV-characteristics and demonstrate the correspondence in their behavior. The coupling between JJ in the stacks leads to the branching of IV-characteristics and a decrease in the hysteretic region. The crucial role of the diffusion current in the formation of the IV-characteristic of the parallel stacks of coupled JJs is demonstrated. We discuss the effect of symmetry in a number of junctions in the stacks and show a decrease of the branching in the symmetrical stacks. The observed effects might be useful for development of superconducting electronic devices based on intrinsic JJs.

The phase dynamics of a closed 0‐π junction is investigated. Such a system can be realized, for example, in a small d(x2−y2)‐wave superconductor embedded in a conventional s‐wave superconducting matrix. The Hamiltonian of the system is derived. We prove that the system can be mapped on a quantum two‐level system when the system size is small enough.

The Sixth Conference on Molecular Reaction Dynamics in Condensed Matter was held Feb. 28 - Mar 3 at the Hotel La Casa del Camino in Laguna Beach, CA, sponsored by AFOSR and UC Irvine, and organized by D. Dlott and A. Apkarian. There were 39 attendees, including professors, graduate students, postdoctoral fellows, technical staff members from national laboratories and a representative from AFOSR. 34 talks were presented. There were 21 invited talks (50 minutes with discussion) and 9 contributed talks (25 minutes with discussion). Lively discussion continued until the wee hours. The conference website is: http://dlottgroup.scs.uiuc.edu/moldyn/. Symposia on the following topics were presented: (1) New frontiers; (2) Multidimensional spectroscopy; (3) Condensed phase dynamics; (4) Chemical reaction dynamics; and (5) Confined molecules: clusters and droplets.

Concerning the spontaneous THz electromagnetic wave emission from intrinsic Josephson junctions, we revisit the theory for intrinsic Josephson effects from standpoints of the couplings between stacked junctions and consequent superconducting phase dynamics. After reviewing the previous simulation works based on the theory, we present recent multi-physics simulation studies suggested by authors to systematically reproduce the emission experiments. Some typical simulation results are exhibited and the future perspective of the simulation is also given.

The phase dynamics of the coupled Josephson junctions in the framework of CCJJ and CCJJ+DC models is studied. The current voltage characteristics (CVC) are numerically calculated for the stacks with different number of junctions at different model parameters. We manifest the difference of these models for the branching at I = Ic and in the hysteretic region. The essential difference is observed in the breakpoint region, where the longitudinal plasma wave is created. We discuss the main features of both models, related with the role of the diffusion current between the superconducting layers.

To model the IV-characteristics of shunted intrinsic Josephson junctions we calculated phase dynamics of a chain of two identical junctions covered by a resistive shunt and with a resistive crosspiece between the shunt and the junctions. The coherent solution of dynamic equations for this system is unstable at some bias currents above critical currents of junctions. We have shown that this instability leads to the multibranch structure of IV-curves in the hysteretic region. The multibranch structure appears due to the random switching of junctions to the superconducting state above their critical currents. We found that the resistance of the interface between a covering shunt and the junctions can regulate the multibranch behaviour.

A classical many-body model for the phase dynamics of randomly pinned charge density waves is found to exhibit stretched exponential relaxation below threshold. The statistics of single particle relaxation is highly non-trivial and can only be deduced from known scaling behaviour of intermittent trajectories in an uncoupled approximation. This is compared with results from present single-particle approaches. The self-similarity properties at the dynamical phase transition at threshold are investigated.

This paper discusses the excitations in a condensed Bose system as manifestations of the dynamics of the phase. It is argued that the standard approach based on spontaneous symmetry breaking is not viable; a superselection rule enforces strict particle conservation. Some recent theoretical results are used to show how the significance of the phase dynamics can be retained without violating the superselection rule.