Dynamics of a Josephson Array in a Resonant Cavity

We derive dynamical equations for a Josephson array coupled to a resonant cavity by applying the Heisenberg equations of motion to a model Hamiltonian described by us earlier [Phys. Rev. B {\bf 63}, 144522 (2001); Phys. Rev. B {\bf 64}, 179902 (E)]. By means of a canonical transformation, we also show that, in the absence of an applied current and dissipation, our model reduces to one described by Shnirman {\it et al} [Phys. Rev. Lett. {\bf 79}, 2371 (1997)] for coupled qubits, and that it corresponds to a capacitive coupling between the array and the cavity mode. From extensive numerical solutions of the model in one dimension, we find that the array locks into a coherent, periodic state above a critical number of active junctions, that the current-voltage characteristics of the array have self-induced resonant steps (SIRS's), that when $N_a$ active junctions are synchronized on a SIRS, the energy emitted into the resonant cavity is quadratic in $N_a$, and that when a fixed number of junctions is biased on a SIRS, the energy is linear in the input power. All these results are in agreement with recent experiments. By choosing the initial conditions carefully, we can drive the array into any of a variety of different integer SIRS's. We tentatively identify terms in the equations of motion which give rise to both the SIRS's and the coherence threshold. We also find higher-order integer SIRS's and fractional SIRS's in some simulations. We conclude that a resonant cavity can produce threshold behavior and SIRS's even in a one-dimensional array with appropriate experimental parameters, and that the experimental data, including the coherent emission, can be understood from classical equations of motion.Comment: 15 pages, 10 eps figures, submitted to Phys. Rev.

The CHESS survey of the L1157-B1 bow-shock: high and low excitation water vapor

Molecular outflows powered by young protostars strongly affect the kinematics and chemistry of the natal molecular cloud through strong shocks resulting in substantial modifications of the abundance of several species. As part of the "Chemical Herschel Surveys of Star forming regions" guaranteed time key program, we aim at investigating the physical and chemical conditions of H20 in the brightest shock region B1 of the L1157 molecular outflow. We observed several ortho- and para-H2O transitions using HIFI and PACS instruments on board Herschel, providing a detailed picture of the kinematics and spatial distribution of the gas. We performed a LVG analysis to derive the physical conditions of H2O shocked material, and ultimately obtain its abundance. We detected 13 H2O lines probing a wide range of excitation conditions. PACS maps reveal that H2O traces weak and extended emission associated with the outflow identified also with HIFI in the o-H2O line at 556.9 GHz, and a compact (~10") bright, higher-excitation region. The LVG analysis of H2O lines in the bow-shock show the presence of two gas components with different excitation conditions: a warm (Tkin~200-300 K) and dense (n(H2)~(1-3)x10^6 cm-3) component with an assumed extent of 10" and a compact (~2"-5") and hot, tenuous (Tkin~900-1400 K, n(H2)~10^3-10^4 cm-3) gas component, which is needed to account for the line fluxes of high Eu transitions. The fractional abundance of the warm and hot H2O gas components is estimated to be (0.7-2)x10^{-6} and (1-3)x10^{-4}, respectively. Finally, we identified an additional component in absorption in the HIFI spectra of H2O lines connecting with the ground state level, probably arising from the photodesorption of icy mantles of a water-enriched layer at the edges of the cloud.Comment: Accepted for publication in A&A. 12 pages, 9 figures, 4 table

Resonant-Cavity-Induced Phase Locking and Voltage Steps in a Josephson Array

We describe a simple dynamical model for an underdamped Josephson junction array coupled to a resonant cavity. From numerical solutions of the model in one dimension, we find that (i) current-voltage characteristics of the array have self-induced resonant steps (SIRS), (ii) at fixed disorder and coupling strength, the array locks into a coherent, periodic state above a critical number of active Josephson junctions, and (iii) when $N_a$ active junctions are synchronized on an SIRS, the energy emitted into the resonant cavity is quadratic with $N_a$. All three features are in agreement with a recent experiment [Barbara {\it et al}, Phys. Rev. Lett. {\bf 82}, 1963 (1999)]}.Comment: 4 pages, 3 eps figures included. Submitted to PRB Rapid Com

Stochastic Resonance in a Dipole

We show that the dipole, a system usually proposed to model relaxation phenomena, exhibits a maximum in the signal-to-noise ratio at a non-zero noise level, thus indicating the appearance of stochastic resonance. The phenomenon occurs in two different situations, i.e. when the minimum of the potential of the dipole remains fixed in time and when it switches periodically between two equilibrium points. We have also found that the signal-to-noise ratio has a maximum for a certain value of the amplitude of the oscillating field.Comment: 4 pages, RevTex, 6 PostScript figures available upon request; to appear in Phys. Rev.

Stochastic Resonance in Nonpotential Systems

We propose a method to analytically show the possibility for the appearance of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our results to the FitzHugh-Nagumo model under a periodic external forcing, showing that the model exhibits stochastic resonance. The procedure that we follow is based on the reduction to a one-dimensional dynamics in the adiabatic limit, and in the topology of the phase space of the systems under study. Its application to other nonpotential systems is also discussed.Comment: Submitted to Phys. Rev.

Theory of Two-Dimensional Josephson Arrays in a Resonant Cavity

We consider the dynamics of a two-dimensional array of underdamped Josephson junctions placed in a single-mode resonant cavity. Starting from a well-defined model Hamiltonian, which includes the effects of driving current and dissipative coupling to a heat bath, we write down the Heisenberg equations of motion for the variables of the Josephson junction and the cavity mode, extending our previous one-dimensional model. In the limit of large numbers of photons, these equations can be expressed as coupled differential equations and can be solved numerically. The numerical results show many features similar to experiment. These include (i) self-induced resonant steps (SIRS's) at voltages V = (n hbar Omega)/(2e), where Omega is the cavity frequency, and n is generally an integer; (ii) a threshold number N_c of active rows of junctions above which the array is coherent; and (iii) a time-averaged cavity energy which is quadratic in the number of active junctions, when the array is above threshold. Some differences between the observed and calculated threshold behavior are also observed in the simulations and discussed. In two dimensions, we find a conspicuous polarization effect: if the cavity mode is polarized perpendicular to the direction of current injection in a square array, it does not couple to the array and there is no power radiated into the cavity. We speculate that the perpendicular polarization would couple to the array, in the presence of magnetic-field-induced frustration. Finally, when the array is biased on a SIRS, then, for given junction parameters, the power radiated into the array is found to vary as the square of the number of active junctions, consistent with expectations for a coherent radiation.Comment: 11 pages, 8 eps figures, submitted to Phys. Rev

Instabilities in Josephson Ladders with Current Induced Magnetic Fields

We report on a theoretical analysis, consisting of both numerical and analytic work, of the stability of synchronization of a ladder array of Josephson junctions under the influence of current induced magnetic fields. Surprisingly, we find that as the ratio of the mutual to self inductance of the cells of the array is increased a region of unstable behavior occurs followed by reentrant stable synchronization. Analytic work tells us that in order to understand fully the cause of the observed instabilities the behavior of the vertical junctions, sometimes ignored in analytic analyses of ladder arrays, must be taken into account.Comment: RevTeX, 4 pages, 3 figure

Stochastic Resonance in Noisy Non-Dynamical Systems

We have analyzed the effects of the addition of external noise to non-dynamical systems displaying intrinsic noise, and established general conditions under which stochastic resonance appears. The criterion we have found may be applied to a wide class of non-dynamical systems, covering situations of different nature. Some particular examples are discussed in detail.Comment: 4 pages, RevTex, 3 PostScript figures available upon reques

Transitions Induced by the Discreteness of Molecules in a Small Autocatalytic System

Autocatalytic reaction system with a small number of molecules is studied numerically by stochastic particle simulations. A novel state due to fluctuation and discreteness in molecular numbers is found, characterized as extinction of molecule species alternately in the autocatalytic reaction loop. Phase transition to this state with the change of the system size and flow is studied, while a single-molecule switch of the molecule distributions is reported. Relevance of the results to intracellular processes are briefly discussed.Comment: 5 pages, 4 figure

Bifurcations in Globally Coupled Map Lattices

The dynamics of globally coupled map lattices can be described in terms of a nonlinear Frobenius--Perron equation in the limit of large system size. This approach allows for an analytical computation of stationary states and their stability. The complete bifurcation behaviour of coupled tent maps near the chaotic band merging point is presented. Furthermore the time independent states of coupled logistic equations are analyzed. The bifurcation diagram of the uncoupled map carries over to the map lattice. The analytical results are supplemented with numerical simulations.Comment: 19 pages, .dvi and postscrip