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We consider, by means of the variational approximation ͑VA͒ and direct numerical simulations of the Gross-Pitaevskii ͑GP͒ equation, the dynamics of two-dimensional ͑2D͒ and 3D condensates with a scattering length containing constant and harmonically varying parts, which can be achieved with an ac magnetic field tuned to the Feshbach resonance. For a rapid time modulation, we develop an approach based on the direct averaging of the GP equation, without using the VA. In the 2D case, both VA and direct simulations, as well as the averaging method, reveal the existence of stable self-confined condensates without an external trap, in agreement with qualitatively similar results recently reported for spatial solitons in nonlinear optics. In the 3D case, the VA again predicts the existence of a stable self-confined condensate without a trap. In this case, direct simulations demonstrate that the stability is limited in time, eventually switching into collapse, even though the constant part of the scattering length is positive ͑but not too large͒. Thus a spatially uniform ac magnetic field, resonantly tuned to control the scattering length, may play the role of an effective trap confining the condensate, and sometimes causing its collapse.

The spin-transfer effect is investigated for the vortex state of a magnetic nanodot. A spin current is shown to act similarly to an effective magnetic field perpendicular to the nanodot. Then a vortex with magnetization (polarity) parallel to the current polarization is energetically favorable. Following a simple energy analysis and using direct spin-lattice simulations, we predict the polarity switching of a vortex. For magnetic storage devices, an electric current is more effective to switch the polarity of a vortex in a nanodot than the magnetic field.

To study how nonlinear waves propagate across Y- and T-type junctions, we consider the two-dimensional (2D) sine-Gordon equation as a model and examine the crossing of kinks and breathers. Comparing energies for different geometries reveals that, for small widths, the angle of the fork plays no role. Motivated by this, we introduce a one-dimensional effective model whose solutions agree well with the 2D simulations for kink and breather solutions. These exhibit two different behaviors: a kink crosses if it has sufficient energy; conversely a breather crosses when v>1-ω, where v and ω are, respectively, its velocity and frequency. This methodology can be generalized to more complex nonlinear wave models.

We introduce an exponentially tapered Josephson flux-flow oscillator that is tuned by applying a bias current to the larger end of the junction. Numerical and analytical studies show that above a threshold level of bias current the static solution becomes unstable and gives rise to a train of fluxons moving toward the unbiased smaller end, as in the standard flux-flow oscillator. An exponentially shaped junction provides several advantages over a rectangular junction including: ͑i͒ smaller linewidth, ͑ii͒ increased output power, ͑iii͒ no trapped flux because of the type of current injection, and ͑iv͒ better impedance matching to a load. ͓S0163-1829͑96͒00646-7͔

We investigate the electromagnetic influence of the surrounding idle (no tunneling) region on static fluxons in window Josephson junctions. We calculated the fluxon width as a function of the size of the idle region for three different window (active tunneling area) geometries, namely elongated truncated rhombus, rectangular and bow-tie and derived approximate expressions for the case of small and large idle regions. The window geometry affects both the fluxon width and the fluxon stability. One can define an effective λJ which depends on the junction width, the idle region width and the inductance ratio and has important consequences on the static and dynamic properties of window Josephson junctions. We also show the effect of the idle region on the maximum tunneling current as a function of the external magnetic field.

International audienceA three-terminal Josephson junction consists of three superconductors coupled coherently to a small nonsuperconducting island, such as a diffusive metal, a single or double quantum dot. A specific resonant single quantum dot three-terminal Josephson junction (Sa,Sb,Sc) biased with voltages (V,−V,0) is considered, but the conclusions hold more generally for resonant semi-conducting quantum wire set-ups. A simple physical picture of the steady state is developed, using Floquet theory. It is shown that the equilibrium Andreev bound states (for V=0) evolve into nonequilibrium Floquet-Wannier-Stark-Andreev (FWS-Andreev) ladders of resonances (for V≠0). These resonances acquire a finite width due to multiple Andreev reflection (MAR) processes. We also consider the effect of an extrinsic line-width broadening on the quantum dot, introduced through a Dynes phenomenological parameter. The DC-quartet current manifests a cross-over between the extrinsic relaxation dominated regime at low voltage to an intrinsic relaxation due to MAR processes at higher voltage. Finally, we study the coupling between the two FWS-Andreev ladders due to Landau-Zener-St\"uckelberg transitions, and its effect on the cross-over in the relaxation mechanism. Three important low-energy scales are identified, and a perspective is to relate those low-energy scales to a recent noise cross-correlation experiment [Y. Cohen {\it et al.}, arXiv:1606.08436]

A three-terminal Josephson junction biased at opposite voltages can sustain a phase-sensitive dccurrent carrying three-body static phase coherence, known as the "quartet current". We calculate the zero-frequency current noise cross-correlations and answer the question of whether this current is noisy (like a normal current in response to a voltage drop) or noiseless (like an equilibrium supercurrent in response to a phase drop). A quantum dot with a level at energy 0 is connected to three superconductors Sa, S b and Sc with gap ∆, biased at Va = V , V b = −V and Vc = 0, and with intermediate contact transparencies. At zero temperature, nonlocal quartets (in the sense of four-fermion correlations) are noiseless at subgap voltage in the nonresonant dot regime 0/∆ 1, which is demonstrated with a semi-analytical perturbative expansion of the cross-correlations. Noise reveals the absence of granularity of the superflow splitting from Sc towards (Sa, S b ) in the nonresonant dot regime, in spite of finite voltage. In the resonant dot regime 0/∆ < ∼ 1, crosscorrelations measured in the (Va, V b ) plane should reveal an "anomaly" in the vicinity of the quartet line Va + V b = 0, related to an additional contribution to the noise, manifesting the phase sensitivity of cross-correlations under the appearance of a three-body phase variable. Phase-dependent effective Fano factors Fϕ are introduced, defined as the ratio between the amplitudes of phase modulations of the noise and the currents. At low bias, the Fano factors Fϕ are of order unity in the resonant dot regime 0/∆ < ∼ 1, and they are vanishingly small in the nonresonant dot regime 0/∆ 1.

To describe the flow of a miscible quantity on a network, we consider the graph wave equation where the standard continuous Laplacian is replaced by the graph Laplacian. The structure of the graph influences strongly the dynamics which is naturally described using the eigenvectors as a basis. Assuming the graph is forced and damped at specific nodes, we derive the amplitude equations. These reveal the importance of a soft node where the eigenvector is zero. For example forcing the network at a resonant frequency reveals that damping can be ineffective if applied to such a soft node, leading to a disastrous resonance and destruction of the network. We give sufficient conditions for the existence of soft nodes and show that these exist for general graphs so that they can be expected for complex physical networks and engineering networks like power grids.

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