Systems which rapidly evolve through symmetry-breaking transitions on timescales comparable to the fluctuation timescale of the single-particle excitations may behave very differently than under controlled near-ergodic conditions. A real-time investigation with high temporal resolution may reveal new insights into the ordering through the transition that are not available in static experiments. We present an investigation of the system trajectory through a normal-to-superconductor transition in a prototype high-temperature superconducting cuprate in which such a situation occurs. Using a multiple pulse femtosecond spectroscopy technique we measure the system trajectory and time-evolution of the single-particle excitations through the transition in La1.9Sr0.1CuO4 and compare the data to a simulation based on time-dependent Ginzburg-Landau theory, using laser excitation fluence as an adjustable parameter controlling the quench conditions in both experiment and theory. The comparison reveals the presence of significant superconducting fluctuations which precede the transition on short timescales. By including superconducting fluctuations as a seed for the growth of superconducting order we can obtain a satisfactory agreement of the theory with the experiment. Remarkably, the pseudogap excitations apparently play no role in this process.The study of the time evolution of complex systems through symmetry breaking transitions (SBT) is of great fundamental interest in different areas of physics [1][2][3]. An SBT of particular general interest is the normal-tosuperconducting (N → S) state transition in which a Lorentz non-invariant system breaks gauge invariance. [4] By studying the N → S transition in time-evolving systems, rather than by slowly varying the temperature through the transition, one can in principle gain new information on the dynamical behavior of elementary excitations which lead to the formation of a superconducting condensate and the collective ordering behavior, leading to new insights into non-ergodic phenomena of collectively ordered systems as well as the mechanism of superconductivity. Particularly, ergodicity breaking in rapidly evolving systems leads to the appearance of topological defects (vortices).The description of the dynamical behavior of the gauge non-invariant systems is given in the timedependent Ginzburg-Landau theory (TDGL theory). It has been first applied to the problem of non-equilibrium phase transitions by Kibble and Zurek who considered the appearance of topological defects throughout the transition.[5, 6] The Kibble-Zurek description has been indirectly confirmed to be correct by static experiments in which trapped vortices were studied. [7,8] In this paper, beyond previous static studies, we study realtime evolution of the superconducting order in the nonequilibrium phase transition. We investigate the applicability of TDGL theory to the phase transition problem and provide a minimal formulation sufficient to describe the data.The paper is organized in the following way: we ...

We investigate the behavior of a mesoscopic one-dimensional ring in an external magnetic field by simulating the time dependent Ginzburg-Landau equations with periodic boundary conditions. We analyze the stability and the different possible evolutions for the phase slip phenomena starting from a metastable state. We find a stability condition relating the winding number of the initial solution and the number of flux quanta penetrating the ring. The analysis of multiple phase slips solutions is based on analytical results and simulations. The role of the ratio of two characteristic times u is studied for the case of a multiple phase slips transition. We found out that if u>>1, consecutive multiple phase slips will be more favorable than simultaneous ones. If u<<1 the opposite is true and we confirm that u>>1 is often a necessary condition to reach the ground state. The influence of the Langevin noise on the kinetics of the phase transition is discussed.Comment: 8 pages, 6 figure

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We consider flux penetration to a 2D superconducting cylinder. We show that in the low field limit the kinetics is deterministic. In the strong field limit the dynamics becomes stochastic. Surprisingly the inhomogeneity in the cylinder reduces the level of stochasticity because of the predominance of Kelvin-Helmholtz vortices.

Abstract. We investigate the behavior of a mesoscopic 1D ring or 2D torus in an external magnetic field by simulating the Time Dependant Ginzburg Landau (TDGL) equations with periodic boundary conditions. In 1D, we analyze the stability and the different possible evolutions for the phase-slip phenomena starting from a metastable state. We used those results to observe the dynamics of a vortex-antivortex pair dissociation in 2D. IntroductionNonequilibrium phenomena in superconductors are a challenging area for both experimental and theoretical research. They are also crucial for the development of applications as they are the key to the appearance of resistive states in superconducting samples and to the possible use of vortex dynamics. In 1D, the resistive phase-slip process foreseen by W. A. Little [1] has been described quantitatively by the LAMH theory developed by J. S. Langer and V. Ambegaokar [2] and extended by D. E. McCumber and N. B. Halperin [3,4]. The LAMH theory describes thermally activated phase-slips (TPS). It evaluates the resistance of a 1D superconductor when driven out of thermodynamical equilibrium by a voltage or current source. Since then, this theory has been accepted to a large extent in rather good agreements with experiments (for a more complete review of theoretical and experimental works, see [5]).More recently, simulations were carried out on different versions of the time dependant Ginzburg Landau (TDGL) equations in order to investigate the dynamics of the process. In particular, the case of the 1D ring has raised interest since it exhibits multiple metastable states which can be reached by phase-slip processes. In [6], the ring is submitted to an electromotive force which constantly accelerates the superconducting electrons. Another approach has been made in [7], where the magnetic field is gradually increased.In the present work, we consider a superconducting ring of thickness d, radius R and length L as represented on figure 1. For simplicity, we consider d << ξ << λ ef f , R ≈ ξ and R << λ ef f , where ξ is the coherence length and λ ef f is the Pearl [8] penetration depth. The first two conditions allow us to treat the ring as one dimensional and the last two conditions account for the mesoscopic size of the ring. We submit this 1D ring to a perpendicular constant magnetic field H, which determines the properties (superfluid density, current etc.) of the stable state. Our approach is different because we observe a relaxation process from the initial state to a more stable one, without any external parameter influencing the dynamics.We also simulated vortex-antivortex dynamics in 2D, starting from a phase-slip line situation. Indeed, the vortex-antivortex pair dissociation is analog to the phase-slip in 1D.