Spontaneous fluxoid formation in superconducting loops

Monaco, R.; Mygind, J.; Rivers, R. J.; Koshelets, V. P.

doi:10.1103/physrevb.80.180501

Cited by 95 publications

(121 citation statements)

References 23 publications

(42 reference statements)

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“…The relevance of this analysis is that experiments are being prepared to provide a rigorous test of the simple KZ scenario for superconducting loops, originally proposed by Zurek more than 25 years ago but, as yet, only partially attempted 7 .…”

Section: Discussionmentioning

confidence: 99%

Defect Formation in Superconducting Rings: External Fields and Finite-Size Effects

2012

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Consistent with the predictions of Kibble and Zurek, scaling behaviour has been seen in the production of fluxoids during temperature quenches of superconducting rings. However, deviations from the canonical behaviour arise because of finite-size effects and stray external fields.Technical developments, including laser heating and the use of long Josephson tunnel junctions, have improved the quality of data that can be obtained. With new experiments in mind we perform large-scale 3D simulations of quenches of small, thin rings of various geometries with fully dynamical electromagnetic fields, at nonzero externally applied magnetic flux. We find that the outcomes are, in practice, indistinguishable from those of much simpler Gaussian analytical approximations in which the rings are treated as one-dimensional systems and the magnetic field fluctuation-free.

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Section: Discussionmentioning

confidence: 99%

Defect Formation in Superconducting Rings: External Fields and Finite-Size Effects

2012

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“…[9] and the density of defects may therefore continue to decrease although no detailed study was performed. Numerous numerical [15][16][17][18][19] and experimental [20][21][22][23][24] papers tested the quantitative consequences of the Kibble-Zurek mechanism with variable results. While the numerical studies claimed that they successfully verified the predictions, the conclusions are less clear in the experimental works that studied vortex formation in superfluid 4 He and 3 He with null results in the former [20] and agreement with the KZ prediction in the latter [21].…”

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confidence: 99%

Kibble-Zurek mechanism and infinitely slow annealing through critical points

2010

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We revisit the Kibble-Zurek mechanism by analyzing the dynamics of phase ordering systems during an infinitely slow annealing across a second order phase transition. We elucidate the time and cooling rate dependence of the typical growing length and we use it to predict the number of topological defects left over in the symmetry broken phase as a function of time, both close and far from the critical region. Our results extend the Kibble-Zurek mechanism and reveal its limitations. PACS numbers:The out of equilibrium dynamics induced by a quench are the focus of intense research [1,2]. Interesting realizations are quenches through a second order phase transition, which take the system from the symmetric phase into the symmetry broken one. Below the transition, times scaling with the system size are needed to reach equilibrium and to realize the spontaneous symmetry breaking process. Before this-typically unreachableasymptotic limit the symmetry is broken only locally: the system is formed by ordered regions of size growing with time [3]. Only when this size reaches the order of the volume of the sample the symmetry is broken globally and the spatial average of the order parameter deviates from zero. The majority of theoretical studies focused on the dynamics after infinitely rapid quenches although experimentally quenches are performed at finite speed. Indeed, since the typical time-scale on which the system evolves is its age, i.e. the time elapsed since crossing the critical point, finite quench time-scales (τ Q ) eventually become short compared to the relaxation time. Thus, they alter the out of equilibrium dynamics at short times only. The opposite limit of an extremely slow annealing, corresponding to very long τ Q , needs a separate treatment. Surprisingly, this has not been studied in detail in the statistical physics literature with, however, some exceptions for disordered systems [4][5][6]. It has, instead, attracted a lot of attention within the cosmology and, more recently, the condensed matter communities. An explanation of the slow dynamics induced by this protocol was given by the so-called Kibble-Zurek (KZ) mechanism [7][8][9][10]. This is an equilibrium scaling argument that yields an estimate for the density of topological defects left over in the ordered phase as a function of the quenching rate close to the critical point. The argument has been recently generalized to study very slow 'quantum annealing' across a quantum phase transitions in isolated systems [11][12][13].The aim of this work is to obtain a more complete picture of the slow dynamics induced by an extremely slow annealing. With numerical and analytical arguments we unveil the limitations of the KZ approach and we obtain a full scaling description of the slow dynamics. Our main result is that the dynamic evolution is characterized by a first adiabatic regime in agreement with KZ, followed by critical coarsening and, finally, standard coarsening at very long times. We find a new universal scaling function that characterizes the gro...

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“…The Kibble-Zurek (KZ) mechanism was initially established for second-order phase transitions [1][2][3][4] under which many experiments tested its validity in different systems such as liquid crystals [5][6][7], 3 He [2,[8][9][10]], 4 He [11], Bose-Einstein condensates [12][13][14][15][16], Josephson tunnel junctions [17][18][19][20][21][22], superconducting films [23] and ferroelectric materials [24] among others. This framework has also been proven to be adequate to shed light on supercritical and subcritical out-of-equilibrium bifurcations performed in optical Kerr-like systems [25] and in thermo-convective systems [26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

The Kibble–Zurek mechanism in a subcritical bifurcation

Miranda¹,

Laroze

González-Viñas

2013

J. Phys.: Condens. Matter

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We present a study of the freezing dynamics of topological defects in a subcritical system by testing the Kibble-Zurek (KZ) mechanism while crossing a tri-stable region in a one-dimensional quintic complex Ginzburg-Landau equation. The critical exponents of the KZ mechanism and the horizon (KZ-scaling regime) are predicted from the quasistatic study, and are in full accordance with the quenched study. The correlation length, in the KZ freezing regime, is corroborated from the number of topological defects and from the spatial correlation function of the order parameter. Furthermore, we characterize the dynamics to differentiate three out-of-equilibrium regimes: the adiabatic, the impulse and the free relaxation. We show that the impulse regime shares a common temporal domain with a fast exponential increase of the order parameter.

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Spontaneous fluxoid formation in superconducting loops

Cited by 95 publications

References 23 publications

Defect Formation in Superconducting Rings: External Fields and Finite-Size Effects

Defect Formation in Superconducting Rings: External Fields and Finite-Size Effects

Kibble-Zurek mechanism and infinitely slow annealing through critical points

The Kibble–Zurek mechanism in a subcritical bifurcation

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