Vortex String Formation in a 3D U(1) Temperature Quench

Antunes, Nuno D.; Bettencourt, Luís M. A.; Zurek, Wojciech H.

doi:10.1103/physrevlett.82.2824

Cited by 133 publications

(137 citation statements)

References 19 publications

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“…The results show no evidence for the formation of topological defects at the anticipated levels, contrary to expectations based both on the old experiment [8], the theory * and the 3 He data [6,7]. * Although a factor f > ∼ 10 in the formula for the string density n ∼ 1/(fξ) 2 could explain the new results and seems consistent with recent numerical studies [10].…”

Section: Introductioncontrasting

confidence: 50%

“…Below T c , on the other hand strings are exponentially suppressed and only those smaller than the temperature dependent length l ≃ T /σ eff (T ) are likely as thermal fluctuations. It is the existence of long strings as thermal fluctuations that will lead to defect formation if the system is suddenly cooled [10]. Although some of the above comments may seem somewhat marginal they establish that the thermodynamics of the U (1) theory under consideration is much richer than the assumptions on which the traditional role of the Ginzburg regime is based.…”

Section: Fig 1 the Dependence Of The Thermal Distribution Of Vortexmentioning

confidence: 87%

“…τ (ǫ(t)) = η m 2 ǫ νz (t) =t (19) z is another critical exponent whose mean-field value is 2, see [10]. This relation is usually solved by assuming a linear dependence in time for ǫ(t) = t/τ Q , where τ q is the rate of the external quench.…”

Section: B Memory Of the Order Parameter Configuration Near Tcmentioning

confidence: 99%

“…Strings and in particular long strings are inherited from high temperature (higher than T c ) topological fluctuations [10].…”

Section: A Strings Survive the Ginzburg Regimementioning

confidence: 99%

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Ginzburg regime and its effects on topological defect formation

2000

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The Ginzburg temperature has historically been proposed as the energy scale of formation of topological defects at a second order symmetry breaking phase transition. More recently alternative proposals which compute the time of formation of defects from the critical dynamics of the system [5], have been gaining both theoretical and experimental support. We investigate, using a canonical model for string formation, how these two pictures compare. In particular we show that prolonged exposure of a critical field configuration to the Ginzburg regime results in no substantial suppression of the final density of defects formed. These results dismiss the recently proposed role of the Ginzburg regime in explaining the absence of topological defects in 4 He pressure quench experiments.

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Section: Introductioncontrasting

confidence: 50%

Section: Fig 1 the Dependence Of The Thermal Distribution Of Vortexmentioning

confidence: 87%

Section: B Memory Of the Order Parameter Configuration Near Tcmentioning

confidence: 99%

“…Strings and in particular long strings are inherited from high temperature (higher than T c ) topological fluctuations [10].…”

Section: A Strings Survive the Ginzburg Regimementioning

confidence: 99%

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Ginzburg regime and its effects on topological defect formation

2000

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“…Computational simulations as well as numerical studies have confirmed the exponents given in both scaling laws [6,7]. The latter scaling exponent relating to defect annihilation has been confirmed experimentally -also using liquid crystals [8,9].…”

supporting

confidence: 53%

Kibble–Zurek Scaling during Defect Formation in a Nematic Liquid Crystal

Fowler

Dierking

2017

ChemPhysChem

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Symmetry breaking phase transitions are often accompanied by the formation of topological defects, like in cosmological theories of the early universe, superfluids, liquid crystals or solid state systems. This scenario is described by the Kibble-Zurek mechanism, which predicts respective scaling laws for the defect density ρ. One such scaling law suggests a relation ~ Q -1/2 with  Q the change of rate of a control parameter. In contrast to the scaling of the defect density during annihilation with ρ~t -1 , which is governed by the attraction of defects of the same strength but opposite sign, the defect formation process, which depends on the rate of change of a physical quantity initiating the transition, is only very scarcely investigated. We here use nematic liquid crystals as a different system to demonstrate the validity of the predicted scaling relation for defect formation. It is found that the scaling exponent is independent of temperature and material employed, thus universal, as predicted.Topological defects[1] are often generated following symmetry breaking phase transitions in many aspects of physics including cosmology, superfluids and liquid crystals. Kibble proposed a universal mechanism by which cosmological defects were formed in the early universe as it expanded and cooled shortly after the Big Bang[2.3]. During a cosmological symmetry breaking phase transition, uncorrelated domains with randomly determined order are produced which subsequently coalesce. Defects are formed that exist between two domains with non-compatible order. The initial density of defects is dependent on the rate at which domains grow which is limited by the finite speed of information transmission (causality). It became known as the "Kibble-Zurek mechanism" after Zurek suggested that

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Brownian motion: a paradigm of soft matter and biological physics

Frey¹,

Kroy²

2005

Ann. Phys.

205

165

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This is a pedagogical introduction to Brownian motion on the occasion of the 100th anniversary of Einstein's 1905 paper on the subject. After briefly reviewing Einstein's work in its contemporary context, we pursue some lines of further developments and applications in soft condensed matter and biology. Over the last century Brownian motion became promoted from an odd curiosity of marginal scientific interest to a guiding theme pervading all of the modern (live) sciences.

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Vortex String Formation in a 3D U(1) Temperature Quench

Cited by 133 publications

References 19 publications

Ginzburg regime and its effects on topological defect formation

Ginzburg regime and its effects on topological defect formation

Kibble–Zurek Scaling during Defect Formation in a Nematic Liquid Crystal

Brownian motion: a paradigm of soft matter and biological physics

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