Universality of Phase Transition Dynamics: Topological Defects from Symmetry Breaking

del Campo, Adolfo; Zurek, Wojciech H.

doi:10.48550/arxiv.1310.1600

Cited by 7 publications

(16 citation statements)

References 160 publications

(330 reference statements)

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“…Let us briefly review the KZM [31][32][33]. Consider a system with a second order phase transition at temperature T c , below which a symmetry is spontaneously broken and an order parameter ψ develops a condensate.…”

Section: Introductionmentioning

confidence: 99%

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Defect Formation beyond Kibble-Zurek Mechanism and Holography

Chesler

García-García

Liu³

2015

Phys. Rev. X

121

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We study the dynamic after a smooth quench across a continuous transition from the disordered phase to the ordered phase. Based on scaling ideas, linear response, and the spectrum of unstable modes, we develop a theoretical framework, valid for any second-order phase transition, for the early-time evolution of the condensate in the broken phase. Our analysis unveils a novel period of nonadiabatic evolution after the system passes through the phase transition, where a parametrically large amount of coarsening occurs before a well-defined condensate forms. Our formalism predicts a rate of defect formation parametrically smaller than the Kibble-Zurek prediction and yields a criterion for the breakdown of Kibble-Zurek scaling for sufficiently fast quenches. We numerically test our formalism for a thermal quench in a (2 þ 1)-dimensional holographic superfluid. These findings, of direct relevance in a broad range of fields including cold atom, condensed matter, statistical mechanics, and cosmology, are an important step toward a more quantitative understanding of dynamical phase transitions.

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Section: Introductionmentioning

confidence: 99%

“…While the KZM is only supposed to determine the density of defects up to an O(1) factor, it often significantly overestimates the real density of defects observed in numerical calculations: one needs a "fudge" factor f multiplying ξ freeze with f = O(10) [33]. See also [35] for a recent discussion.…”

Section: Introductionmentioning

confidence: 99%

Defect Formation beyond Kibble-Zurek Mechanism and Holography

Chesler

García-García

Liu³

2015

Phys. Rev. X

121

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“…Given the success of the KZ mechanism [4], and the recent experimental interest it has created, for example [5,6], one may ask whether other scenarios exist that are able to strongly constrain out of equilibrium dynamics using a small set of universal collective modes, leaving an imprint on the macroscopic spatial structure of the system.…”

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confidence: 99%

“…We define the modes to be those which are regular on the future event horizon. 4 In addition we must select the mode which is regular at infinity, so that on the right hand side of the obstacle we require Imk ≥ 0, and on the left, Imk ≤ 0. Of course, a right hand side mode in isolation is not regular because it blows up as x → −∞, but such modes can appear on the right hand side of a regular NESS.…”

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confidence: 99%

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Universal Spatial Structure of Nonequilibrium Steady States

Sonner

Withers

2017

Phys. Rev. Lett.

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We describe a large family of nonequilibrium steady states (NESS) corresponding to forced flows over obstacles. The spatial structure at large distances from the obstacle is shown to be universal, and can be quantitatively characterized in terms of certain collective modes of the strongly coupled many body system, which we define in this work. In holography, these modes are spatial analogues of quasinormal modes, which are known to be responsible for universal aspects of relaxation of time dependent systems. These modes can be both hydrodynamical or nonhydrodynamical in origin. The decay lengths of the hydrodynamic modes are set by η/s, the shear viscosity over entropy density ratio, suggesting a new route to experimentally measuring this ratio. We also point out a new class of nonequilibrium phase transitions, across which the spatial structure of the NESS undergoes a dramatic change, characterized by the properties of the spectrum of these spatial collective modes.

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Breaking symmetry, breaking ground

Hindmarsh¹

2016

J. Phys. A: Math. Theor.

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Topology of cosmic domains and strings [1], written in 1976, launched the field of cosmic topological defects, and was seminal for the enormous expansion in research linking particle physics to cosmology in the last few decades. Topological defects are extended structures in field theories, which exist in continuous ordered media, and are also present in models of particle physics which extend the Standard Model. In our three dimensions of space, these structures may have their energy concentrated around points, lines, or planes. For example, superfluid Helium can support linear structures called vortices, around which the fluid circulates without viscosity. A prototype for the Standard Model of particle physics known as the Georgi-Glashow model exhibits spherically symmetric topological defects from which magnetic field lines emerge -these defects are therefore magnetic monopoles.The paper showed how to predict what topological defects would form at a symmetry-breaking phase transition in the early universe, and also made an estimate of the average separation of the defects. All one needs to know are the symmetries of the ground state before and after the phase transition: the mathematical theory of topology can then be applied to calculate what structures are allowed. More specifically, n-dimensional objects will form in d space dimensions if a certain topological quantity, the homotopy group of order d − n − 1, is non-trivial -that is, is larger than the trivial group consisting of the identity element only.The paper led to some immensely important developments. It was one of the seeds of the theory of cosmic inflation, as the lack of any evidence for magnetic monopoles in the universe meant that there was a contradiction between the idea of Grand Unification of forces (taken very seriously in the late 1970s) and the standard hot Big Bang. Inflation -a period of accelerated expansion -was partly motivated by its feature of diluting any population of monopoles to unobservably low densities [2].Kibble's proposal that linear topological defects -cosmic strings -could produce density perturbations was taken up by Zel'dovich [3] and Vilenkin [4], who used strings to construct a theory of galaxy formation. For a while, strings rivalled the currently accepted one based on the quantum fluctuations during inflation. It is interesting that Kibble himself was pessimistic about cosmic strings having any observable consequence,

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Universality of Phase Transition Dynamics: Topological Defects from Symmetry Breaking

Cited by 7 publications

References 160 publications

Defect Formation beyond Kibble-Zurek Mechanism and Holography

Defect Formation beyond Kibble-Zurek Mechanism and Holography

Universal Spatial Structure of Nonequilibrium Steady States

Breaking symmetry, breaking ground

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