Topological defect

Adiabatic process

Combinatorics

Physics

Universality (dynamical systems)

Topology (electrical circuits)

Mathematics

Topological order

Poisson distribution

Statistical physics

Statistics

Phase transition

Probability distribution

Cumulant

Negative binomial distribution

Merge (version control)

Information retrieval

Geometry

Computer science

Quantum mechanics

Quantum

Scaling

Physical Review Letters

We consider the number distribution of topological defects resulting from the finite-time crossing of a continuous phase transition and identify signatures of universality beyond the mean value, predicted by the Kibble-Zurek mechanism. Statistics of defects follows a binomial distribution with N Bernouilli trials associated with the probability of forming a topological defect at the locations where multiple domains merge. All cumulants of the distribution are predicted to exhibit a common universal power-law scaling with the quench time in which the transition is crossed. Knowledge of the distribution is used to discuss the onset of adiabatic dynamics and bound rare events associated with large deviations.Received 16 December 2019Accepted 28 April 2020DOI:https://doi.org/10.1103/PhysRevLett.124.240602© 2020 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCritical phenomenaPhase transitionsQuantum phase transitionsSecond order phase transitionsSpontaneous symmetry breakingStructural phase transitionTopological defectsVortices in superfluidsPhysical SystemsCollective dynamicsTrapped ionsTechniquesBrownian dynamicsLangevin equationZ_2 symmetryCondensed Matter & Materials PhysicsGeneral PhysicsStatistical Physics

Full Counting Statistics of Topological Defects after Crossing a Phase Transition