Abstract
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 non-adiabatic 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 break-down of Kibble-Zurek scaling for sufficiently fast quenches. We numerically test our formalism for a thermal quench in a 2 + 1 dimensional holographic superfluid. These findings, of direct relevance in a broad range of fields including cold atom, condensed matter, statistical mechanism and cosmology, are an important step towards a more quantitative understanding of dynamical phase transitions.
Highlights
Driving a system smoothly from a disordered to an ordered phase unveils the rich, and still poorly understood, phenomenology of dynamical phase transitions, a research theme of interest in vastly different fields
We develop a formalism to describe a period of nonadiabatic growth of the order parameter ψ after tfreeze
We test the predictions of the previous section by constructing numerical solutions for the time evolution of a (2 þ 1)-dimensional holographic superfluid after a quench across a second-order phase transition
Summary
Driving a system smoothly from a disordered to an ordered phase unveils the rich, and still poorly understood, phenomenology of dynamical phase transitions, a research theme of interest in vastly different fields. Numerical simulations [4,5,6,7,8,9,10,11,12,13,14] have confirmed the spontaneous generation of defects and the scaling exponent of the defect density with the quench rate predicted by the KZM. The KZM has been generalized to quantum phase transitions [15,16,17] and has been employed to compute correlation functions [18] in the scaling region. The system can respond adiabatically to the change in temperature until τeqðtÞ ∼ jtj This condition defines the freeze-out time and length scale. A second motivation of this paper is to test the scaling predicted by the KZM and its refinement in strongly coupled systems using holographic duality. Will verify key features of the coarsening physics discussed .
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