Critical initial-slip scaling for the noisy complex Ginzburg-Landau equation (Q2834785)

A perturbative field-theoretical renormalization group method is used to investigate the universal critical behavior of the dynamics near the continuous non-equilibrium driven-dissipative phase transition in a complex Ginzburg-Landau equation with additive white noise (for wide perspectives on the field, see [\textit{U. C. Täuber}, Critical dynamics -- a field theory approach to equilibrium and non-equilibrium scaling behavior. Cambridge: Cambridge University Press (2014)], or [\textit{A. Kamenev}, Field theory of non-equilibrium systems. Cambridge: Cambridge University Press (2011; Zbl 1267.82003)]). The motivation of this work is to better understand experimental realizations of systems with strong light-matter coupling and a large number of degrees of freedom, which are especially useful for the analysis of phase transitions among distinct non-equilibrium stationary states, as in some Bose-Einstein condensates, arrays of microcavities, certain optomechanical setups, or pumped semiconductor quantum wells inside optical cavities. Also, the paper is a valuable contribution towards the ultimate goal to obtain a complete and systematic classification of non-equilibrium dynamical criticality.NEWLINENEWLINEThe starting point of the paper is a mesoscopic dynamical model based on a noisy, dissipative Gross-Pitaevski partial differential equation (or nonlinear Schrödinger equation) with complex coefficients motivated by experimental studies on driven-dissipative Bose-Einstein condensation [\textit{L. M. Sieberer} et al., ``Nonequilibrium functional renormalization for driven-dissipative Bose-Einstein condensation'', Phys. Rev. B 89, No. 13, Article ID 134310, 34 p. (2014; \url{doi:10.1103/PhysRevB.89.134310})]. Equivalently, this non-equilibrium kinetics can be viewed as a relaxational A model dynamics of a non-conserved complex parameter field originating from a complex-valued Landau-Ginszburg functional [\textit{U. C. Täuber} and \textit{S. Diehl}, ``Perturbative field-theoretical renormalization group approach to driven-dissipative Bose-Einstein criticality'', Phys. Rev. X 4, No. 2, Article ID 021010, 21 p. (2014; \url{doi:10.1103/PhysRevX.4.021010})]. The universal critical behaviour of this system is studied in the early stages of its relaxation from a Gaussian-weighted fully randomized initial state after quenching it into the critical regime. In this critical aging regime, time translation dynamics is broken, and the dynamics is characterized by the stationary static and dynamic critical exponents, as well as in independent ``initial-slip'' exponent, which is the focus of interest of the present work. The main conclusion is that to first order in the dimensional expansion about the upper critical dimension, this initial-slip exponent characterizing the critical aging scaling in the non-equilibrium complex Ginzburg-Landau equation is identical to its equilibrium model A counterpart. This means that quantum coherence effects do not modify this universal scaling exponent with respect to that for the equilibrium system without drive, owing to the temporal locality of the one-loop Feynman diagram or, equivalently, that the phase term in the correlation propagator is annihilated. An alternative demonstration and generalization of this result is proposed by employing the one-loop renormalization group flow equations to construct a suitable complex spherical model A extension indicating that the former conclusion likely remains true to all orders in the perturbation expansion. The paper contains a wide introduction providing a rich view of the problem and its applications.