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

Abstract

We employ the perturbative field-theoretic renormalization group method to investigate the universal critical behavior near the continuous non-equilibrium phase transition in the complex Ginzburg-Landau equation with additive white noise. This stochastic partial differential describes a remarkably wide range of physical systems: coupled non-linear oscillators subject to external noise near a Hopf bifurcation instability; spontaneous structure formation in non-equilibrium systems, e.g., in cyclically competing populations; and driven-dissipative Bose--Einstein condensation, realized in open systems on the interface of quantum optics and many-body physics, such as cold atomic gases and exciton-polaritons in pumped semiconductor quantum wells in optical cavities. Our starting point is a noisy, dissipative Gross-Pitaevski or non-linear Schrödinger equation, or equivalently purely relaxational kinetics originating from a complex-valued Landau-Ginzburg functional, which generalizes the standard equilibrium model A critical dynamics of a non-conserved complex order parameter field. We study the universal critical behavior of this system in the early stages of its relaxation from a Gaussian-weighted fully randomized initial state. In this critical aging regime, time translation invariance is broken, and the dynamics is characterized by the stationary static and dynamic critical exponents, as well as an independent `initial-slip' exponent. We show that to first order in the dimensional expansion about the upper critical dimension, this initial-slip exponent in the complex Ginzburg-Landau equation is identical to its equilibrium model A counterpart. We furthermore employ the renormalization group flow equations as well as construct a suitable complex spherical model extension to argue that this conclusion likely remains true to all orders in the perturbation expansion.

arXiv comment18 pages, 4 figures

References in corpus (27)

• Quantum fluids of light
• The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
• Cold atoms in cavity-generated dynamical optical potentials
• Quantised Vortices in an Exciton-Polariton Fluid
• Quantum Many-Body Phenomena in Coupled Cavity Arrays
• Dynamical Critical Phenomena in Driven-Dissipative Systems
• Quantum many-body dynamics in optomechanical arrays
• Circuit QED lattices: towards quantum simulation with superconducting circuits
• Ageing Properties of Critical Systems
• Slowing and stopping light using an optomechanical crystal array
• Generalized Dynamic Scaling for Critical Magnetic Systems
• Real-time observation of fluctuations at the driven-dissipative Dicke phase transition
• Energy Relaxation in a 1-D Polariton Condensate
• Non-equilibrium Functional Renormalization for Driven-Dissipative Bose-Einstein Condensation
• Universal correlators and distributions as experimental signatures of 2+1 Kardar-Parisi-Zhang growth
• Perturbative Field-Theoretical Renormalization Group Approach to Driven-Dissipative Bose-Einstein Criticality
• Phenomenology of ageing in the Kardar-Parisi-Zhang equation
• The effects of violating detailed balance on critical dynamics
• Non-equilibrium relaxation in a stochastic lattice Lotka-Volterra model
• Slow relaxation and aging kinetics for the driven lattice gas
• Ageing in the critical contact process: a Monte Carlo study
• Universal critical behavior of noisy coupled oscillators: A renormalization group study
• Universal short-time dynamics: boundary functional renormalization group for a temperature quench
• Short-time scaling behavior of growing interfaces
• Non-equilibrium relaxation and critical aging for driven Ising lattice gases
• Spherical model of growing interfaces
• Ageing of the 2+1 dimensional Kardar-Parisi-Zhang model

Cited by in corpus (7)

• Universal short time quantum critical dynamics of finite size systems
• Dynamic scaling of the restoration of rotational symmetry in Heisenberg quantum antiferromagnets
• Renormalization Group in the Problem of Active Scalar Advection
• Short-imaginary-time quantum critical dynamics in the J-Q${}_3$ spin chain
• Random Walk on a Random Surface: Implications of Non-perturbative Concepts and Dynamical Emergence of Galilean Symmetry
• Noise crosscorrelations can induce instabilities in coupled driven models
• Short-time dynamics in phase-ordering kinetics