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

Abstract

We employ the perturbative fieldtheoretic 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 nonlinear 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 nonlinear 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 aboutmore » the upper critical dimension, this initial-slip exponent in the complex Ginzburg–Landau equation is identical to its equilibrium model A counterpart. Here, 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.« less

Authors:

Liu, Weigang ^[1]; Täuber, Uwe C. ^[1]

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+ Show Author Affiliations

1. Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

Publication Date:

Mon Oct 03 00:00:00 EDT 2016

Research Org.:

Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:

1855178

Alternate Identifier(s):

OSTI ID: 1328220

Grant/Contract Number:  

FG02-09ER46613; SC0002308

Resource Type:

Accepted Manuscript

Journal Name:

Journal of Physics. A, Mathematical and Theoretical

Additional Journal Information:

Journal Volume: 49; Journal Issue: 43; Journal ID: ISSN 1751-8113

Publisher:

IOP Publishing

Country of Publication:

United States

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING; critical aging; non-equilibrium relaxation; complex Ginzburg–Landau equation; driven-dissipative Bose–Einstein condensation; renormalization group