Pattern formation from Gauge/Gravity Duality

Abstract

In the framework of the AdS/CFT correspondence, we find a neutral complex scalar field dynamics in a $2+1$ dimensional black hole background which can provide a scheme for studying the pattern formation process in $1+1$ dimensional reaction-diffusion systems. The patterns include plane wave, defect turbulence, phase turbulence, spatio-temporal intermittency where defect chaos coexists with stable plane wave, and coherent structures. A phase diagram is obtained by studying the linear instability of the plane wave solutions to determine the onset of the holographic version of the BFN instability. Near the critical temperature the holographic model is dual to the one-dimensional complex Ginzburg-Landau equation (CGLE), which has been studied extensively in reaction-diffusion systems. While at low temperature the holographic theory is different from CGLE.

arXiv comment8 pages,6 figures

References in corpus (21)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• The World of the Complex Ginzburg-Landau Equation
• Building an AdS/CFT superconductor
• Breaking an Abelian gauge symmetry near a black hole horizon
• Quasinormal Modes of AdS Black Holes and the Approach to Thermal Equilibrium
• Quasinormal modes and holography
• Holographic model of superfluidity
• An introduction to the Ginzburg-Landau theory of phase transitions and nonequilibrium patterns
• Disordered Regimes of the one-dimensional complex Ginzburg-Landau equation
• Quantum phase transitions in holographic models of magnetism and superconductors
• Holographic Superfluids and the Dynamics of Symmetry Breaking
• Modulated Amplitude Waves and the Transition from Phase to Defect Chaos
• Modulated Amplitude Waves and Defect Formation in the One-Dimensional Complex Ginzburg-Landau Equation
• Bekki-Nozaki Amplitude Holes in Hydrothermal Nonlinear Waves
• Vortex motion quantifies strong dissipation in a holographic superfluid
• Dynamical Phase Transition from Nonequilibrium Dynamics of Dark Solitons
• Heating up quadruply quantized vortices: Splitting patterns and dynamical transitions
• Dynamical evolution of spinodal decomposition in holographic superfluids
• Structural phase transition and its critical dynamics from holography
• Universal Critical Exponents of Non-Equilibrium Phase Transitions from Holography