Local scale-invariances in the bosonic contact and pair-contact processes

Abstract

Local scale-invariance for ageing systems without detailed balance is tested through studying the dynamical symmetries of the critical bosonic contact process and the critical bosonic pair-contact process.Their field-theoretical actions can be split into a Schrödinger-invariant term and a pure noise term. It is shown that the two-time response and correlation functions are reducible to certain multipoint response functions which depend only on the Schrödinger-invariant part of the action. For the bosonic contact process, the representation of the Schrödinger group can be derived from the free diffusion equation, whereas for the bosonic pair-contact process, a new representation of the Schrödinger group related to a non-linear Schrödinger equation with dimensionful couplings is constructed. The resulting predictions of local scale-invariance for the two-time responses and correlators are completely consistent with the exactly-known results in both models.

arXiv commentLatex2e, 28 pp, with IOP macros. A new paragraphe was added in the first section. Version to appear in J. Phys. A: Math. Gen

References in corpus (23)

• Theory of Phase Ordering Kinetics
• SCHRÖdinger Invariance and Strongly Anisotropic Critical Systems
• Ageing Properties of Critical Systems
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Phenomenology of local scale invariance: from conformal invariance to dynamical scaling
• Schr"odinger invariance and space-time symmetries
• Growth Laws for Phase Ordering
• `Real' vs `Imaginary' Noise in Diffusion-Limited Reactions
• Scale and conformal invariance in field theory: a physical counterexample
• Local scale-invariance and ageing in noisy systems
• Speckle from phase ordering systems
• Two-time autocorrelation function in phase-ordering kinetics from local scale-invariance
• Off equilibrium dynamics in the 3d-XY system
• Off equilibrium dynamics in 2d-XY system
• Exact Exponent $\lambda$ of the Autocorrelation Function for a Soluble Model of Coarsening
• Fluctuations in the coarsening dynamics of the O(N) model: are they similar to those in glassy systems?
• Response Functions in Phase Ordering Kinetics
• Corrections to local scale invariance in the non-equilibrium dynamics of critical systems: numerical evidences
• Dynamical symmetries of semi-linear Schrödinger and diffusion equations
• Perturbation Expansion in Phase-Ordering Kinetics: I. Scalar Order Parameter
• Ageing without detailed balance in the bosonic contact and pair-contact processes: exact results
• Phase transitions and correlations in the bosonic pair contact process with diffusion: Exact results
• Phase-ordering kinetics: ageing and local scale-invariance

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• Non-Relativistic Holography -- A Group-Theoretical Perspective
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• Ageing in the contact process: Scaling behavior and universal features
• Slow, bursty dynamics as the consequence of quenched network topologies
• On non-local representations of the ageing algebra
• Ageing in bosonic particle-reaction models with long-range transport
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• Autocorrelation functions in phase-ordering kinetics from local scale-invariance
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• The non-equilibrium response of the critical Ising model: Universal scaling properties and Local Scale Invariance
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