Renormalization Group Calculation for the Reaction $kA\to \varnothing$

Abstract

The diffusion-controlled reaction $kA\to \varnothing$ is known to be strongly dependent on fluctuations in dimensions $d\le d_c=2/(k-1)$. We develop a field theoretic renormalization group approach to this system which allows explicit calculation of the observables as expansions in ${\epsilon }^{1/(k-1)}$, where $\epsilon =d_c-d$. For the density it is found that, asymptotically, $n\sim A_k{t}^{-d/2}$. The decay exponent is exact to all orders in $\epsilon$, and the amplitude $A_k$ is universal, and is calculated to second order in ${\epsilon }^{1/(k-1)}$ for $k=2,3$. The correlation function is calculated to first order, along with a long wavelength expansion for the second order term. For $d=d_c$ we find $n\sim A_k(\ln t/t{)}^{1/(k-1)}$ with an exact expression for $A_k$. The formalism can be immediately generalized to the reaction $kA\to \ell A$, $\ell <k$, with the consequence that the density exponent is the same, but the amplitude is modified.

24 pages (harvmac), 8 figures appended, OUTP-93-39S

References in corpus (1)

• Exact Results for a Three-Body Reaction-Diffusion System

Cited by in corpus (159)

• Universality classes in nonequilibrium lattice systems
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Theory of Branching and Annihilating Random Walks
• Rare Events Statistics in Reaction--Diffusion Systems
• Field Theory of Branching and Annihilating Random Walks
• Effects of Fluctuations on Propagating Fronts
• The Field Theory Approach to Percolation Processes
• Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction
• Entanglement and dynamics of diffusion-annihilation processes with Majorana defects
• Master equations and the theory of stochastic path integrals
• `Real' vs `Imaginary' Noise in Diffusion-Limited Reactions
• Diffusion-annihilation processes in complex networks
• Critical properties of the reaction - diffusion model 2A -> 3A, 2A ->0
• Scaling of Reaction Zones in the A+B->0 Diffusion-Limited Reaction
• The non-equilibrium phase transition of the pair-contact process with diffusion
• The Reaction-Diffusion Front for $A+B\to \varnothing$ in One Dimension
• Anomalous diffusion with absorption: Exact time-dependent solutions
• Towards Classification of Phase Transitions in Reaction--Diffusion Models
• Dynamics of Nonequilibrium Deposition
• Field Theory Approaches to Nonequilibrium Dynamics
• Coarsening and persistence in a class of stochastic processes interpolating between the Ising and voter models
• Non-equilibrium Phase Transitions with Long-Range Interactions
• On the nature of different types of absorbing states
• Population oscillations in spatial stochastic Lotka-Volterra models: A field-theoretic perturbational analysis
• FLUCTUATION EFFECTS AND MULTISCALING OF THE REACTION-DIFFUSION FRONT FOR A+B->0
• Proportion of Unaffected Sites in a Reaction-Diffusion Process
• Smooth Phases, Roughening Transitions and Novel Exponents in One-dimensional Growth Models
• Bosonic reaction-diffusion processes on scale-free networks
• Brownian motion: a paradigm of soft matter and biological physics
• Multicritical behavior in coupled directed percolation processes
• Phase Transitions and Scaling in Systems Far From Equilibrium
• Fluctuation Kinetics in a Multispecies Reaction-Diffusion System
• Formal Solution of a Class of Reaction-Diffusion Models: Reduction to a Single-Particle Problem
• Activated aging dynamics and negative fluctuation-dissipation ratios
• Measurement of a reaction-diffusion crossover in exciton-exciton recombination inside carbon nanotubes using femtosecond optical absorption
• Disorder-Induced Anomalous Kinetics in the $A+A\to \varnothing$ Reaction
• Reaction Diffusion Models in One Dimension with Disorder
• Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem
• Asymptotic form of the approach to equilibrium in reversible recombination reactions
• Universal finite-size scaling amplitudes in anisotropic scaling
• Novel non-equilibrium critical behavior in unidirectionally coupled stochastic processes
• Pair Contact Process with Diffusion: Failure of Master Equation Field Theory
• Persistence in the Voter model: continuum reaction-diffusion approach
• Cluster-Cluster Aggregation as an Analogue of a Turbulent Cascade : Kolmogorov Phenomenology, Scaling Laws and the Breakdown of self-similarity
• Algebraic coarsening in voter models with intermediate states
• The binding dynamics of tropomyosin on actin
• Branching and annihilating Levy flights
• Ageing in the critical contact process: a Monte Carlo study
• Non-equilibrium dynamics of spin facilitated glass models
• Persistence properties of a system of coagulating and annihilating random walkers
• Multi-Scaling of the $n$-point density function for coalescing Brownian motions
• Does hardcore interaction change absorbing type critical phenomena?
• A renormalization group study of a class of reaction-diffusion model, with particles input
• Phase transition of a two dimensional binary spreading model
• Anomalous relaxation kinetics of biological lattice-ligand binding models
• Collective Particle Flow through Random Media
• Critical behavior of an even offspringed branching and annihilating random walk cellular automaton with spatial disorder
• Breakdown of Kolmogorov scaling in models of cluster aggregation with deposition
• Driven Pair Contact Process with Diffusion
• First-Passage Exponents of Multiple Random Walks
• Similarity transformation in one-dimensional reaction-diffusion systems; voting model as an example
• The Effect of Static Disorder and Reactant Segregation on the $A+B\to \varnothing$ Reaction
• Stochastic spatial models in ecology: a statistical physics approach
• On the universality of a class of annihilation-coagulation models
• Reaction-diffusion processes and non-perturbative renormalisation group
• Phase transition classes in triplet and quadruplet reaction diffusion models
• Large scale emergent properties of an autocatalytic reaction-diffusion model subject to noise
• Long Range Hops and the Pair Annihilation Reaction A+A->0: Renormalization Group and Simulation
• Survival probability of a diffusing test particle in a system of coagulating and annihilating random walkers
• Multi-species pair annihilation reactions
• Fluctuation-dissipation relations in plaquette spin systems with multi-stage relaxation
• Diffusion-limited Reactions of hard-core Particles in one-dimension
• Imaginary noise and parity conservation in the reaction A+A <--> 0
• Slow Coarsening in an Ising Chain with Competing Interactions
• Interfacial Reactions: Mixed Order Kinetics and Segregation Effects
• On the Validity of the Law of Mass Action in Three-Dimensional Coagulation Processes
• Symmetry and species segregation in diffusion-limited pair annihilation
• Critical behaviour of annihilating random walk of two species with exclusion in one dimension
• The one-dimensional contact process: duality and renormalisation
• The A+B -> 0 annihilation reaction in a quenched random velocity field
• Path-Integral Formulation of Stochastic Processes for the Exclusive Particle Systems
• Persistence in the One-Dimensional A+B -> 0 Reaction-Diffusion Model
• Apparent Rate Constant for Diffusion-Controlled Three molecular (catalytic) reaction
• Kang-Redner Anomaly in Cluster-Cluster Aggregation
• Some exact results in branching and annihilating random walks
• Anomalous Dimension in a Two-Species Reaction-Diffusion System
• Large-scale universality in quantum reaction-diffusion from Keldysh field theory
• Critical branching-annihilating random walk of two species
• The Reaction Process A+A->O in Sinai Disorder
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Cluster mean-field approximations with the coherent-anomaly-method analysis for the driven pair contact process with diffusion
• Generating function, path integral representation, and equivalence for stochastic exclusive particle systems
• Branching-annihilating random walks in one dimension: Some exact results
• Stochastic Aggregation of Point Particles Revisited
• Reaction, Levy Flights, and Quenched Disorder
• Reactive Turbulent Flow in Low-Dimensional, Disordered Media
• Photon pair condensation by engineered dissipation
• Numerical Observation of Disorder-Induced Anomalous Kinetics in the A + A -> 0 Reaction
• Multi-Scaling of Correlation Functions in Single Species Reaction-Diffusion Systems
• Annihilating random walks in one-dimensional disordered media
• Segregation in diffusion-limited multispecies pair annihilation
• Surface Critical Behavior in Systems with Non-Equilibrium Phase Transitions
• Exact correlations in the one-dimensional coagulation-diffusion process by the empty-interval method
• Diffusion-annihilation proecesses in weighted scale-free networks with identical degree sequence
• Field theoretic renormalization group for a nonlinear diffusion equation
• Fluctuation Effects in Steric Reaction-Diffusion Systems
• Correlated Initial Conditions in Directed Percolation
• Study of Anomalous Kinetics of The Annihilation Reaction A+A->0
• Application of the Bogolyubov's theory of weakly non-ideal Bose gas on the A+A, A+B, B+B reaction-diffusion system
• Vicious Lévy flights
• Two-Species Reaction-Diffusion System with Equal Diffusion Constants: Anomalous Density Decay at Large Times
• Encounter-controlled coalescence and annihilation on a one-dimensional growing domain
• Three-Species Diffusion-Limited Reaction with Continuous Density-Decay Exponents
• Shear Flows and Segregation in the Reaction $A+B\to \varnothing$
• Field-theoretic technique for irreversible reaction processes
• Two-point correlation functions of the diffusion-limited annihilation in one dimension
• Field-theoretic methods
• $A+A\to \varnothing$ model with a bias towards nearest neighbor
• Ionic Reactions in Two Dimensions with Disorder
• Criticality in a Vlasov-Poisson system - a fermionic universality class
• Two-loop calculation of anomalous kinetics of the reaction $A+A\to \varnothing$ in randomly stirred fluid
• Phase transitions of the binary production 2A->3A, 4A->0 model
• Branching annihilating random walks with parity conservation on a square lattice
• Two-Dimensional Diffusion in the Presence of Topological Disorder
• Path-integral representation for a stochastic sandpile
• Monte Carlo simulations of bosonic reaction-diffusion systems
• Numerical Simulation of the Trapping Reaction with Mobile and Reacting Traps
• Boundary effects in reaction-diffusion processes
• Field theories and quantum methods for stochastic reaction-diffusion systems
• Long-Range and Many-Body Effects in Coagulation Processes
• Monte Carlo simulations of bosonic reaction-diffusion systems and comparison to Langevin equation description
• ``Superfast'' Reaction in Turbulent Flow with Potential Disorder
• Single-Species Three-Particle Reactions in One Dimension
• Reaction-controlled diffusion
• One-dimensional annihilating random walk with long-range interaction
• Coherent State path-integral simulation of many particle systems
• Persistence in q-state Potts model: A Mean-Field approach
• Reaction-controlled diffusion: Monte Carlo simulations
• Effect of bias in a reaction diffusion system in two dimensions
• Reaction Diffusion and Ballistic Annihilation Near an Impenetrable Boundary
• One-dimensional spin-anisotropic kinetic Ising model subject to quenched disorder
• Fluctuation Effects in the Pair-Annihilation Process with Lévy Dynamics
• Kinetic Regimes and Cross-Over Times in Many-Particle Reacting Systems
• Effects of intrinsic noise on a cubic autocatalytic reaction diffusion system
• Reaction-diffusion on the fully-connected lattice: $A+A\to A$
• Reaction Diffusion Systems and Extensions of Quantum Stochastic Processes
• Computing macroscopic reaction rates in reaction-diffusion systems using Monte Carlo simulations
• Reaction-diffusion dynamics of the weakly dissipative Fermi gas
• Ordering statistics of 4 random walkers on the line
• Absorbing state phase transitions with a non-accessible vacuum
• Kinetics of Quantum Reaction-Diffusion systems
• Corrections to reaction-diffusion dynamics above the upper critical dimension
• Reaction-diffusion with a time-dependent reaction rate: the single-species diffusion-annihilation process
• Dispersion Coefficients by a Field-Theoretic Renormalization of Fluid Mechanics
• Path integral evaluation of the one-loop effective potential in field theory of diffusion-limited reactions
• Scaling properties of one-dimensional cluster-cluster aggregation with Levy diffusion
• Two-species reaction-diffusion system in the presence of random velocity fluctuations
• Effect of Compressibility on the Annihilation Process
• Approximate calculation of functional integrals arising from the operator approach