Generating function, path integral representation, and equivalence for stochastic exclusive particle systems

Abstract

We present the path integral representation of the generating function for classical exclusive particle systems. By introducing hard-core bosonic creation and annihilation operators and appropriate commutation relations, we construct the Fock space structure. Using the state vector, the generating function is defined and the master equation of the system is transformed into the equation for the generating function. Finally, the solution of the linear equation for the generating function is derived in the form of the path integral. Applying the formalism, the equivalence of reaction-diffusion processes of single species and two species are described.

References in corpus (16)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Renormalization Group Calculation for the Reaction $kA\to \varnothing$
• The universality class of absorbing phase transitions with a conserved field
• Field Theory of Branching and Annihilating Random Walks
• Absorbing Phase Transitions of Branching-Annihilating Random Walks
• The non-equilibrium phase transition of the pair-contact process with diffusion
• Pair contact process with diffusion - A new type of nonequilibrium critical behavior?
• Novel universality class of absorbing transitions with continuously varying critical exponents
• Non-equilibrium phase transitions in one-dimensional kinetic Ising models
• Cyclically coupled spreading and pair annihilation
• Pair Contact Process with Diffusion: Failure of Master Equation Field Theory
• Phase transition of a two dimensional binary spreading model
• Universality in the pair contact process with diffusion
• Pair contact process with a particle source
• Stochastic cellular automaton for the coagulation-fission-process 2A->3A, 2A->A
• Dynamical mean-field approximation for pair contact process with a particle source

Cited by in corpus (13)

• Towards Classification of Phase Transitions in Reaction--Diffusion Models
• Crossover from the pair contact process with diffusion to directed percolation
• Nontrivial critical crossover between directed percolation models: Effect of infinitely many absorbing states
• Critical decay exponent of the pair contact process with diffusion
• Nonequilibrium Phase Transitions into Absorbing States: Focused around the pair contact process with diffusion
• Crossover from the parity-conserving pair contact process with diffusion to other universality classes
• Three different routes from the directed Ising to the directed percolation class
• Monte Carlo simulations of bosonic reaction-diffusion systems
• A coupled two-species model for the pair contact process with diffusion
• Critical Study on the Absorbing Phase Transition in a Four-State Predator-Prey Model in One Dimension
• Generating Function for Particle-Number Probability Distribution in Directed Percolation
• Universality-class crossover by a nonorder field introduced to the pair contact process with diffusion
• Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach