Approximate calculation of functional integrals arising from the operator approach

Abstract

We apply the operator approach to a stochastic system belonging to a class of death-birth processes, which we introduce utilizing the master equation approach. By employing Doi- Peliti formalism we recast the master equation in the form of a Schrödinger-like equation. Therein appearing pseudo-Hamiltonian is conveniently expressed in a suitable Fock space, constructed using bosonic-like creation and annihilation operators. The kernel of the associated time evolution operator is rewritten using a functional integral, for which we propose an approximate method that allows its analytical treatment. The method is based on the expansion in eigenfunctions of the Hamiltonian generating given functional integral. In this manner, we obtain approximate values for the probabilities of the system being in the first and second states for the case of the pure birth process.

References in corpus (16)

• Power laws, Pareto distributions and Zipf's law
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Rare Events Statistics in Reaction--Diffusion Systems
• Spectral theory of metastability and extinction in birth-death systems
• Towards Classification of Phase Transitions in Reaction--Diffusion Models
• Metastability in a stochastic neural network modeled as a velocity jump Markov process
• Path Integrals and Perturbation Theory for Stochastic Processes
• Survival probability of a diffusing test particle in a system of coagulating and annihilating random walkers
• Field-theoretic approach to the universality of branching processes
• Model A of critical dynamics: 5-loop $\epsilon$ expansion study
• Anomalous Dimension in a Two-Species Reaction-Diffusion System
• Study of Anomalous Kinetics of The Annihilation Reaction A+A->0
• Field-theoretic technique for irreversible reaction processes
• Construction of stochastic hybrid path integrals using "quantum-mechanical'' operators
• Advanced field-theoretical methods in stochastic dynamics and theory of developed turbulence
• Operator Approach to the Master Equation for the One-Step Process