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Composite Molecules and Decoupling in Reaction Diffusion Models
John F. Dawson, Fred Cooper, Bogdan Mihaila
The Gray-Scott model can be thought of as an effective theory at large spatiotemporal scales coming from a more fundamental theory valid at shorter spatiotemporal scales. The more…
Auxiliary Field Loop Expansion of the Effective Action for Stochastic Partial Differential Equations
Fred Cooper, John F. Dawson
We present an alternative to the perturbative diagrammatic approach for studying stochastic dynamics. Our approach is based on an auxiliary field loop expansion for the path integr…
Auxiliary Field Loop expansion for the Effective Action for Stochastic Partial Differential equations II
Fred Cooper
We extend our discussion of effective actions for stochastic partial differential equations to systems that give rise to a Martin-Siggia-Rose (MSR) type of action. This type of act…
Auxiliary Field Loop Expansion for the Effective Action for Stochastic Partial Differential Equations I
Fred Cooper
Using a path integral formulation for correlation functions of stochastic partial differential equations based on the Onsager-Machlup approach, we show how, by introducing a compos…
Effects of intrinsic noise on a cubic autocatalytic reaction diffusion system
Fred Cooper, Gourab Ghoshal, Juan Pérez-Mercader
Starting from our recent chemical master equation derivation of the model of an autocatalytic reaction-diffusion chemical system with reactions $U+2V {\stackrel {λ_0}{\rightarrow}}…
Composite Bound States and Broken U(1) symmetry in the Chemical Master Equation derivation of the Gray-Scott Model
Fred Cooper, Gourab Ghoshal, Juan Pérez-Mercader
We give a first principles derivation of the stochastic partial differential equations that describe the chemical reactions of the Gray-Scott model (GS): $U+2V {\stackrel λ{\righta…