• Corpus ID: 232233346

Path integrals for stochastic hybrid reaction-diffusion processes

@inproceedings{Bressloff2021PathIF,
  title={Path integrals for stochastic hybrid reaction-diffusion processes},
  author={Paul C. Bressloff},
  year={2021}
}
We construct a functional path integral for a stochastic hybrid reaction-diffusion (RD) equation, in which the reaction term depends on the discrete state of a randomly switching environment. We proceed by spatially discretizing the RD system and using operator methods and coherent spin states to derive a path integral representation of the lattice model. The path integral specifies the distribution of trajectories in a state-space consisting of the set of local concentrations and the… 

Figures from this paper

References

SHOWING 1-10 OF 89 REFERENCES
Spin coherent states and stochastic hybrid path integrals
Stochastic hybrid systems involve a coupling between a discrete Markov chain and a continuous stochastic process. If the latter evolves deterministically between jumps in the discrete state, then the
Coherent spin states and stochastic hybrid path integrals
TLDR
The path integral is used to derive a system of Langevin equations in the semi-classical limit, which extends previous diffusion approximations based on a quasi-steady-state reduction and is equivalent to an alternative representation that was previously derived using Doi–Peliti operators.
Path integrals and large deviations in stochastic hybrid systems.
  • P. Bressloff, J. Newby
  • Mathematics, Medicine
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2014
TLDR
This work constructs a path-integral representation of solutions to a stochastic hybrid system, consisting of one or more continuous variables evolving according to a piecewise-deterministic dynamics, and derives a large deviation action principle from this representation to derive the optimal paths of escape from a metastable state in a bistable neural network.
Moment equations for a piecewise deterministic PDE
We analyze a piecewise deterministic PDE consisting of the diffusion equation on a finite interval ? with randomly switching boundary conditions and diffusion coefficient. We proceed by spatially
Construction of stochastic hybrid path integrals using operator methods
  • P. Bressloff
  • Physics, Biology
    Journal of Physics A: Mathematical and Theoretical
  • 2021
TLDR
This paper presents an alternative derivation of the path integral based on operator methods, and shows how this provides a more efficient and flexible framework for constructing hybrid path integrals in the weak noise limit.
The Diffusion Limit of Transport Equations Derived from Velocity-Jump Processes
TLDR
It is shown that under an appropriate scaling of space and time the asymptotic behavior of solutions of such equations can be approximated by the solution of a diffusion equation obtained via a regular perturbation expansion.
On the Hamiltonian structure of large deviations in stochastic hybrid systems
TLDR
The connection between large deviation theory and more applied approaches to stochastic hybrid systems is developed by highlighting a common underlying Hamiltonian structure by evaluating the rate function of a large deviation principle in terms of a classical action, whose Hamiltonian is given by the Perron eigenvalue of a linear equation.
Construction of stochastic hybrid path integrals using "quantum-mechanical'' operators.
Stochastic hybrid systems involve the coupling between discrete and continuous stochastic processes. They are finding increasing applications in cell biology, ranging from modeling promoter noise in
Diffusive transport in the presence of stochastically gated absorption.
TLDR
This work focuses on how stochastic gating affects the attenuation of particle absorption with distance from a localized source in a one-dimensional domain and shows that gating leads to slower, nonexponential attenuation.
Path-Integral Methods for Analyzing the Effects of Fluctuations in Stochastic Hybrid Neural Networks
  • P. Bressloff
  • Physics, Medicine
    Journal of mathematical neuroscience
  • 2015
TLDR
A variational principle for maximum-likelihood paths of escape from a metastable state (large deviations in the small noise limit ϵ→0$\epsilon\rightarrow0$) is derived and the resulting Langevin equation can be used to analyze the effects of fluctuations within the basin of attraction of a metastables state, ignoring theeffects of large deviations.
...
1
2
3
4
5
...