Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Effective action for stochastic partial differential equations.

D Hochberg1, C Molina-París, J Pérez-Mercader

  • 1Laboratorio de Astrofísica Espacial y Física Fundamental, Apartado 50727, 28080 Madrid, Spain. hochberg@laeff.esa.es

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

A turn for the worse: The impact of deteriorating healthcare spending in South Africa.

South African medical journal = Suid-Afrikaanse tydskrif vir geneeskunde·2026
Same author

Insights into the heterogeneity of pneumococcal polysaccharide vaccine immunogenicity in older adults.

Immunity & ageing : I & A·2026
Same author

Hospital readmission after surviving sepsis: An analysis of infection recurrence, risk factors and long-term survival.

Journal of critical care·2026
Same author

Enacted and internalized stigma as predictors of successful treatment outcome among newly diagnosed tuberculosis patients in Gauteng, South Africa.

Frontiers in psychology·2026
Same author

The ANCog: A French self-report scale for assessing subjective cognitive complaints in rehabilitation samples.

Psychiatry research·2025
Same author

Histamine Dynamics During Ingestive Behavior Measured by the Novel Biosensor HisLightG.

Journal of neurochemistry·2025
Same journal

Efficient Monte Carlo simulations using a shuffled nested Weyl sequence random number generator.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics·2002
Same journal

Spatiotemporal dynamics of electromagnetic pulses in saturating nonlinear optical media with normal group velocity dispersion.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics·2002
Same journal

Soliton-breather reaction pathways.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics·2002
Same journal

Calculation of electromagnetic properties of regular and random arrays of metallic and dielectric cylinders.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics·2002
Same journal

Electromagnetic convective cells in a nonuniform dusty plasma.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics·2002
Same journal

Stability of neural networks and solitons of field theory.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics·2002
See all related articles

This study introduces a functional integral method to analyze one-loop physics in stochastic partial differential equations (SPDEs) with Gaussian noise. It establishes a framework for extracting effective actions and potentials, drawing parallels with quantum field theory (QFT).

Area of Science:

  • Mathematical Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • Stochastic partial differential equations (SPDEs) are crucial for modeling complex systems with inherent randomness, such as turbulence and pattern formation.
  • Existing research shows connections between certain SPDEs and non-quantum field theories with links to quantum field theory (QFT).
  • A systematic extension of these ideas is needed to fully exploit the relationship between SPDEs and field theories.

Purpose of the Study:

  • To develop a functional integral formalism for extracting one-loop physics from arbitrary SPDEs with Gaussian noise.
  • To demonstrate how to define and compute the effective action and effective potential for SPDEs.
  • To explore the physical interpretation and QFT-analogous features of these quantities in the SPDE context.

Related Experiment Videos

Main Methods:

  • Establishment of a functional integral formalism for the characteristic functional (partition function) of SPDEs.
  • Systematic extraction of all one-loop physics for arbitrary SPDEs subjected to arbitrary Gaussian noise.
  • Application of zeta function technology for finiteness at one loop, enabling a minimalist approach using physical fields.
  • Derivation of the one-loop effective action and its specialization to the effective potential for constant fields.

Main Results:

  • A general method is presented to extract one-loop physics from any SPDE with Gaussian noise.
  • The amplitude of the noise's two-point function is identified as the loop-counting parameter, analogous to Planck's constant in QFT.
  • A general expression for the one-loop effective potential of SPDEs with translation-invariant Gaussian noise is derived.
  • Key features of effective actions and potentials in QFT are shown to carry over to SPDEs.

Conclusions:

  • The developed functional integral formalism provides a powerful tool for analyzing SPDEs, particularly at one-loop order.
  • The analogy with QFT is strengthened by the identification of the noise amplitude as a loop-counting parameter and the carry-over of effective action concepts.
  • This work offers a minimalist and technically advantageous approach to understanding the physics of interacting, non-Gaussian fluctuations in SPDEs.