General Conclusion

  • Malo TarpinEmail author
Part of the Springer Theses book series (Springer Theses)


This manuscript describes the application of the tools of the NPRG framework to two out-of-equilibrium systems. On the one hand, we used the modified local potential approximation to investigate the absorbing phase transition occurring in the diffusive epidemic process and its coarse-grained counterpart, the directed percolation with a conserved quantity. On the other hand, we investigated the large wave-number expansion of the exact RG flow equation of the correlation functions in fully developed turbulence.


  1. Bec J, Khanin K (2007) Burgers turbulence. Phys Rep 447(1):1–66. Scholar
  2. Benitez F et al (2016) Langevin equations for reaction-diffusion processes. Phys Rev Lett 117(10):100601. Scholar
  3. Canet L et al (2011) Nonperturbative renormalization group for the Kardar-Parisi-Zhang equation: general framework and first applications. Phys Rev E 84(6):061128. Scholar
  4. Canet L, Delamotte B, Wschebor N (2016) Fully developed isotropic turbulence: nonperturbative renormalization group formalism and fixed-point solution. Phys Rev E 93(6):063101. Scholar
  5. Canet L et al (2017) Spatiotemporal velocity-velocity correlation function in fully developed turbulence. Phys Rev E 95(2):023107. Scholar
  6. Chaturvedi S, Gardiner CW (1978) The Poisson representation. II two-time correlation functions. J Stat Phys 18(5):501–522.
  7. Droz M, McKane A (1994) Equivalence between Poisson representation and Fock space formalism for birth-death processes. J Phys A: Math Gen 27(13):L467ADSMathSciNetCrossRefGoogle Scholar
  8. Drummond PD (2004) Gauge Poisson representations for birth/death master equations. Eur Phys J B - Condens Matter Complex Syst 38(4):617–634. Scholar
  9. Gardiner CW (2009) Stochastic methods, 4th edn. Springer, BerlinzbMATHGoogle Scholar
  10. Gardiner CW, Chaturvedi S (1977) The Poisson representation. I. A new technique for chemical master equations. J Stat Phys 17(6):429.
  11. Guioth J, Lecomte V, Tarpin M Comparing different constructions of field theories for interacting particle systems (in prep.)Google Scholar
  12. Howard MJ, Täuber UC (1997) ‘Real’ versus ‘imaginary’ noise in diffusion-limited reactions. J Phys A: Math Gen 30(22):7721ADSMathSciNetCrossRefGoogle Scholar
  13. Lohse D, Müller-Groeling A (1995) Bottleneck effects in turbulence: scaling phenomena in \(r\) versus \(p\) space. Phys Rev Lett 74(10):1747–1750. Scholar
  14. Muñoz MA (1998) Nature of different types of absorbing states. Phys Rev E 57(2):1377–1383. Scholar
  15. Pagani C (2015) Functional renormalization group approach to the Kraichnan model. Phys Rev E 92(3):033016. Scholar
  16. Tarpin M, Canet L, Wschebor N (2018) Breaking of scale invariance in the time dependence of correlation functions in isotropic and homogeneous turbulence. Phys Fluids 30(5):055102. Scholar
  17. Wiese KJ (2016) Coherent-state path integral versus coarse-grained effective stochastic equation of motion: from reaction diffusion to stochastic sandpiles. Phys Rev E 93(27):042117. Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institut für Theoretische Physik der Universität HeidelbergHeidelbergGermany

Personalised recommendations