Geodesic
Quantum field renormalization group in the theory of stochastic Langmuir turbulence
Teoretičeskaâ i matematičeskaâ fizika, Tome 78 (1989) no. 3, pp. 368-383 
L. Ts. Adzhemyan; A. N. Vasil'ev; M. Gnatich; Yu. M. Pis'mak. Quantum field renormalization group in the theory of stochastic Langmuir turbulence. Teoretičeskaâ i matematičeskaâ fizika, Tome 78 (1989) no. 3, pp. 368-383. http://geodesic.mathdoc.fr/item/TMF_1989_78_3_a5/
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     author = {L. Ts. Adzhemyan and A. N. Vasil'ev and M. Gnatich and Yu. M. Pis'mak},
     title = {Quantum field renormalization group in~the theory of~stochastic {Langmuir} turbulence},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {368--383},
     year = {1989},
     volume = {78},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_78_3_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Quantum field theory renormalization group is used for analysing the Langmuir stochastic turbulence of plasma described by the Zakharov equations [1] with random noises. Existence of the dissipative scaling critical regime is proved, for which all the critical exponents are nontrivial and are calculated in the framework of the $4-\varepsilon$ expansion up to $\varepsilon^2$. An explicit expression is obtained for the scaling asymptotics of the longitudinal dielectric permeability $\varepsilon_\parallel(\omega,k)$ in the neighbourhood of a “critical point” $\varepsilon_\parallel(\omega_e,0)=0$ ($\omega_e$ is the Langmuir frequency). The expression implies, in particular, that the usual dispersion law of the Langmuir waves $\omega-\omega_l\sim k^2$ is substitutted for small $k$ by the law $\omega-\omega_l\sim k^{2-\gamma_a}$ in which the exponent $\gamma_a$ is known up to $\varepsilon^2$.

[1] Zakharov V. E., ZhETF, 62 (1972), 1745–1759

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