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TMF, 2014, Volume 178, Number 3, Pages 416–432 (Mi tmf8594)  

This article is cited in 2 scientific papers (total in 2 papers)

The Kardar–Parisi–Zhang equation and its matrix generalization

L. V. Borkab, S. L. Ogarkovb

a Institute for Theoretical and Experimental Physics, Moscow, Russia
b Dukhov All-Russia~Research Institute of Automatics, Moscow, Russia

Abstract: We study the problem of the condensate (stochastic average) origination for an auxiliary field in the Kardar–Parisi–Zhang equation and its matrix generalization. We cannot reliably conclude that there is a condensate for the Kardar–Parisi–Zhang equation in the framework of the one-loop approximation improved by the renormalization group method. The matrix generalization of the Kardar–Parisi–Zhang equation permits a positive answer to the question of whether there is a nonzero condensate, and the problem can be solved exactly in the large-$N$ limit.

Keywords: Kardar–Parisi–Zhang equation, renormalization group, effective potential, $1/N$-expansion

DOI: https://doi.org/10.4213/tmf8594

Full text: PDF file (507 kB)
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English version:
Theoretical and Mathematical Physics, 2014, 178:3, 359–373

Bibliographic databases:

PACS: 64.60.Ht
MSC: 82C27,82C28
Received: 10.09.2013
Revised: 23.09.2013

Citation: L. V. Bork, S. L. Ogarkov, “The Kardar–Parisi–Zhang equation and its matrix generalization”, TMF, 178:3 (2014), 416–432; Theoret. and Math. Phys., 178:3 (2014), 359–373

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. V. Antonov, P. I. Kakin, “Random interface growth in a random environment: Renormalization group analysis of a simple model”, Theoret. and Math. Phys., 185:1 (2015), 1391–1407  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. Cooper F., Dawson J.F., “Auxiliary Field Loop Expansion of the Effective Action For a Class of Stochastic Partial Differential Equations”, Ann. Phys., 365 (2016), 118–154  crossref  mathscinet  zmath  adsnasa  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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