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arXiv:1309.4892 · Progress of Theoretical and Experimental Physics

Microscopic identification of dissipative modes in relativistic field theories

Yohei Saito, Hirotsugu Fujii, Kazunori Itakura A, Osamu Morimatsu

Published May 1, 2015• 1 citation
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Abstract

We present an argument to support the existence of dissipative modes in relativistic field theories. For an |$O(N)$||$\varphi ^4$| theory in spatial dimension |$1\leq d\le 3$|⁠, the two-point function of |$\varphi$| is shown to develop a pole of the form |$p_0\sim i\Gamma ^{-1} ({\boldsymbol{{ {p}}}}^2+m^2)$| at small energy |$p_0$| and momentum |${\boldsymbol{{ {p}}}}$|⁠, with a nonzero finite coefficient or relaxation constant, |$\Gamma$|⁠, when evaluated in the two-particle irreducible (2PI) framework at the next-leading order (NLO) of |$1/N$| expansion. In contrast, an NLO calculation in the one-particle irreducible (1PI) framework fails to give a nonzero |$\Gamma$|⁠. The dissipative mode emerges from multiple scattering of a particle with other particles, which is appropriately treated in the 2PI–NLO calculation through the resummation of secular terms to improve the long-time behavior of the two-point function. Assuming that this slow dissipative mode survives at the critical point, one can identify the dynamic critical exponent |$z$| for the two-point function as |$z=2-\eta$|⁠. We also discuss possible improvement of the result.

DOI
10.1093/ptep/ptv065

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From quantum to classical dynamics: Dynamic crossover in the relativistic O(N)O(N)O(N) model
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