Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow
Abstract
In relativistic kinetic theory, the one-particle distribution function is approximated by an asymptotic perturbative power series in the Knudsen number which is divergent. For the Bjorken flow, we expand the distribution function in terms of its moments and study their nonlinear evolution equations. The resulting coupled dynamical system can be solved for each moment consistently using a multiparameter transseries which makes the constitutive relations inherit the same structure. A new nonperturbative dynamical renormalization scheme is born out of this formalism that goes beyond the linear response theory.We show that there is a Lyapunov function, also known as dynamical potential, which is, in general, a function of the moments and time satisfying Lyapunov stability conditions along renormalization group flows connected to the asymptotic hydrodynamic fixed point. As a result, the transport coefficients get dynamically renormalized at every order in the time-dependent perturbative expansion by receiving nonperturbative corrections present in the transseries. The connection between the integration constants and the UV data is discussed using the language of dynamical systems. Furthermore, we show that the first dissipative correction in the Knudsen number to the distribution function is not only determined by the known effective shear viscous term but also a new high-energymore »
- Authors:
- Publication Date:
- Research Org.:
- North Carolina State University, Raleigh, NC (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); BEST (Beam Energy Scan Theory) DOE Topical Collaboration; National Science Foundation (NSF)
- OSTI Identifier:
- 1526329
- Alternate Identifier(s):
- OSTI ID: 1609462
- Grant/Contract Number:
- FG02-03ER41260; SC0013036; NSF PHY-1125915
- Resource Type:
- Published Article
- Journal Name:
- Physical Review. D.
- Additional Journal Information:
- Journal Name: Physical Review. D. Journal Volume: 99 Journal Issue: 11; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Astronomy & Astrophysics; Physics
Citation Formats
Behtash, Alireza, Kamata, Syo, Martinez, Mauricio, and Shi, Haosheng. Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.99.116012.
Behtash, Alireza, Kamata, Syo, Martinez, Mauricio, & Shi, Haosheng. Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow. United States. https://doi.org/10.1103/PhysRevD.99.116012
Behtash, Alireza, Kamata, Syo, Martinez, Mauricio, and Shi, Haosheng. Fri .
"Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow". United States. https://doi.org/10.1103/PhysRevD.99.116012.
@article{osti_1526329,
title = {Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow},
author = {Behtash, Alireza and Kamata, Syo and Martinez, Mauricio and Shi, Haosheng},
abstractNote = {In relativistic kinetic theory, the one-particle distribution function is approximated by an asymptotic perturbative power series in the Knudsen number which is divergent. For the Bjorken flow, we expand the distribution function in terms of its moments and study their nonlinear evolution equations. The resulting coupled dynamical system can be solved for each moment consistently using a multiparameter transseries which makes the constitutive relations inherit the same structure. A new nonperturbative dynamical renormalization scheme is born out of this formalism that goes beyond the linear response theory.We show that there is a Lyapunov function, also known as dynamical potential, which is, in general, a function of the moments and time satisfying Lyapunov stability conditions along renormalization group flows connected to the asymptotic hydrodynamic fixed point. As a result, the transport coefficients get dynamically renormalized at every order in the time-dependent perturbative expansion by receiving nonperturbative corrections present in the transseries. The connection between the integration constants and the UV data is discussed using the language of dynamical systems. Furthermore, we show that the first dissipative correction in the Knudsen number to the distribution function is not only determined by the known effective shear viscous term but also a new high-energy nonhydrodynamic mode. It is demonstrated that the survival of this new mode is intrinsically related to the nonlinear mode-to-mode coupling with the shear viscous term. Finally, we comment on some possible phenomenological applications of the proposed nonhydrodynamic transport theory.},
doi = {10.1103/PhysRevD.99.116012},
journal = {Physical Review. D.},
number = 11,
volume = 99,
place = {United States},
year = {Fri Jun 14 00:00:00 EDT 2019},
month = {Fri Jun 14 00:00:00 EDT 2019}
}
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