Non equilibrium dynamics of mixing, oscillations, and equilibration: A model study
Abstract
The nonequilibrium dynamics of mixing, oscillations and equilibration is studied in a field theory of flavored neutral mesons that effectively models two flavors of mixed neutrinos, in interaction with other mesons that represent a thermal bath of hadrons or quarks and charged leptons. This model describes the general features of neutrino mixing and relaxation via charged currents in a medium. The reduced density matrix and the nonequilibrium effective action that describes the propagation of neutrinos is obtained by integrating out the bath degrees of freedom. We obtain the dispersion relations, mixing angles and relaxation rates of ``neutrino'' quasiparticles. The dispersion relations and mixing angles are of the same form as those of neutrinos in the medium, and the relaxation rates are given by $$\Gamma_1(k) = \Gamma_{ee}(k) \cos^2\theta_m(k)+\Gamma_{\mu\mu}(k)\sin^2\theta_m(k); \Gamma_2(k)= \Gamma_{\mu\mu}(k) \cos^2\theta_m(k)+\Gamma_{ee}(k)\sin^2\theta_m(k) $$ where $$\Gamma_{\alpha\alpha}(k)$$ are the relaxation rates of the flavor fields in \emph{absence} of mixing, and $$\theta_m(k)$$ is the mixing angle in the medium. A WeisskopfWigner approximation that describes the asymptotic time evolution in terms of a nonhermitian Hamiltonian is derived. At long time $$>>\Gamma^{1}_{1,2}$$ ``neutrinos'' equilibrate with the bath. The equilibrium density matrix is nearly diagonal in the basis of eigenstates of an \emph{effective Hamiltonian that includes selfenergy corrections in the medium}. The equilibration of ``sterile neutrinos'' via activesterile mixing is discussed.
 Authors:
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org.:
 Physics Division
 OSTI Identifier:
 934708
 Report Number(s):
 LBNL416E
TRN: US0803840
 DOE Contract Number:
 DEAC0205CH11231
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review D; Journal Volume: 75; Related Information: Journal Publication Date: 12 April 2007
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72; APPROXIMATIONS; CHARGED CURRENTS; DEGREES OF FREEDOM; DENSITY MATRIX; DISPERSION RELATIONS; EIGENSTATES; HADRONS; HAMILTONIANS; LEPTONS; MESONS; NEUTRINOS; OSCILLATIONS; QUARKS; RELAXATION; SELFENERGY; neutrino, mixing angle; neutrino, oscillation; meson, interaction; charged current; density matrix, reduced; effective action; dispersion relations; neutrino, quasiparticle; neutrino, width; effective Hamiltonian; Langevin equation, solution; correlation function
Citation Formats
Ho, Chiu Man, Boyanovsky, D., and Ho, C. M.. Non equilibrium dynamics of mixing, oscillations, and equilibration: A model study. United States: N. p., 2006.
Web.
Ho, Chiu Man, Boyanovsky, D., & Ho, C. M.. Non equilibrium dynamics of mixing, oscillations, and equilibration: A model study. United States.
Ho, Chiu Man, Boyanovsky, D., and Ho, C. M.. Fri .
"Non equilibrium dynamics of mixing, oscillations, and equilibration: A model study". United States.
doi:. https://www.osti.gov/servlets/purl/934708.
@article{osti_934708,
title = {Non equilibrium dynamics of mixing, oscillations, and equilibration: A model study},
author = {Ho, Chiu Man and Boyanovsky, D. and Ho, C. M.},
abstractNote = {The nonequilibrium dynamics of mixing, oscillations and equilibration is studied in a field theory of flavored neutral mesons that effectively models two flavors of mixed neutrinos, in interaction with other mesons that represent a thermal bath of hadrons or quarks and charged leptons. This model describes the general features of neutrino mixing and relaxation via charged currents in a medium. The reduced density matrix and the nonequilibrium effective action that describes the propagation of neutrinos is obtained by integrating out the bath degrees of freedom. We obtain the dispersion relations, mixing angles and relaxation rates of ``neutrino'' quasiparticles. The dispersion relations and mixing angles are of the same form as those of neutrinos in the medium, and the relaxation rates are given by $\Gamma_1(k) = \Gamma_{ee}(k) \cos^2\theta_m(k)+\Gamma_{\mu\mu}(k)\sin^2\theta_m(k); \Gamma_2(k)= \Gamma_{\mu\mu}(k) \cos^2\theta_m(k)+\Gamma_{ee}(k)\sin^2\theta_m(k) $ where $\Gamma_{\alpha\alpha}(k)$ are the relaxation rates of the flavor fields in \emph{absence} of mixing, and $\theta_m(k)$ is the mixing angle in the medium. A WeisskopfWigner approximation that describes the asymptotic time evolution in terms of a nonhermitian Hamiltonian is derived. At long time $>>\Gamma^{1}_{1,2}$ ``neutrinos'' equilibrate with the bath. The equilibrium density matrix is nearly diagonal in the basis of eigenstates of an \emph{effective Hamiltonian that includes selfenergy corrections in the medium}. The equilibration of ``sterile neutrinos'' via activesterile mixing is discussed.},
doi = {},
journal = {Physical Review D},
number = ,
volume = 75,
place = {United States},
year = {Fri Dec 22 00:00:00 EST 2006},
month = {Fri Dec 22 00:00:00 EST 2006}
}

The nonequilibrium dynamics of mixing, oscillations, and equilibration is studied in a field theory of flavored neutral mesons that effectively models two flavors of mixed neutrinos, in interaction with other mesons that represent a thermal bath of hadrons or quarks and charged leptons. This model describes the general features of neutrino mixing and relaxation via charged currents in a medium. The reduced density matrix and the nonequilibrium effective action that describes the propagation of neutrinos is obtained by integrating out the bath degrees of freedom. We obtain the dispersion relations, mixing angles and relaxation rates of neutrino quasiparticles. The dispersionmore »

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