# Non equilibrium dynamics of mixing, oscillations, and equilibration: A model study

## Abstract

The non-equilibrium 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 non-equilibrium 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 Weisskopf-Wigner approximation that describes the asymptotic time evolution in terms of a non-hermitian 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 self-energy corrections in the medium}. The equilibration of ``sterile neutrinos'' via active-sterile 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):
- LBNL-416E

TRN: US0803840

- DOE Contract Number:
- DE-AC02-05CH11231

- 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; SELF-ENERGY; 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 non-equilibrium 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 non-equilibrium 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 Weisskopf-Wigner approximation that describes the asymptotic time evolution in terms of a non-hermitian 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 self-energy corrections in the medium}. The equilibration of ``sterile neutrinos'' via active-sterile 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}

}