#

Non-equilibrium particles

from __future__ import division
import numpy
from common import GRID, linear_interpolation
from common.integrators import lambda_integrate


name = 'non-equilibrium'

#

@lambda_integrate()
def density(particle):
    return numpy.vectorize(lambda y: (
        particle.distribution(y) * y**2
        * particle.dof / 2. / numpy.pi**2 / particle.params.a**3
    ), otypes=[numpy.float_])

#

Energy density

$\begin{equation} \rho = \frac{g}{2 \pi^2} \frac{m^4}{x^4} \int dy y^2 \sqrt{y^2 + \frac{M_N^2 x^2}{m^2}} f(y) \end{equation}$

@lambda_integrate()
def energy_density(particle):

    return numpy.vectorize(lambda y: (
        particle.distribution(y)
        * y**2 * particle.conformal_energy(y)
        * particle.dof / 2. / numpy.pi**2 / particle.params.a**4
    ), otypes=[numpy.float_])

#

Pressure

$\begin{equation} p = \frac{g}{6 \pi^2} \frac{m^4}{x^4} \int \frac{dy \, y^4 f(y)} { \sqrt{y^2 + \frac{M_N^2 x^2}{m^2}} } \end{equation}$

@lambda_integrate()
def pressure(particle):

    return numpy.vectorize(lambda p: (
        particle.distribution(p) * p ** 4
        / particle.conformal_energy(p)
        * particle.dof / 6. / numpy.pi**2 / particle.params.a**4
    ), otypes=[numpy.float_])

#

Master equation terms

#

Numerator

$\begin{equation} -\frac{g}{2 \pi^2} \int dy \, y^2 \sqrt{y^2 + \frac{M_N^2 x^2}{m^2}} I_{coll}(y) \end{equation}$

@lambda_integrate()
def numerator(particle):
    integral = linear_interpolation(particle.collision_integral / particle.params.x,
                                    particle.grid.TEMPLATE)
    return numpy.vectorize(lambda y: (
        -1. * particle.dof / 2. / numpy.pi**2
        * y**2 * particle.conformal_energy(y)
        * integral(y)
    ), otypes=[numpy.float_])

#

Denominator

$\begin{equation} 0 \end{equation}$

def denominator(particle):

    return 0.