Deepak Mallubhotla
6231ecc203
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85 lines
2.1 KiB
Python
85 lines
2.1 KiB
Python
import pynam.util
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from typing import Callable
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import numpy as np
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SMALL_X_BOUNDARY = 1e3
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def get_zeta_p_integrand(
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eps: Callable[[float], complex]
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) -> Callable[[float, float], complex]:
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"""Gets the integrand function zeta_p_integrand(u, y).
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Returns zeta_p_integrand(u, y), a complex valued function of two momenta in units of vacuum wavelength.
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:param eps:
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:return:
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"""
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def zeta_p_integrand(y: float, u: float) -> complex:
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"""
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Here y and u are in units of vacuum wavelength, coming from Ford-Weber / from the EWJN noise expressions.
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:param u:
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:param y:
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:return:
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"""
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u2 = u**2
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y2 = y**2
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k2 = u2 + y2
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k = np.sqrt(k2)
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eps_value = eps(k)
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term_1 = y2 / (eps_value - k2)
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term_2 = u2 / eps_value
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return (term_1 + term_2) / k2
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return zeta_p_integrand
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def get_zeta_p_function(eps: Callable[[float], complex]):
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def integrand1_small_x(x: float, u: float) -> complex:
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u2 = u**2
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x2 = x**2
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eps_value = eps(u * np.sqrt(1 + x**2))
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return (x2 / (eps_value - 1 - x2)) / ((1 + x2) * u2)
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def integrand1_big_x(x: float, u: float) -> complex:
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u2 = u**2
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x2 = x**2
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eps_value = eps(u * x)
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return 1 / ((eps_value - x2) * u2)
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# 1 / (eps(u * sqrt(1 + x^2))) * 1 / (1 + x^2)
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def integrand2_small_x(x: float, u: float) -> complex:
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x2 = x**2
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eps_value = eps(u * np.sqrt(1 + x**2))
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return 1 / (eps_value * (1 + x2))
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def integrand2_big_x(x: float, u: float) -> complex:
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x2 = x**2
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eps_value = eps(u * x)
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return 1 / (eps_value * x2)
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def zeta_p(u: float) -> complex:
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# zeta_p_integrand = get_zeta_p_integrand(eps)
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i1_small = pynam.util.complex_quad(
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lambda x: integrand1_small_x(x, u), 0, SMALL_X_BOUNDARY, epsabs=1e-12
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)
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i1_big = pynam.util.complex_quad(
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lambda x: integrand1_big_x(x, u), SMALL_X_BOUNDARY, np.inf, epsabs=1e-12
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)
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i2_small = pynam.util.complex_quad(
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lambda x: integrand2_small_x(x, u), 0, SMALL_X_BOUNDARY, epsabs=1e-12
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)
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i2_big = pynam.util.complex_quad(
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lambda x: integrand2_big_x(x, u), SMALL_X_BOUNDARY, np.inf, epsabs=1e-12
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)
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integral = sum(term[0] for term in [i1_small, i2_small, i1_big, i2_big])
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return integral * 2j * u
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return zeta_p
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