65 lines
1.4 KiB
Python
65 lines
1.4 KiB
Python
import numpy as np
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from numpy.lib.scimath import sqrt as csqrt
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import pynam.util
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def g(w, wp):
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return ((wp * (w + wp)) + 1) / (csqrt(wp ** 2 - 1) * csqrt((w + wp) ** 2 - 1))
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def s(k, e, v):
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return (e - 1j * v) / k
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def f(k, e, v):
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sv = s(k, e, v)
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logv = np.log(np.real_if_close((sv + 1) / (sv - 1)) + 0j)
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return (1 / k) * (2 * sv + ((1 - sv**2) * logv))
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def i1(w, wp, k, v):
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gv = g(w, wp)
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e1 = csqrt((w + wp) ** 2 - 1)
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e2 = csqrt(wp ** 2 - 1)
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f_upper = f(k, np.real(e1 - e2), np.imag(e1 + e2) + 2 * v) * (gv + 1)
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f_lower = f(k, np.real(-e1 - e2), np.imag(e1 + e2) + 2 * v) * (gv - 1)
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return f_upper + f_lower
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def i2(w, wp, k, v):
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gv = g(w, wp)
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e1 = csqrt((w + wp) ** 2 - 1)
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e2 = csqrt(wp ** 2 - 1)
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f_upper = f(k, np.real(e1 - e2), np.imag(e1 + e2) + 2 * v) * (gv + 1)
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f_lower = f(k, np.real(e1 + e2), np.imag(e1 + e2) + 2 * v) * (gv - 1)
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return f_upper + f_lower
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def a(w, k, v, t):
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result = pynam.util.complex_quad(
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lambda wp: np.tanh((w + wp) / (2 * t)) * (i1(w, wp, k, v)),
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1 - w, 1,
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epsabs=1e-10
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)
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return result[0]
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def b_int(wp, w, k, v, t):
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return (np.tanh((w + wp) / (2 * t)) * i1(w, wp, k, v)) - (np.tanh(wp / (2 * t)) * i2(w, wp, k, v))
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def b(w, k, v, t, b_max=np.inf):
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return pynam.util.complex_quad(
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lambda wp: b_int(wp, w, k, v, t), 1, b_max
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)[0]
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def sigma_nam(w, k, v, t):
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return -1j * (3 / 4) * (v / w) * (-a(w, k, v, t) + b(w, k, v, t))
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