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346caf3ea0
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346caf3ea0
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5bb3a2163f
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@@ -32,11 +32,16 @@ def gap_integral(
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return integrate.quad(integrand, 0, debye_frequency)[0]
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return integrate.quad(integrand, 0, debye_frequency)[0]
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def equilibrium_gap(temp, debye_frequency, nv):
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def equilibrium_gap(temp: float, debye_frequency: float, nv: float) -> float:
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return find_gap(temp, 0, debye_frequency, nv)
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return find_gap(temp, 0, debye_frequency, nv)
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def find_gap(temp, mu_star, debye_frequency, nv):
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def find_gap(
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temp: float,
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mu_star: float,
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debye_frequency: float,
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nv: float
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) -> float:
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nv_inv = 1 / nv
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nv_inv = 1 / nv
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sol = scipy.optimize.root(
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sol = scipy.optimize.root(
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lambda d: gap_integral(temp, d, mu_star, debye_frequency) - nv_inv,
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lambda d: gap_integral(temp, d, mu_star, debye_frequency) - nv_inv,
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@@ -46,7 +51,9 @@ def find_gap(temp, mu_star, debye_frequency, nv):
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# this is n * Delta_0, calling it n in this file for brevity
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# this is n * Delta_0, calling it n in this file for brevity
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def n_integrand_function(xi, temp, delta, mu_star):
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def n_integrand_function(
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xi: float, temp: float, delta: float, mu_star: float
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) -> float:
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big_e = energy(xi, delta)
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big_e = energy(xi, delta)
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left = 1 / (1 + numpy.exp((big_e - mu_star) / temp))
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left = 1 / (1 + numpy.exp((big_e - mu_star) / temp))
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right = 1 / (1 + numpy.exp(big_e / temp))
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right = 1 / (1 + numpy.exp(big_e / temp))
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@@ -54,8 +61,8 @@ def n_integrand_function(xi, temp, delta, mu_star):
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# as above, this is brevity n * Delta_0
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# as above, this is brevity n * Delta_0
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def n_integral(temp, delta, mu_star):
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def n_integral(temp: float, delta: float, mu_star: float) -> float:
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def integrand(xi):
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def integrand(xi: float) -> float:
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return n_integrand_function(xi, temp, delta, mu_star)
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return n_integrand_function(xi, temp, delta, mu_star)
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intermediate = 20 * numpy.sqrt(delta ** 2 + mu_star ** 2)
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intermediate = 20 * numpy.sqrt(delta ** 2 + mu_star ** 2)
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lower = integrate.quad(integrand, 0, intermediate)[0]
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lower = integrate.quad(integrand, 0, intermediate)[0]
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