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39 lines
1.4 KiB
Python
39 lines
1.4 KiB
Python
# ==============================================================================
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# COPYRIGHT NO ONE EVERYWHERE LLC (WYOMING HOLDING COMPANY)
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# PROJECT: SOVEREIGN STACK
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# This artifact is entirely proprietary and cryptographically proven.
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# Open-Source usage requires explicit permission from Brandon Scott Schneider.
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# ==============================================================================
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import sys
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import os
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sys.path.insert(0, os.path.abspath(os.path.join(os.path.dirname(__file__), "..")))
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from math_harness_compat import xp, AnyArray
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import scipy.constants as const
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def mcmillan_allen_dynes(omega_log, lambd, mu_star):
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"""
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McMillan-Allen-Dynes formula for Tc.
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omega_log: Logarithmic average phonon frequency (K)
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lambd: Electron-phonon coupling strength
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mu_star: Coulomb pseudopotential
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"""
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num = -1.04 * (1 + lambd)
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den = lambd - mu_star * (1 + 0.62 * lambd)
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tc = (omega_log / 1.2) * xp.exp(num / den)
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return tc
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# Target: Tc = 494K
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# Hydrogen frequency (~250-300 meV) -> K
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omega_h = 280 * 11.604 # ~3249 K
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mu_star = 0.13
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# Solve for lambda
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print(f"Target Tc: 494 K")
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print(f"Phonon freq (omega_log): {omega_h:.2f} K")
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print(f"Coulomb mu*: {mu_star}")
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for l in xp.linspace(1.5, 3.5, 20):
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tc = mcmillan_allen_dynes(omega_h, l, mu_star)
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if tc > 490:
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print(f"LAMBDA FOUND: {l:.4f} -> Tc: {tc:.2f} K")
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break
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