Derives distinct scaling laws N_c vs B_c for beating nodes in graphene quantum oscillations to distinguish pseudomagnetic fields (N_c ∝ B_c²), valley imbalance (N_c ∝ B_c), and energy splitting mechanisms.
Gauge fields in graphene,
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Pauli-reduced spectrum of Dirac oscillator in uniform non-Abelian background yields λ_FM = g²β²/4m (aligned), λ_S = -g²β(β-2ρ)/4m (singlet), λ_T = -g²β(β+2ρ)/4m (triplet) with quadratic vs linear scaling.
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Non-Abelian Dirac oscillator in a uniform Yang--Mills background: spin--isospin mixing and singlet--triplet splitting
Pauli-reduced spectrum of Dirac oscillator in uniform non-Abelian background yields λ_FM = g²β²/4m (aligned), λ_S = -g²β(β-2ρ)/4m (singlet), λ_T = -g²β(β+2ρ)/4m (triplet) with quadratic vs linear scaling.