Substrate-Induced Propagation Anisotropy in a Phenomenological Two-Channel Model for One-Dimensional Conductors

Propagation anisotropy in one-dimensional conductors is commonly interpreted within the framework of Tomonaga–Luttinger liquid theory, where electron–electron interactions lead to distinct channel-dependent excitation velocities. In this work, we investigate a complementary mechanism in which propagation anisotropy arises from structured substrate modulation. We develop a quantitative two-channel effective-medium transport model incorporating position-dependent dielectric and magnetic coupling terms within an effective spinor Hamiltonian. Under an adiabatic envelope approximation, the coupled spinor dynamics are reduced to an effective scalar propagation equation suitable for numerical simulation. The model predicts that spatial modulation of substrate response can generate measurable channel-dependent velocity splitting, wave-packet deformation, and propagation delay. Numerical simulations show that dielectric modulation, magnetic modulation, relative phase shifts, and moderate disorder influence transport anisotropy in distinct and tunable ways. For experimentally realistic parameter ranges, the predicted propagation delay lies in the picosecond regime over micrometer-scale transport distances. Comparison with conventional Tomonaga–Luttinger liquid theory suggests that substrate-induced effects may coexist with intrinsic many-body interactions and contribute appreciably to observed transport behavior. The proposed framework provides a quantitative phenomenological tool for analyzing substrate-controlled anisotropic transport and offers experimentally testable predictions for low-dimensional quantum systems.