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This research extends London equations to account for spatial density gradients in superconductors, revealing that magnetic field expulsion is more sensitive than previously modeled. By introducing a hyperbolic phase-amplitude coupling into quantum hydrodynamics, the study provides new theoretical tools for understanding electrodynamics in non-uniform materials. These advances directly impact fundamental models of superconductivity and could influence future designs of high-performance quantum devices.
Modified Quantum Phase Could Aid Superconductivity Research

Superconducting materials typically expel magnetic fields uniformly, yet this behaviour now appears subject to subtle spatial variations. The standard equations governing this effect, the London equations, are extended by a new geometric structure linking a material’s density to its quantum phase. This means the Meissner effect, a superconductor’s complete expulsion of a magnetic field, becomes sensitive to how density changes across the material itself.
C. Dedes at South Thames College in London extends the Madelung transformation with a hyperbolic phase-amplitude coupling, offering a new approach to quantum hydrodynamics. This construction introduces geometric properties into the Bohmian description, resulting in modified continuity equations and quantum forces. Interpreting this framework through a complex macroscopic order parameter reveals alterations to superconducting electrodynamics, specifically impacting the Meissner response with sensitivity to spatial density gradients. The findings advance understanding of complex group velocities, dissipative wave propagation, and amplitude-sensitive transport within quantum systems. The London equations, foundational to understanding superconducting electrodynamics, now exhibit contributions 40% greater than previously calculated due to…
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