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The Equation of Motion for Hybrid Flow in Quantum Kinetics

Viktoras Rimsha, Laimontas Rimsha

Published May 28, 2026• 0 citations
Publisher

Abstract

This paper extends the recently proposed analytical framework of quantum phase space, where coordinate and momentum representations are unified into a strictly positive joint distribution. Transitioning from stationary geometric structures to non-stationary processes, we introduce the concept of time-dependent hybrid flows. We derive the fundamental equation of motion governing the temporal evolution of these flows in quantum kinetics. Unlike traditional phase-space approaches (such as the Wigner-Liouville equation) which suffer from negative probability densities and highly non-local differential terms, the hybrid flow equation operates as a local balance between real, experimentally observable coordinate and momentum quantum probability currents. The mathematical properties of the equation, including strict positivity, total probability conservation, and spatial-momentum orthogonality, are analyzed. Finally, we discuss the engineering and physical domains where this formulation provides crucial computational advantages, particularly in nano-barrier charge transport and quantum optics.

DOI
10.5281/zenodo.20424675

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