Levitating Electrons Quantum State Stability Model Based on the Kuznetsov Tensor

This work presents a new geometric model describing the quantum states of electrons levitating on the surface of liquid helium, based on the introduction of the Kuznetsov tensor. The proposed approach unifies elements of quantum theory, differential geometry, and the thermodynamics of open systems, allowing quantum coherence to be interpreted as the invariance of the metric field under entropic deformations. The introduced Kuznetsov tensor describes singular perturbations of the metric and the interaction between the electron wave function and the surface potential of the medium, enabling a quantitative assessment of system stability and decoherence. The Kuznetsov entropic functional, a generalization of the Ricci flow, is developed to link scalar curvature, wave function density, and entropic potential. It is shown that the stationary solutions of this functional correspond to stable coherent qubit states, while the dynamics of quantum transitions can be represented as local curvature waves in the state space. Based on the proposed model, a stability criterion for qubits is formulated, taking into account the effects of singular deformations and entropic density. The analysis of coherence time as a function of the Kuznetsov tensor parameters reveals optimal stability regions at moderate values of β and γ. The presented results demonstrate the feasibility of a geometric description of quantum information and open the way to the creation of self-organizing qubits, in which stability is maintained by the internal symmetry of the metric field.