Quantum Historical Dependence Operator: A Novel Approach to Quantum Dynamics

Jincheng Zhang

Published Aug 17, 2026• 0 citations

Abstract

This paper introduces the Quantum Historical Dependence Operator (QHDO), a fundamentally new approach to quantum dynamics. The core concept challenges the traditional view of quantum states solely relying on the present Hamiltonian and temporal evolution. Instead, the QHDO posits that quantum states are intrinsically dependent on their entire historical trajectory. This dependence is formalized as: [ψ(t) = F(H_t)], where ψ(t) represents the quantum state at time t, H_t is the Hamiltonian at time t, and F is a function that encapsulates the historical influence. The motivation stems from observations within non-Markovian quantum systems, suggesting that past interactions significantly shape the present state. The QHDO offers a potentially transformative perspective, challenging established models of quantum dynamics and holding significant implications for understanding complex quantum phenomena and potentially paving the way for future technological advancements. This work lays the groundwork for further exploration and development of this novel operator. ---

DOI: 10.5281/zenodo.21974456

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