A Non-Hermitian Potential Well Formalism for Conscious--Preconscious--Subliminal Processing

We propose a phenomenological model of the Global Neuronal Workspace (GNW) in which early sensory processing generates an effective complex-valued landscape governing the dynamics of high-level stimulus representations. This landscape provides a dynamical bridge between sensory encoding and conscious access, enabling both processes to be described within a unified framework. High-level representations are encoded in a cloud function defined on a Hilbert space over a perceptual state space, thereby combining the holistic structure of mental images with a neural implementation. Its dynamics is governed by a nonlinear Schrödinger-type equation in imaginary time with a non-Hermitian, non-normal Hamiltonian and a nonlinear Lotka–Volterra-type term that preserves norm and enables spatially nonlocal interactions. The Hermitian and anti-Hermitian parts of the Hamiltonian generate complementary processes: recognition via dissipative localization at minima of the GNW landscape and information broadcasting via spatial spreading across the state space. The resulting dynamics reproduces the subliminal–preconscious–conscious hierarchy of sensory processing. Conscious access corresponds to the emergence of a bound state, which occurs only when both the GNW landscape depth and the degree of top-down attention exceed threshold values. The resulting framework provides a tractable dynamical description linking sensory processing, attention, and conscious access within a unified dynamical setting.