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

Abstract: 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.