| name | non-hermitian-gnw-consciousness |
| description | Non-Hermitian Potential Well Formalism for modeling the Global Neuronal Workspace (GNW) consciousness framework. Uses nonlinear Schrödinger-type equation in imaginary time with non-Hermitian, non-normal Hamiltonian and Lotka-Volterra-type term to reproduce subliminal-preconscious-conscious hierarchy. Maps conscious access to bound-state emergence in complex-valued landscape. Use for consciousness modeling, neural field theory, GNW theory, and quantum-inspired cognitive dynamics. |
| activation | non-hermitian consciousness, GNW model, global neuronal workspace, consciousness formalism, subliminal processing, preconscious buffer, cloud function, neural field theory, Lotka-Volterra neural dynamics, bound state consciousness, potential well neural model |
| tags | ["neuroscience","consciousness","neural-field-theory","gnw","non-hermitian","mathematical-modeling","cognitive-science"] |
| version | 1.0.0 |
| author | Hermes Agent |
| category | neuroscience |
| created | 2026-07-13T00:00:00.000Z |
| source_arxiv | 2607.08302v1 |
Non-Hermitian Potential Well Formalism for GNW Consciousness
Source Paper
Title: A Non-Hermitian Potential Well Formalism for Conscious–Preconscious–Subliminal Processing
Authors: Vasily Lubashevskiy (Tokyo International University), Ihor Lubashevsky (HSE University, Moscow)
arXiv: 2607.08302v1 [q-bio.NC, nlin.AO]
Published: 2026-07-09
License: CC BY 4.0
Core Innovation
Proposes a phenomenological model of the Global Neuronal Workspace (GNW) using a non-Hermitian Schrödinger-type equation in imaginary time with a Lotka–Volterra-type nonlinear term. This provides the first tractable dynamical framework that unifies sensory encoding, attention, and conscious access within a single mathematical formalism.
Key Concepts
1. Cloud Function Ψ(x,t)
- High-level stimulus representations encoded as cloud functions in Hilbert space ℍ = L²(ℝᴺ)
- |Ψ(x,t)|² interpreted as normalized density over perceptual configurations
- Nonlocality in ℝᴺ represents perceptual uncertainty from neural sensory processing
- Combines holistic structure of mental images with neural implementation
2. Complex-Valued GNW Landscape Ω(x)
- Early sensory processing generates an effective complex-valued potential landscape
- Ω(x) = V(x) + iW(x), where:
- V(x) (real/Hermitian part): Recognition via dissipative localization at landscape minima
- W(x) (imaginary/anti-Hermitian part): Information broadcasting via spatial spreading
- Landscape depth proportional to bottom-up sensory activation strength
3. Governing Equation
∂Ψ/∂t = -ĤΨ + nonlinear Lotka-Volterra term
where Ĥ is a non-Hermitian, non-normal Hamiltonian:
- Hermitian component → dissipative dynamics driving Ψ toward landscape minima (recognition)
- Anti-Hermitian component → spatial spreading / broadcasting across state space
- Nonlinear term → preserves norm (∫|Ψ|² = 1) while enabling spatially nonlocal interactions
4. Three Processing Regimes
