Non Hermitian Conscious Preconscious Subliminal

---
name: non-hermitian-conscious-preconscious-subliminal
category: neuroscience
description: Non-Hermitian Potential Well Formalism for modeling conscious-preconscious-subliminal processing hierarchy. Uses nonlinear Schrödinger-type equations in imaginary time with non-Hermitian Hamiltonians to unify sensory encoding and conscious access.
trigger_words: non-Hermitian, conscious access, GNW, Global Neuronal Workspace, subliminal, preconscious, potential well, Schrödinger equation, Lotka-Volterra, consciousness modeling, sensory processing
version: "1.0"
created: "2026-07-12"
source: "arXiv:2607.08302v1"
authors: "Vasily Lubashevskiy, Ihor Lubashevsky"
---

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

## Paper Info
- **Title**: A Non-Hermitian Potential Well Formalism for Conscious--Preconscious--Subliminal Processing
- **arXiv**: 2607.08302v1
- **Date**: 2026-07-09
- **Category**: q-bio.NC (Neuroscience), nlin.AO (Adaptation & Self-Organizing)
- **Authors**: Vasily Lubashevskiy, Ihor Lubashevsky

## Core Contributions

### 1. Unified GNW Dynamical Framework
Proposes a phenomenological model of the **Global Neuronal Workspace (GNW)** where:
- Early sensory processing generates an **effective complex-valued landscape** governing high-level stimulus representation dynamics
- This landscape provides a **dynamical bridge** between sensory encoding and conscious access
- Both processes described within a **single unified mathematical framework**

### 2. Mathematical Formalism
High-level representations are encoded as:
- **Cloud function** on a Hilbert space over perceptual state space
- Combines holistic mental image structure with neural implementation
- Dynamics governed by a **nonlinear Schrödinger-type equation in imaginary time**

The Hamiltonian has two key components:
- **Non-Hermitian, non-normal Hamiltonian** with nonlinear Lotka-Volterra-type term
- **Hermitian part**: Recognition via dissipative localization at GNW landscape minima
- **Anti-Hermitian part**: Information broadcasting via spatial spreading across state space

### 3. Subliminal-Preconscious-Conscious Hierarchy
The model reproduces the three-tier processing hierarchy:
- **Subliminal**: Below threshold — no bound state forms
- **Preconscious**: Partial activation — transient dynamics
- **Conscious**: Emergence of a **bound state** when BOTH:
  - GNW landscape depth exceeds threshold
  - Top-down attention degree exceeds threshold

### 4. Conscious Access as Bound State Emergence
- Conscious access = emergence of a bound state in the complex potential well
- Requires dual threshold crossing (landscape depth + attention)
- Provides quantitative criterion for conscious vs. unconscious processing

## Practical Applications

### When to Apply
- Modeling conscious access dynamics in neural systems
- Analyzing subliminal vs. supraliminal processing
- Building dynamical models of awareness and attention
- Studying the neural correlates of consciousness (NCC)

### Key Parameters
1. **GNW landscape depth**: Determines recognition strength
2. **Top-down attention degree**: Controls information broadcasting
3. **Bound state threshold**: Dual-criteria for conscious access

### Workflow
1. Define the perceptual state space and cloud function representation
2. Construct the non-Hermitian Hamiltonian (Hermitian + anti-Hermitian parts)
3. Add Lotka-Volterra nonlinear term for norm preservation
4. Simulate imaginary-time Schrödinger dynamics
5. Identify bound state emergence as conscious access event

## Key Insights
- Consciousness emerges as a dynamical phase transition (bound state formation)
- Hermitian/anti-Hermitian decomposition maps to recognition/broadcasting duality
- Complex-valued landscape unifies sensory encoding and conscious access
- Lotka-Volterra term enables spatially nonlocal interactions while preserving norm
- Dual-threshold mechanism explains why attention modulates conscious access

## Related Skills
- `consciousness-usk-framework` — Information-theoretic consciousness theory
- `iit-critical-review` — Integrated Information Theory analysis
- `canonical-functionalism-consciousness` — Mathematical refinement of computationalism
- `non-hermitian-gnw-consciousness` — Related non-Hermitian GNW work

## References
- arXiv:2607.08302v1 — Full paper with mathematical derivations
- Global Neuronal Workspace (Dehaene et al.) — Original GNW theory