[Paper Review] A Possible Mechanism of Biological Memories in terms of Quantum Fluids

Tsunehiro Kobayashi|arXiv (Cornell University)|Jul 4, 2003

Advanced Thermodynamics and Statistical Mechanics2 references3 citations

TL;DR

This paper proposes a quantum fluid-based mechanism for biological memory, where zero-energy standing waves in 2D quantum fluids confined in polygonal units generate stable vortex patterns that represent memories. Stimuli awaken these patterns through selective excitation, enabling energy-efficient, infinitely variable, and perfectly recoverable memory recall—offering a novel physical model for neural memory and thinking processes.

ABSTRACT

A mechanism of memories, especially biological memories, is studied in terms of quantum fluids. Two-dimensional flows in central potentials $V_a(ρ)=-a^2g_aρ^{2(a-1)}$ ($a ot=0$ and $ρ=\sqrt{x^2+y^2}$) have zero-energy eigenstates that degenerate infinitely for all $a$. It is shown that stable standing waves constructed from the zero-energy flows are confined in various types of polygons which can be the minimum units of memory systems. Vortex patterns awoken in the units by stimuli correspond to the memories of the stimuli. This memory system is not a system for preserving memories as usual but that for awaking memories. The system has interesting properties; (i) the absolute economy as for the energy consumption, (ii) the infinite variety for a huge number of memories, (iii) the perfect recovery of the system from any disturbances by stimuli, and (iv) the large flexibility in the construction of the system. A process for thinking is also proposed in terms of this memory system.

Motivation & Objective

• To explore a fundamental physical mechanism for biological memory beyond classical neural models.
• To investigate how quantum fluid dynamics in two-dimensional systems with specific central potentials can support memory-like functions.
• To explain the energy efficiency, infinite memory capacity, and robustness of memory systems through zero-energy eigenstates and infinite degeneracy.
• To propose a physical model for thinking processes based on hierarchical vortex pattern interactions in quantum fluid units.
• To establish a connection between quantum hydrodynamics and cognitive functions such as recognition and memory recall.

Proposed method

• Analyzes two-dimensional Schrödinger equations with central potentials $V_a(\rho) = -a^2 g_a \rho^{2(a-1)}$ to identify zero-energy eigenstates.
• Applies conformal transformations $\zeta_a = z^a$ to reduce the eigenvalue problem to a plane-wave solution in $\zeta_a$-space, revealing universal behavior across different $a$ values.
• Constructs stable standing wave solutions using polynomials $f_n^\pm(u_a, v_a)$ multiplied by $e^{\pm i k_a u_a}$, ensuring time-independent, zero-energy states.
• Confines these zero-energy states within polygonal potential wells (e.g., quadrangles), forming minimum memory units where vortex patterns emerge upon stimulation.
• Uses the infinite degeneracy of zero-energy states to generate a vast variety of distinct vortex patterns corresponding to different memories.
• Proposes a hierarchical process where stimuli are converted into wave signals, selectively excite memory units via selection rule (I), and propagate through free motion perpendicular to the $xy$-plane for recognition and higher-order processing.

Experimental results

Research questions

• RQ1 Can zero-energy quantum fluid states in 2D systems support stable, long-lived memory patterns through vortex formation?
• RQ2 How does the infinite degeneracy of zero-energy states enable a vast number of distinct memory representations?
• RQ3 What physical mechanism allows perfect recovery of memory states after external disturbances, given the absence of time dependence in zero-energy states?
• RQ4 How might such a system underlie the recognition of familiar stimuli and the hierarchical processing of information in thinking?
• RQ5 What role do conformal transformations and the $\zeta_a$-space mapping play in unifying the behavior of different potential parameters $a$ and $g_a$?

Key findings

• Zero-energy eigenstates exist for all $a \neq 0$ in 2D quantum fluids under the potential $V_a(\rho) = -a^2 g_a \rho^{2(a-1)}$, forming stable standing waves.
• The infinite degeneracy of these zero-energy states allows for an arbitrarily large number of distinct vortex patterns, enabling a huge memory capacity.
• The system exhibits perfect recovery from disturbances because zero-energy states are time-independent and non-decaying, ensuring complete restoration after perturbation.
• Vortex patterns formed in polygonal confinement units (e.g., quadrangles) serve as stable, topologically protected representations of stimuli, functioning as memory units.
• The system operates not by preserving memories but by awakening them via stimulus-induced excitation, with recognition achieved through selective wave number matching.
• A hierarchical thinking process is proposed, where vortex patterns are transmitted and transformed across multiple blocks via perpendicular motion, enabling higher-order cognition through vortex creation and annihilation.