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arXiv:physics/0307031

A Possible Mechanism of Biological Memories in terms of Quantum Fluids

Tsunehiro Kobayashi

Published Jul 4, 2003• 3 citations
arXivHTMLPDF

Abstract

A mechanism of memories, especially biological memories, is studied in terms of quantum fluids. Two-dimensional flows in central potentials $V_a(ρ)=-a^2g_aρ^{2(a-1)}$ ($a\not=0$ 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.

DOI
10.48550/arxiv.physics/0307031

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A mechanism of memories, especially biological memories, is studied in terms of quantum fluids. Two-dimensional flows in central potentials Va(ρ)=−a2gaρ2(a−1)V_a(ρ)=-a^2g_aρ^{2(a-1)}Va​(ρ)=−a2ga​ρ2(a−1) (a≠0a\not=0a=0 and ρ=x2+y2ρ=\sqrt{x^2+y^2}ρ=x2+y2​) have zero-energy eigenstates that degenerate infinitely for all aaa. 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.
Time-dependent processes accompanied by vortex creations and annihilations are investigated in terms of the eigenstates in conjugate spaces of Gel'fand triplets in 2-dimensions. Creations and annihilations of vortices are described by the insertions of unstable eigenstates with complex-energy eigenvalues into stable states written by the superposition of eigenstates with zero-energy eigenvalues. Some concrete examples are presented in terms of the eigenfunctions of the 2-dimensional parabolic potential barrier, i.e., −mγ2(x2+y2)/2-m γ^2 (x^2+y^2)/2−mγ2(x2+y2)/2. We show that the processes accompanied by vortex creations and annihilations can be analyzed in terms of the eigenfunctions in the conjugate spaces of Gel'fand triplets. Throughout these examinations we point out three interesting properties of the zero-energy flows. (i) Mechanisms using the zero-energy flows are absolutely economical from the viewpoint of energy consumption. (ii) An enormous amount of informations can be discriminated in terms of the infinite variety of the zero-energy flows. (iii) The zero-energy flow patterns are absolutely stable in any disturbance by inserting arbitrary decaying flows with complex-energy eigenvalues.
We show that zero-energy flows appear in many particle systems as well as in single particle cases in 2-dimensions. Vortex patterns constructed from the zero-energy flows can be investigated in terms of the eigenstates in conjugate spaces of Gel'fand triplets. Stable patterns are written by the superposition of zero-energy eigenstates. On the other hand vortex creations and annihilations are described by the insertions of unstable eigenstates with complex-energy eigenvalues into the stable patterns. Some concrete examples are presented in the 2-dimensional parabolic potential barrier case. We point out three interesting properties of the zero-energy flows (i) the absolute economy as for the energy consumption, (ii) the infinite variety of the vortex patterns, and (iii) the perfect stability of the vortex patterns.
We show that zero-energy flows appear in many particle systems as same as in single particle cases in 2-dimensions. Vortex patterns constructed from the zeroenergy flows can be investigated in terms of the eigenstates in conjugate spaces of Gel’fand triplets. Stable patterns are written by the superposition of zero-energy eigenstates. On the other hand vortex creations and annihilations are described by the insertions of unstable eigenstates with complex-energy eigenvalues into the stable patterns. Some concrete examples are presented in the 2-dimensional parabolic potential barrier case. We point out three interesting properties of the zero-energy flows; (i) the absolute economy as for the energy consumption, (ii) the infinite variety of the vortex patterns, and (iii) the absolute stability of the vortex patterns Keywords: Zero-energy solutions, vortex creations and annihilations, quantum mechanics, Gel’fand triplets,
This paper proposes a novel approach to biological information processing by leveraging the principles of quantum memory. The core idea is to mimic the memory function of biological neurons using quantum memory models, thereby accelerating and enhancing the efficiency of biological information handling. This research explores the potential of quantum memory to emulate key aspects of neuronal operation, specifically focusing on the rapid processing and storage of biological information. The theoretical framework developed herein outlines a computational model based on quantum memory interactions, demonstrating a pathway towards achieving significant improvements in biological information processing speed and capacity. This work presents a fundamental investigation into the intersection of quantum mechanics and neuroscience, offering a new perspective on the mechanisms underlying biological memory and potentially paving the way for advanced bio-computing architectures. The presented model utilizes the following key equations to illustrate the core concepts: (Δs) = (H(s) * ∇s) + (G(s, s') * s') where: Δs represents the change in state of the quantum memory. H(s) is the Hamiltonian operator describing the quantum memory's energy levels. ∇s is the gradient operator, representing the influence of external stimuli. G(s, s') is the coupling strength between neighboring quantum memories. s and s' represent the states of the quantum memories. Further equations exploring the dynamics include: (ds/dt) = (H(s) * s) - (∑G(s, s') * s') and the state update rule: s(t+Δt) = U(Δt) * s(t) where: U(Δt) is the time evolution operator, describing the quantum dynamics over a small time interval Δt. This research contributes to the nascent field of quantum biology and provides a foundational model for future investigations into quantum-enhanced biological systems. ---
The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.
Abstract: This paper discusses quantum-inspired models of Livings from the viewpoint of the second law of thermodynamics. It concentrates on Hadamard’s instability of the corresponding parabolic PDE for motions against the time arrow. The instability is removed by adding imaginary components to state variables. The evolution from present to past in a virtual (mental) space is interpreted as memories of the Livings under consideration. Quantum-like entanglement of memories and real motions are found and discussed.