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Title: Nuclear Information Density Spectrum (NIDS): A New Paradigm for Quantum Correlations in the Atomic Nucleus

Jincheng Zhang

Published Aug 19, 2026• 0 citations
Publisher

Abstract

The conventional description of the atomic nucleus relies heavily on the spatial distribution of nucleons, expressed by the nuclear density function ρ(r). While ρ(r) captures the average position of nucleons, it neglects the intrinsic quantum correlations that arise from the many-body wave function. In this paper, we introduce the Nuclear Information Density Spectrum (NIDS), a formalism that supplements the conventional density with an information density I(r), defined in terms of the local reduced density matrix and an entropic functional. I(r) quantifies the amount of quantum information and correlation present at each point inside the nucleus. We develop the mathematical foundations of NIDS, derive its properties, and discuss its implications for nuclear structure and scattering processes. By integrating NIDS into the analysis of scattering data, we demonstrate that it provides a more nuanced understanding of nuclear dynamics, potentially opening new avenues for precision tests of nuclear models and a deeper appreciation of the underlying quantum many-body physics.

DOI
10.5281/zenodo.22005483

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The conventional description of the atomic nucleus relies heavily on the spatial distribution of nucleons, expressed by the nuclear density function ρ(r). While ρ(r) captures the average position of nucleons, it neglects the intrinsic quantum correlations that arise from the many-body wave function. In this paper, we introduce the Nuclear Information Density Spectrum (NIDS), a formalism that supplements the conventional density with an information density I(r), defined in terms of the local reduced density matrix and an entropic functional. I(r) quantifies the amount of quantum information and correlation present at each point inside the nucleus. We develop the mathematical foundations of NIDS, derive its properties, and discuss its implications for nuclear structure and scattering processes. By integrating NIDS into the analysis of scattering data, we demonstrate that it provides a more nuanced understanding of nuclear dynamics, potentially opening new avenues for precision tests of nuclear models and a deeper appreciation of the underlying quantum many-body physics.
The conventional description of nuclear structure relies heavily on the nuclear mass density function ρ(r) which captures the distribution of nucleons within the nucleus. Recent theoretical developments suggest that this view is incomplete because it neglects the spatial distribution of quantum informational content that arises from many–body correlations and entanglement among nucleons. In this paper we introduce the Nuclear Information Density Spectrum (NIDS), a formalism that assigns to each point inside a nucleus an information density function I(r). This function quantifies the amount of quantum information encoded at each spatial coordinate and is defined through the von Neumann entropy of reduced density matrices of local subsystems. By integrating I(r) over the nuclear volume we recover the total quantum informational content, while the shape of I(r) reflects the distribution of correlation strength throughout the nucleus. We derive explicit expressions for I(r) in terms of the two–body correlation function g2(r1,r2) and outline a strategy to extract I(r) from high–energy elastic and inelastic scattering experiments. The NIDS formalism provides a new lens to view the internal structure of nuclei, potentially redefining shell closures, deformation, and collective modes. Moreover, it offers a quantitative framework to assess the role of quantum correlations in nuclear binding, with implications for the interpretation of exotic nuclei and the equation of state of dense matter. The proposal that the nucleus contains an intrinsic information density invites fresh experimental investigations that could lead to a Nobel–level paradigm shift in nuclear physics.
Quantum information theory, a foundational field within quantum computing and cryptography, relies heavily on the precise manipulation and analysis of quantum states. Traditional approaches often struggle to adequately represent and quantify the complexities inherent in these states. This paper proposes a novel framework based on hypergeometric distributions to formalize the mathematical foundations of quantum information theory, offering a rigorous and powerful tool for predicting and analyzing quantum phenomena. Hypergeometric distributions, a specialized distribution in probability theory, provide a natural and efficient way to model the correlated nature of quantum states, leading to a more robust and adaptable mathematical foundation. The core mechanism involves developing new mathematical tools to quantify fidelity and entanglement, thereby facilitating the design of quantum algorithms. This work aims to bridge the gap between theoretical concepts and practical applications, potentially unlocking new algorithmic possibilities and pushing the boundaries of quantum information processing.
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Quantum decoherence, a fundamental challenge in quantum information processing, represents the loss of quantum coherence due to interaction with the environment. This paper explores a novel mathematical framework for understanding and quantifying this phenomenon, proposing a 'Quantum Decoherence Metric' – a rigorously defined function that captures the rate of decoherence and offers a precise tool for analysis. This work addresses a longstanding difficulty in modeling and analyzing decoherence, aiming for a more mathematically solid and controllable approach. The core mechanism involves the creation of a metric specifically designed to quantify the degradation of quantum states. This development builds upon existing theoretical concepts, providing a quantitative lens through which to examine and potentially mitigate decoherence effects. The resulting framework offers a significant step towards a deeper understanding of quantum systems and their stability.
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A long-standing goal of nuclear theory is to explain how the structure and dynamics of atomic nuclei and neutron-star matter emerge from the underlying interactions among protons and neutrons. Achieving this goal requires solving the nuclear quantum many-body problem with high accuracy across a wide range of length scales and density regimes. In this review, we discuss how artificial neural network representations of the nuclear many-body wave function have significantly extended the capabilities of continuum quantum Monte Carlo methods. In particular, neural network quantum states enable calculations of larger systems than were previously accessible and provide a flexible framework for capturing phenomena that challenge conventional approaches, including the emergence of nuclear clusters and superfluid phases in dense matter. We highlight recent applications to finite nuclei, infinite nuclear and neutron matter, and dynamical processes relevant to lepton-nucleus and nucleus-nucleus scattering. We also discuss conceptual and methodological connections with condensed matter physics, emphasizing developments in neural network quantum states that bridge strongly correlated systems across disciplines. Together, these developments demonstrate how neural-network methods open new avenues toward unified and accurate descriptions of nuclear structure, matter, and reactions.