Information Theoretical Analysis of Quantum Mixedness in a Finite Model of Interacting Fermions
In this study, we utilize information theory tools to investigate notable features of the quantum degree of mixedness (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mi>f</...
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MDPI AG
2025-01-01
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| author | Diana Monteoliva Angelo Plastino Angel Ricardo Plastino |
| author_facet | Diana Monteoliva Angelo Plastino Angel Ricardo Plastino |
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| description | In this study, we utilize information theory tools to investigate notable features of the quantum degree of mixedness (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mi>f</mi></msub></semantics></math></inline-formula>) in a finite model of <i>N</i> interacting fermions. This model serves as a simplified proxy for an atomic nucleus, capturing its essential features in a more manageable form compared to a realistic nuclear model, which would require the diagonalization of matrices with millions of elements, making the extraction of qualitative features a significant challenge. Specifically, we aim to correlate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mi>f</mi></msub></semantics></math></inline-formula> with particle number fluctuations and temperature, using the paradigmatic Lipkin model. Our analysis reveals intriguing dependencies of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mi>f</mi></msub></semantics></math></inline-formula> on the total fermion number, showcasing distinct behaviors at different temperatures. Notably, we find that the degree of quantum mixedness exhibits a strong dependence on the total fermion number, with varying trends across different temperature regimes. Remarkably, this dependence remains unaffected by the strength of the fermion–fermion interaction (as long as it is non-zero), underscoring the robustness of the observed phenomena. Through comprehensive numerical simulations, we provide illustrative graphs depicting these dependencies, offering valuable insights into the fundamental characteristics of quantum many-body fermion systems. Our findings illuminate the intricate dynamics of the degree of mixedness, a crucial quantum property, with potential implications for diverse fields ranging from condensed matter physics to quantum information science. |
| format | Article |
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| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-01-01 |
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| spelling | doaj-art-f1e8543c39f943ab84e8de02fca1d2e62025-01-24T13:31:45ZengMDPI AGEntropy1099-43002025-01-012713710.3390/e27010037Information Theoretical Analysis of Quantum Mixedness in a Finite Model of Interacting FermionsDiana Monteoliva0Angelo Plastino1Angel Ricardo Plastino2UNLP-Comisión de Investigaciones Científicas Provincia de Buenos Aires, La Plata 1900, ArgentinaInstituto de Física La Plata, CCT-CONICET, Universidad Nacional de La Plata, La Plata 1900, ArgentinaCeBio-Departamento de Ciencias Básicas, Universidad Nacional del Noroeste Provincia de Buenos Aires (UNNOBA), CONICET, Junin 6000, ArgentinaIn this study, we utilize information theory tools to investigate notable features of the quantum degree of mixedness (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mi>f</mi></msub></semantics></math></inline-formula>) in a finite model of <i>N</i> interacting fermions. This model serves as a simplified proxy for an atomic nucleus, capturing its essential features in a more manageable form compared to a realistic nuclear model, which would require the diagonalization of matrices with millions of elements, making the extraction of qualitative features a significant challenge. Specifically, we aim to correlate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mi>f</mi></msub></semantics></math></inline-formula> with particle number fluctuations and temperature, using the paradigmatic Lipkin model. Our analysis reveals intriguing dependencies of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mi>f</mi></msub></semantics></math></inline-formula> on the total fermion number, showcasing distinct behaviors at different temperatures. Notably, we find that the degree of quantum mixedness exhibits a strong dependence on the total fermion number, with varying trends across different temperature regimes. Remarkably, this dependence remains unaffected by the strength of the fermion–fermion interaction (as long as it is non-zero), underscoring the robustness of the observed phenomena. Through comprehensive numerical simulations, we provide illustrative graphs depicting these dependencies, offering valuable insights into the fundamental characteristics of quantum many-body fermion systems. Our findings illuminate the intricate dynamics of the degree of mixedness, a crucial quantum property, with potential implications for diverse fields ranging from condensed matter physics to quantum information science.https://www.mdpi.com/1099-4300/27/1/37Lipkin modelmany fermion systemsmixedness-degreefinite temperatureSU2 symmetry |
| spellingShingle | Diana Monteoliva Angelo Plastino Angel Ricardo Plastino Information Theoretical Analysis of Quantum Mixedness in a Finite Model of Interacting Fermions Entropy Lipkin model many fermion systems mixedness-degree finite temperature SU2 symmetry |
| title | Information Theoretical Analysis of Quantum Mixedness in a Finite Model of Interacting Fermions |
| title_full | Information Theoretical Analysis of Quantum Mixedness in a Finite Model of Interacting Fermions |
| title_fullStr | Information Theoretical Analysis of Quantum Mixedness in a Finite Model of Interacting Fermions |
| title_full_unstemmed | Information Theoretical Analysis of Quantum Mixedness in a Finite Model of Interacting Fermions |
| title_short | Information Theoretical Analysis of Quantum Mixedness in a Finite Model of Interacting Fermions |
| title_sort | information theoretical analysis of quantum mixedness in a finite model of interacting fermions |
| topic | Lipkin model many fermion systems mixedness-degree finite temperature SU2 symmetry |
| url | https://www.mdpi.com/1099-4300/27/1/37 |
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