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      Entropy of pure states: not all wave functions are born equal

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      1 , a , * ,
      4open
      EDP Sciences
      Many-body Hilbert space, Free module, Logical entropy, Quantum entropy, Bargmann space

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          Abstract

          Many-body Hilbert space has the algebraic structure of a finitely generated free module. All N-body wave functions in d dimensions can be generated by a finite number of N! d − 1 of generators called shapes, with symmetric-function coefficients. Physically the shapes are vacuum states, while the symmetric coefficients are bosonic excitations of these vacua. It is shown here that logical entropy can be used to distinguish fermion shapes by information content, although they are pure states whose usual quantum entropies are zero. The construction is based on the known algebraic structure of fermion shapes. It is presented for the case of N fermions in three dimensions. The background of this result is presented as an introductory review.

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          Most cited references17

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          On a Hilbert space of analytic functions and an associated integral transform part I

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            Two-dimensional Hubbard model: Numerical simulation study

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              The Theory of Complex Spectra

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                Author and article information

                Contributors
                Role: Guest Editor
                Journal
                fopen
                https://www.4open-sciences.org
                4open
                4open
                EDP Sciences
                2557-0250
                25 January 2022
                25 January 2022
                2022
                : 5
                : ( publisher-idID: fopen/2022/01 )
                : 3
                Affiliations
                [1 ] Department of Physics, Faculty of Science, University of Zagreb, , 10000 Zagreb, Croatia,
                Author notes
                [* ]Corresponding author: dks@ 123456phy.hr
                [a]

                Supported by the Croatian Science Foundation Project No. IP-2018-01-7828.

                Author information
                https://orcid.org/0000-0002-1383-0674
                Article
                fopen210010
                10.1051/fopen/2021006
                157b7575-1777-47fe-9eec-02e30deec992
                © D.K. Sunko, Published by EDP Sciences, 2022

                This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                History
                : 16 September 2021
                : 17 November 2021
                Page count
                Figures: 2, Tables: 0, Equations: 64, References: 19, Pages: 10
                Funding
                Funded by: Hrvatska Zaklada za Znanost http://dx.doi.org/10.13039/501100004488
                Award ID: IP-2018-01-7828
                Categories
                Physics - Applied Physics
                Research Article
                Logical Entropy
                Custom metadata
                4open 2022, 5, 3
                2022
                2022
                2022
                yes

                Medicine,Chemistry,Physics,Mathematics,Materials science,Life sciences
                Logical entropy,Many-body Hilbert space,Quantum entropy,Free module,Bargmann space

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