Quasi-Magical Fermion Numbers and Thermal Many-Body Dynamics
2. Statistical Notion of Order
3. SU2-Based Fermion Models
3.1. Lipkin Model
3.2. The AFP Model
3.3. Hamiltonian Matrices
4. Statistical Mechanics Indicators
5. Singular Values for the Fermion Numbers
- The larger the value of N, the more stable the system becomes, as indicated by the behavior of the Lipkin free energy.
- This is not so in the AGFO case, where there is an absolute free energy minimum at a specific “magic” number.
- The main discovery with respect to the AFP entropy is the singular N value around N∼60 (the same as above). It signals not only stability but a loss of information.
- As regards Lipkin’s entropy, we have rather a lot to say. For small N numbers, the entropy almost vanishes, indicating a system in a mixed state close to the ground state. Then, and rather suddenly (magic number), as N grows, the system leaves the state described above and passes to a much more mixed state, losing information. The new state, however, remains stable as N continues to increase.
- AFPs D. The degree of order is large, in general, as the system lies in a state close to the ground state, as we saw above. However, for the same quasi-magic number N as above, the system abandons that state, passing to a much more mixed state and losing “order” as a consequence. This situation reverts back to the original one as N keeps growing.
- Lipkin’s D. The situation is much more complicated here than it was for the AFP model. For very small N values, this system lies in a disordered state. For moderate N values, a large degree of order is attained. Then, at the quasi-magic N value, the degree of order diminishes and then remains constant as N keeps increasing.
Data Availability Statement
Conflicts of Interest
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Plastino, A.; Monteoliva, D.; Plastino, A.R. Quasi-Magical Fermion Numbers and Thermal Many-Body Dynamics. Axioms 2023, 12, 493. https://doi.org/10.3390/axioms12050493
Plastino A, Monteoliva D, Plastino AR. Quasi-Magical Fermion Numbers and Thermal Many-Body Dynamics. Axioms. 2023; 12(5):493. https://doi.org/10.3390/axioms12050493Chicago/Turabian Style
Plastino, Angelo, Diana Monteoliva, and Angel Ricardo Plastino. 2023. "Quasi-Magical Fermion Numbers and Thermal Many-Body Dynamics" Axioms 12, no. 5: 493. https://doi.org/10.3390/axioms12050493