https://doi.org/10.1140/epjp/s13360-022-02828-y
Regular Article
Fermions on a torus knot
1
Departamento de Física, Universidade Federal do Ceará (UFC), C.P. 6030, Campus do Pici, 60455-760, Fortaleza, CE, Brazil
2
Departamento de Física, Universidade Federal do Maranhão (UFMA), Campus Universitário do Bacanga, 65080-805, São Luís, MA, Brazil
3
Departamento de Física, Universidade Estadual do Maranhão (UEMA), Cidade Universitária Paulo VI, 65055-310, São Luís, MA, Brazil
4
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T.Road, 700108, Kolkata, India
Received:
2
September
2021
Accepted:
15
May
2022
Published online:
21
May
2022
In this work, we investigate the effects of a nontrivial topology (and geometry) of a system considering interacting and noninteracting particle modes, which are restricted to follow a closed path over the torus surface. In order to present a prominent thermodynamical investigation of this system configuration, we carry out a detailed analysis using statistical mechanics within the grand canonical ensemble approach to deal with noninteracting fermions. In an analytical manner, we study the following thermodynamic functions in such context: the Helmholtz free energy, the mean energy, the magnetization and the susceptibility. Further, we take into account the behavior of Fermi energy of the thermodynamic system. Finally, we briefly outline how to proceed in case of interacting fermions.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
