Eur. Phys. J. Plus (2022) 137: 614
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

^a dilto@fisica.ufc.br

Received: 2 September 2021
Accepted: 15 May 2022
Published online: 21 May 2022

Abstract

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.