Fermions on a torus knot
arXiv:2108.07336 · doi:10.1140/epjp/s13360-022-02828-y
Abstract
In this work, we investigate the effects of a nontrivial topology (and geometry) of a system considering \textit{interacting} and \textit{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 \textit{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 \textit{interacting} fermions.
arXiv comment25 pages, and 13 figures
References in corpus (20)
- Quantum mechanics on curved 2D systems with electric and magnetic fields
- Quantum mechanics of a spin-orbit coupled electron constrained to a space curve
- Geometry effects in confined space
- Quantum statistics of ideal gases in confined space
- Structural and Electronic Properties of a Carbon Nanotorus: Effects of Delocalized Vs Localized Deformations
- Thermodynamic properties in higher-derivative electrodynamics
- Higher-derivative Lorentz-breaking dispersion relations: a thermal description
- Quantum mechanics of a constrained particle and the problem of prescribed geometry-induced potential
- Topology and phase transitions: from an exactly solvable model to a relation between topology and thermodynamics
- Lorentz-violating scenarios in a thermal reservoir
- How does geometry affect quantum gases?
- Bouncing universe in a heat bath
- Thermal aspects of interacting quantum gases in Lorentz-violating scenarios
- Magnetization ground state and reversal modes of magnetic nanotori
- Geometric effects resulting from square and circular confinements for a particle constrained to a space curve
- Dependence of critical level statistics on the sample shape
- The Classical and Quantum Mechanics of a Particle on a Knot
- Particle on a Torus Knot: Constrained Dynamics and Semi-Classical Quantization in a Magnetic Field
- Quantum Mechanics of Particle on a torus knot: Curvature and Torsion Effects
- Particle on a Torus Knot: Anholonomy and Hannay Angle
Cited by in corpus (7)
- Higher-derivative Lorentz-breaking dispersion relations: a thermal description
- How does geometry affect quantum gases?
- Bouncing universe in a heat bath
- Particles in Loop Quantum Gravity formalism: a thermodynamical description
- Thermodynamics of massless particles in curved spacetime
- Thermodynamics of a quantum ring modified by Lorentz violation
- Quantum gases on a torus