Thermodynamics of Statistical Anyons
Nathan M. Myers and Sebastian DeffnerAbstract:In low-dimensional systems, indistinguishable particles can display statistics that interpolate between bosons and fermions. Signatures of these “anyons” have been detected in two-dimensional quasiparticle excitations of the fractional quantum Hall effect, however experimental access to these quasiparticles remains limited. As an alternative to these “topological anyons,” we propose “statistical anyons” realized through a statistical mixture of particles with bosonic and fermionic symmetry. We show that the framework of statistical anyons is equivalent to the generalized exclusion statistics (GES) pioneered by Haldane, significantly broadening the range of systems to which GES apply. We develop the full thermodynamic characterizations of these statistical anyons, including both equilibrium and nonequilibrium behavior. To develop a complete picture, we compare the performance of quantum heat engines with working mediums of statistical anyons and traditional topological anyons, demonstrating the effects of the anyonic phase in both local equilibrium and fully nonequilibrium regimes. In addition, methods of optimizing engine performance through shortcuts to adiabaticity are investigated, using both linear response and fast-forward techniques.Summary:
In general, elementary particles are classified as fermions or bosons. Fermions, forbidden from occupying the same quantum state by the Pauli exclusion principle, tend to repel each other, while bosons, an infinite number of which can occupy the same state, tend to bunch together. However, there exists another class, “anyone,” that can manifest as quasiparticles. These anyons can display behavior anywhere between fermions and bosons. Anyons can be classified into two main categories. For “topological” anyons, which only exist in two dimensions, exchanging the positions of two particles and then exchanging them back can lead to a different quantum state. “Generalized exclusion statistics” (GES) anyons, which have no limitations on their dimensionality, loosen the restrictions of the exclusion principle to allow varying numbers of particles to occupy the same state. Anyons present tantalizing possibilities for applications in quantum devices, with a specific variety of topological anyons being the key to a theoretical type of error-resistant quantum computer. However, topological anyons have proven extremely difficult to detect and control experimentally, making it challenging to study their behavior. In this paper, we propose a conceptually simple and experimentally feasible framework for studying anyons using statistical mixtures of bosons and fermions.
We apply this framework of “statistical anyons” in a comprehensive examination of the thermodynamics of anyons. We show that statistical anyons are equivalent to GES anyons, and we demonstrate that, while they cannot replicate the exchange properties of topological anyons, they can be used to exactly replicate their thermodynamic behavior. We explore how the unique properties of anyons can be applied in the paradigmatic thermodynamic device—the heat engine. These results establish statistical anyons as a theoretically straightforward and experimentally tractable method of examining anyon thermodynamics and open the door to potential thermodynamics-based methods of detecting and controlling topological anyons.
Posted: October 19, 2021, 1:04 PM