Symmetries and statistical behavior in fermion systems

J. B. French, J. P. Draayer

Dunlop, Joe, A. Tejero, Michalis Skotiniotis +1 more

The behavior of a collection of identical particles is intimately linked to the symmetries of their wavefunction under particle exchange. Topological anyons, arising as quasiparticles in low-dimensional systems, interpolate between bosons and fermions, picking up a complex phase when exchanged. Recent research has demonstrated that similar statistical behavior can arise with mixtures of bosonic and fermionic pairs, offering theoretical and experimental simplicity. We introduce an alternative implementation of such \emph{statistical anyons}, based on promoting or suppressing the population of symmetric states via a symmetry generating Hamiltonian. The scheme has numerous advantages: anyonic statistics emerge in a single particle pair, extending straightforwardly to larger systems; the statistical properties can be dynamically adjusted; and the setup can be simulated efficiently. We show how exchange symmetry can be exploited to improve the performance of heat engines, and demonstrate a reversible work extraction cycle in which bosonization and fermionization replace compression and expansion strokes. Additionally, we investigate emergent thermal properties, including critical phenomena, in large statistical anyon systems.

Stefano Longhi

In multiparticle quantum interference, bosons show rather generally the tendency to bunch together, while fermions cannot. This behavior, which is rooted in the different statistics of the particles, results in a higher coincidence rate P for fermions than for bosons, i.e., P ( b o s ) < P ( f e r m ) . However, in lossy systems, such a general rule can be violated because bosons can avoid lossy regions. Here it is shown that, in a rather general optical system showing passive parity–time ( P T ) symmetry, at the P T symmetry breaking phase transition point, the coincidence probabilities for bosons and fermions are equalized, while in the broken P T phase, the reversal P ( b o s ) > P ( f e r m ) is observed. Such effect is exemplified by considering the passive P T -symmetric optical directional coupler.

節夫 三沢

Leon N. Cooper

Gautam Goswami, Pratul Bandyopadhyay

The Zp spin system in two dimensions from the point of view of fractional statistics is studied herein. It is found that, for p≤4, the system represents a gas of particles having a specific fermion number when p=2 corresponds to fermion number 1 and p=3 and 4 corresponds to a fractional fermion number. However, for p≥5, the corresponding system does not represent particles having any specific statistics; rather, it represents a hedgehog behavior. The XY model represented by a Zp spin system at p→∞ limit corresponds to bosonic kinks composed of vortex–antivortex pairs below a certain temperature. The two massive phases observed in a Zp system for 2≤p≤4 is related to their intrinsic fermionic character, and the three phases observed for p≥5 when a massless phase occurs in between two massive phases is related to the hedgehog behavior of the corresponding particles so far as their statistics is concerned. The XY model corresponding to a Zp spin system at p→∞ represents massive bosonic kinks as bound states of vortex–antivortex pairs below a certain temperature when the spin waves are massless and, as the temperature goes up, the bound states dissociate and massless kinks and massive spin waves appear. The nonexistence of an ordered phase for a continuous symmetry model is related to the inherent bosonic character of the corresponding particles.