Some genreal features of the scattering of boson-based anyons with an added nonstatistical interaction are discussed. Periodicity requirements of the phase shifts are derived, and used to illustrate the danger inherent in separating these phase shifts into the well-known pure Aharanov-Bohm phase shifts, and an additional set which arises due to the interaction. It is proven that the added phase shifts, although due to the nonstatistical interaction, necessarily change as the statistical parameter is varied, keeping the interaction fixed. A hard-disk interaction provides a concrete illustration of these general ideas. In the latter part of the paper, scattering with an additional hard-disk interaction is studied in detail, with an eye towards providing a criterion for the validity of the mean-field approximation for anyons, which is the first step in virtually any treatment of this system. We find, consistent with previous work, that the approximation is justified if the statistical interaction is weak, and that it must be more weak for boson-based than for fermion-based anyons.
Some general features of the scattering of boson-based anyons with an added non-statistical interaction are discussed.Periodicity requirements of the phase shifts are derived, and used to illustrate the danger inherent in separating these phase shifts into the well-known pure Aharanov-Bohm phase shifts, and an additional set which arise due to the interaction.It is proven that the added phase shifts, although due to the non-statistical interaction, necessarily change as the statistical parameter is varied, keeping the interaction fixed.A hard-disk interaction provides a concrete illustration of these general ideas.
Some general features of the scattering of boson-based anyons with an added non-statistical interaction are discussed.Periodicity requirements of the phase shifts are derived, and used to illustrate the danger inherent in separating these phase shifts into the well-known pure Aharanov-Bohm phase shifts, and an additional set which arise due to the interaction.It is proven that the added phase shifts, although due to the non-statistical interaction, necessarily change as the statistical parameter is varied, keeping the interaction fixed.A hard-disk interaction provides a concrete illustration of these general ideas.
We examine an approach to justifying the mean field approximation for the anyon gas, using the scattering of anyons. Parity violation permits a nonzero average scattering angle, from which one can extract a mean radius of curvature for anyons. If this is larger than the interparticle separation, one expects that the graininess of the statistical magnetic field is unimportant, and that the mean field approximation is good. We argue that a non-conventional interaction between anyons is crucial, in which case the criterion for validity of the approximation is identical to the one deduced using a self-consistency argument.
In textbook physics, all particles are categorized as either bosons or fermions. When exchanging two bosons, the corresponding wavefunction is dressed with an exchange phase
φ=0, whereas for fermions the exchange phase is
φ=π, reflecting the well-known symmetrization postulate of quantum mechanics. While this is true in three spatial dimensions, one- and two-dimensional systems can host particles with non-trivial exchange phase
0≤φ<2π, so-called anyons, which exhibit exchange statistics intermediate between those of bosons and fermions. Here, we consider a Hubbard-type model for one-dimensional anyons, consisting in a discrete lattice on which anyons can tunnel and interact.\\ We first address the case of two anyons on an infinite lattice and solve the Schrödinger equation analytically, deriving bound- and scattering state solutions. We demonstrate the existence of scattering resonances related to the anyonic exchange phase. We confirm this via numerical simulations of two-wavepacket scattering dynamics, where we observe Wigner time delays and lateral shifts. These two phenomena are accurately explained by studying the behavior of the scattering phase in the analytical solution. By further introducing a potential barrier, we model two-anyon interference on a beamsplitter and show that the exchange phase allows to interpolate between bosonic bunching and fermionic antibunching behaviors.\\ We further examine many-anyon systems from the perspective of quantum chaos. Comparing the eigenvalue statistics, in particular the mean level-splitting-ratio with random matrix predictions, allows us to identify the non-interacting limit of the anyon-Hubbard model as chaotic, in sharp contrast to the bosonic case, which we attribute to the effective interaction mediated by the exchange phase. We further consider the collective delocalization of eigenstates in the site basis via their fractal dimensions as an additional indicator of quantum chaos. Lastly, we discuss signatures of many-body interference in the long-time average variance
Δnj of a single site's population, and the dependence of these on the exchange phase. In the chaotic regime, we find that
Δnj neither significantly depends on the initial state, nor on the exchange phase.