Abstract
Fluid states of matter can locally exhibit characteristics of the onset of crystalline order. Traditionally this has been theoretically investigated using multipoint correlation functions. However new measurement techniques now allow multiparticle configurations of cold atomic systems to be observed directly. This has led to a search for new techniques to characterize the configurations that are likely to be observed. One of these techniques is the configuration density (CD), which has been used to argue for the formation of “Pauli crystals” by non-interacting electrons in e.g. a harmonic trap. We show here that such Pauli crystals do not exist, but that other other interesting spatial structures can occur in the form of an “anti-Crystal”, where the fermions preferentially avoid a lattice of positions surrounding any given fermion. Further, we show that configuration densities must be treated with great care as naive application can lead to the identification of crystalline structures which are artifacts of the method and of no physical significance. We analyze the failure of the CD and suggest methods that might be more suitable for characterizing multiparticle correlations which may signal the onset of crystalline order. In particular, we introduce neighbour counting statistics (NCS), which is the full counting statistics of the particle number in a neighborhood of a given particle. We test this on two dimensional systems with emerging triangular and square crystal structures.
Highlights
Fluid states of matter can locally exhibit characteristics of the onset of crystalline order
In refs. 3,4 the authors proposed that multi-particle states in certain systems of non-interacting fermions should show crystal-like patterns, which could be seen in experiments, due to the effective inter-particle repulsion caused by the Pauli exclusion principle
To demonstrate that the probability density of typical configurations that would be seen in an experiment is far from the maximal probability density, we constructed a histogram of the probability densities from samples generated using Monte Carlo (MC) importance sampling
Summary
Fluid states of matter can locally exhibit characteristics of the onset of crystalline order. In cold atomic systems on optical lattices it is possible to directly measure actual multi-particle configurations of bosons[1] or fermions[2], by measuring the positions of all particles in a single shot. This creates an interest in characterizing more fully the configurations that might appear in such experiments. This would be of particular interest in small, low dimensional or low temperature fluid systems, where thermal and quantum fluctuations can wash out any local structure in the average density, but perhaps not in multi-particle correlations. It allows e.g. for a clear identification of shells of neighbors
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
