Quantum Levy flights and multifractality of dipolar excitations in a random system

We consider dipolar excitations propagating via dipole-induced exchange among immobile molecules randomly spaced in a lattice. The character of the propagation is determined by long-range hops (Levy flights). We analyze the eigen-energy spectra and the multifractal structure of the wavefunctions. In 1D and 2D all states are localized, although in 2D the localization length can be extremely large leading to an effective localization-delocalization crossover in realistic systems. In 3D all eigenstates are extended but not always ergodic, and we identify the energy intervals of ergodic and non-ergodic states. The reduction of the lattice filling induces an ergodic to non-ergodic transition, and the excitations are mostly non-ergodic at low filling.Comment: 5 pages, 6 figure

A Probabilistic Embedding Clustering Method for Urban Structure Detection

Urban structure detection is a basic task in urban geography. Clustering is a core technology to detect the patterns of urban spatial structure, urban functional region, and so on. In big data era, diverse urban sensing datasets recording information like human behaviour and human social activity, suffer from complexity in high dimension and high noise. And unfortunately, the state-of-the-art clustering methods does not handle the problem with high dimension and high noise issues concurrently. In this paper, a probabilistic embedding clustering method is proposed. Firstly, we come up with a Probabilistic Embedding Model (PEM) to find latent features from high dimensional urban sensing data by learning via probabilistic model. By latent features, we could catch essential features hidden in high dimensional data known as patterns; with the probabilistic model, we can also reduce uncertainty caused by high noise. Secondly, through tuning the parameters, our model could discover two kinds of urban structure, the homophily and structural equivalence, which means communities with intensive interaction or in the same roles in urban structure. We evaluated the performance of our model by conducting experiments on real-world data and experiments with real data in Shanghai (China) proved that our method could discover two kinds of urban structure, the homophily and structural equivalence, which means clustering community with intensive interaction or under the same roles in urban space.Comment: 6 pages, 7 figures, ICSDM201

Quantum phases of interacting phonons in ion traps

The vibrations of a chain of trapped ions can be considered, under suitable experimental conditions, as an ensemble of interacting phonons, whose quantum dynamics is governed by a Bose--Hubbard Hamiltonian. In this work we study the quantum phases which appear in this system, and show that thermodynamical properties, such as critical parameters and critical exponents, can be measured in experiments with a limited number of ions. Besides that, interacting phonons in trapped ions offer us the possibility to access regimes which are difficult to study with ultracold bosons in optical lattices, like models with attractive or site--dependent phonon-phonon interactions.Comment: 10 page

Disorderless quasi-localization of polar gases in one-dimensional lattices

One-dimensional polar gases in deep optical lattices present a severely constrained dynamics due to the interplay between dipolar interactions, energy conservation, and finite bandwidth. The appearance of dynamically-bound nearest-neighbor dimers enhances the role of the $1/r^3$ dipolar tail, resulting, in the absence of external disorder, in quasi-localization via dimer clustering for very low densities and moderate dipole strengths. Furthermore, even weak dipoles allow for the formation of self-bound superfluid lattice droplets with a finite doping of mobile, but confined, holons. Our results, which can be extrapolated to other power-law interactions, are directly relevant for current and future lattice experiments with magnetic atoms and polar molecules.Comment: 5 + 2 Page

Bosonization and entanglement spectrum for one-dimensional polar bosons on disordered lattices

The extended Bose-Hubbard model subjected to a disordered potential is predicted to display a rich phase diagram. In the case of uniform random disorder one finds two insulating quantum phases -- the Mott-insulator and the Haldane insulator -- in addition to a superfluid and a Bose glass phase. In the case of a quasiperiodic potential further phases are found, eg the incommensurate density wave, adiabatically connected to the Haldane insulator. For the case of weak random disorder we determine the phase boundaries using a perturbative bosonization approach. We then calculate the entanglement spectrum for both types of disorder, showing that it provides a good indication of the various phases.Comment: Submitted to NJ

Universal Quantum Degeneracy Point for Superconducting Qubits

The quantum degeneracy point approach [D. Vion et al., Science 296, 886 (2002)] effectively protects superconducting qubits from low-frequency noise that couples with the qubits as transverse noise. However, low-frequency noise in superconducting qubits can originate from various mechanisms and can couple with the qubits either as transverse or as longitudinal noise. Here, we present a quantum circuit containing a universal quantum degeneracy point that protects an encoded qubit from arbitrary low-frequency noise. We further show that universal quantum logic gates can be performed on the encoded qubit with high gate fidelity. The proposed scheme is robust against small parameter spreads due to fabrication errors in the superconducting qubits.Comment: 7 pages, 4 figure