Matrix Product States for Trial Quantum Hall States

We obtain an exact matrix-product-state (MPS) representation of a large series of fractional quantum Hall (FQH) states in various geometries of genus 0. The states in question include all paired k=2 Jack polynomials, such as the Moore-Read and Gaffnian states, as well as the Read-Rezayi k=3 state. We also outline the procedures through which the MPS of other model FQH states can be obtained, provided their wavefunction can be written as a correlator in a 1+1 conformal field theory (CFT). The auxiliary Hilbert space of the MPS, which gives the counting of the entanglement spectrum, is then simply the Hilbert space of the underlying CFT. This formalism enlightens the link between entanglement spectrum and edge modes. Properties of model wavefunctions such as the thin-torus root partitions and squeezing are recast in the MPS form, and numerical benchmarks for the accuracy of the new MPS prescription in various geometries are provided.Comment: 5 pages, 1 figure, published versio

Correlation properties of continuous-time autoregressive processes delayed by the inverse of the stable subordinator

We define the delayed Lévy-driven continuous-time autoregressive process via the inverse of the stable subordinator. We derive correlation structure for the observed non-stationary delayed Lévy-driven continuous-time autoregressive processes of order p, emphasizing low orders, and we show they exhibit long-range dependence property. Distributional properties are discussed as wel

Ehrenfest-Brillouin-type correlated continuous time random walk and fractional Jacobi diffusion

Continuous time random walks (CTRWs) have random waiting times between particle jumps. Based on Ehrenfest-Brillouin-type model motivated by economics, we define the correlated CTRW that converge to the fractional Jacobi diffusion Y (E(t)), t ≥ 0, defined as a time change of Jacobi diffusion process Y (t) to the inverse E(t) of the standard stable subordinator. In the CTRW considered in this paper, the jumps are correlated so that in the limit the outer process Y (t) is not a L´evy process but a diffusion process with non-independent increments. The waiting times between jumps are selected from the domain of attraction of a stable law, so that the correlated CTRWs with these waiting times converge to Y (E(t))

Quantum scars of bosons with correlated hopping

Recent experiments on Rydberg atom arrays have found evidence of anomalously slow thermalization and persistent density oscillations, which have been interpreted as a many-body analog of the phenomenon of quantum scars. Periodic dynamics and atypical scarred eigenstates originate from a “hard” kinetic constraint: the neighboring Rydberg atoms cannot be simultaneously excited. Here we propose a realization of quantum many-body scars in a 1D bosonic lattice model with a “soft” constraint in the form of density-assisted hopping. We discuss the relation of this model to the standard Bose-Hubbard model and possible experimental realizations using ultracold atoms. We find that this model exhibits similar phenomenology to the Rydberg atom chain, including weakly entangled eigenstates at high energy densities and the presence of a large number of exact zero energy states, with distinct algebraic structure

Heavy-tailed fractional Pearson diffusions

We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a nonMarkovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and Fisher-Snedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation

Reactive Dye Degradation by AOPs; Development of a Kinetic Model for UV/H2O2 Process

An application of UV/H2O2 process for the treatment of model wastewater containing organic reactive azo dye C.I. Reactive Blue 137 (RB137) was studied. The efficiency of applied process for decolorization and mineralization of RB137 model solution is discussed. The influence of operating process parameters, initial pH and initial concentration of H2O2, as well as initial dye mass concentration on process effectiveness was investigated. Both direct UV photolysis and OH radical attack were assumed as RB137 degradation mechanisms and a detailed kinetic model for dye degradation by UV/H2O2 process was proposed. The predicted system behavior was compared with experimentally obtained results of decolorization and mineralization of RB137 wastewater. A sensitivity analysis for the evaluation of importance of each reaction used in the model development was also included

Reactive Dye Degradation by AOPs; Development of a Kinetic Model for UV/H2O2 Process

An application of UV/H2O2 process for the treatment of model wastewater containing organic reactive azo dye C.I. Reactive Blue 137 (RB137) was studied. The efficiency of applied process for decolorization and mineralization of RB137 model solution is discussed. The influence of operating process parameters, initial pH and initial concentration of H2O2, as well as initial dye mass concentration on process effectiveness was investigated. Both direct UV photolysis and OH radical attack were assumed as RB137 degradation mechanisms and a detailed kinetic model for dye degradation by UV/H2O2 process was proposed. The predicted system behavior was compared with experimentally obtained results of decolorization and mineralization of RB137 wastewater. A sensitivity analysis for the evaluation of importance of each reaction used in the model development was also included

Approximation of heavy-tailed fractional Pearson diffusions in Skorokhod topology

Continuous time random walks (CTRWs) have random waiting times between particle jumps. We establish fractional diffusion approximation via correlated CTRWs. Instead of a random walk modeling particle jumps in the classical CTRW model, we use discrete-time Markov chain with correlated steps. The waiting times are selected from the domain of attraction of a stable law

Quantum Hall Effects in Graphene-Based Two-Dimensional Electron Systems

In this article we review the quantum Hall physics of graphene based two-dimensional electron systems, with a special focus on recent experimental and theoretical developments. We explain why graphene and bilayer graphene can be viewed respectively as J=1 and J=2 chiral two-dimensional electron gases (C2DEGs), and why this property frames their quantum Hall physics. The current status of experimental and theoretical work on the role of electron-electron interactions is reviewed at length with an emphasis on unresolved issues in the field, including assessing the role of disorder in current experimental results. Special attention is given to the interesting low magnetic field limit and to the relationship between quantum Hall effects and the spontaneous anomalous Hall effects that might occur in bilayer graphene systems in the absence of a magnetic field