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Scale-invariant puddles in graphene: Geometric properties of electron-hole distribution at the Dirac point.
The carrier density profile of the ground state of graphene in the presence of particle-particle interaction and random charged impurity in zero gate voltage is characterized and the charge field is non-Gaussian with unusual Kondev relations, which can be regarded as a new class of two-dimensional random-field surfaces. Expand
Entanglement dynamics in short- and long-range harmonic oscillators
We study the time evolution of the entanglement entropy in the short and long-range coupled harmonic oscillators that have well-defined continuum limit field theories. We first introduce a method toExpand
First-passage-time processes and subordinated Schramm-Loewner evolution.
The first-passage-time processes of the anomalous diffusion on the self-similar curves in two dimensions are studied and natural parametrized subordinated Schramm-Loewner evolution (NS-SLE) is defined as a mathematical tool that can model diffusion on fractal curves. Expand
Controlling Anderson localization in disordered heterostrctures with Lévy-type distribution
In this paper, we propose a disordered heterostructure in which the distribution of the refractive index of one of its constituents follows a Levy-type distribution characterized by the exponent α.Expand
Quantum entanglement entropy and classical mutual information in long-range harmonic oscillators
We study different aspects of quantum von Neumann and R\'enyi entanglement entropy of one-dimensional long-range harmonic oscillators that can be described by well-defined nonlocal field theories. WeExpand
Contour lines of the discrete scale-invariant rough surfaces.
The fractal properties of the 2D DSI rough surfaces apart from possessing the discrete scale-invariance property follow the properties ofThe contour lines of the corresponding scale-Invariant rough surfaces, and this hypothesis is checked by calculating numerous fractal exponents of the contours by using numerical calculations. Expand
Discrete scale invariance and stochastic Loewner evolution.
This study introduces a large class of fractal curves with discrete scale invariance (DSI) and argues that, up to the fractal dimension calculations, all the WM functions follow the behavior of the corresponding brownian motion. Expand
Scaling characteristics of one-dimensional fractional diffusion processes in the presence of power-law distributed random noise.
It is shown that the fractional diffusion processes in the presence of μ-stable Lévy noise display special scaling properties in the probability distribution function (PDF), and the diffusion entropy analysis is applied to extract the growth exponent β and to confirm the validity of the numerical analysis. Expand
Characterization of the anisotropy of rough surfaces: Crossing statistics
In this paper, we propose the use of crossing statistics and its generalizations as a new framework to characterize the anisotropy of a 2D rough surface. The proposed method is expandable to higherExpand
Entropy production of selfish drivers: Implications for efficiency and predictability of movements in a city.
It is found that entropy production is a good order parameter to distinguish the low- and high-congestion phases and randomness in the movements can reduce the uncertainty in the destination time intervals. Expand