Related papers: The OSSS Method in Percolation Theory
The van der Waals liquid orthoterphenyl has long been used as a model system in the study of the glass transition. Motivated by mode-coupling theory, extensive experiments have been undertaken to monitor the onset of structural relaxation…
In this paper we study Poisson processes of so-called "fat" cylinders in hyperbolic space. As our main result we show that this model undergoes a percolation phase transition. We prove this by establishing a novel link between the fat…
Percolation phenomena are pervasive in nature, ranging from capillary flow, crack propagation, ionic transport, fluid permeation, etc. Modeling percolation in highly-branched media requires the use of numerical solutions, as problems can…
A two-dimension extension of the Self-organized Gradient Percolation (SGP) method initially developed for the one-dimensional simulation is proposed. The initialization in the two directions is considered as the analytic solution of the 2D…
Exact diagonalization techniques are a powerful method for studying many-body problems. Here, we apply this method to systems of few bosons in an optical lattice, and use it to demonstrate the emergence of interesting quantum phenomena like…
We continue our work on developing techniques for studying turbulence with spectroscopic data. We show that Doppler-broadened absorption spectral lines, in particularly, saturated absorption lines, can be used within the framework of the…
We study percolation properties of the upper invariant measure of the contact process on $\mathbb{Z}^d$. Our main result is a sharp percolation phase transition with exponentially small clusters throughout the subcritical regime and a…
We prove phase transitions for continuum percolation in a Boolean model based on a Cox point process with nonstabilizing directing measure. The directing measure, which can be seen as a stationary random environment for the classical…
Many polarisation techniques have been harnessed for decades in biological and clinical research, each based upon measurement of the vectorial properties of light or the vectorial transformations imposed on light by objects. Various…
While methods based on density-functional perturbation theory have dramatically improved our understanding of electron-phonon contributions to transport in materials, methods for accurately capturing electron-electron scattering relevant to…
We study the analogue of Poisson ensembles of Markov loops ('loop soups') in the setting of one-dimensional diffusions. We give a detailed description of the corresponding intensity measure. The properties of this measure on loops lead us…
We study the empirical process arising from a multi-dimensional diffusion process with periodic drift and diffusivity. The smoothing properties of the generator of the diffusion are exploited to prove the Donsker property for certain…
This script is based on the notes the author prepared to give a set of six lectures at the Les Houches School "Integrability in Atomic and Condensed Matter Physics" in the summer of 2018. The school had its focus on the application of…
The spin-boson (SB) model is a standard prototype for quantum dissipation, which we generalize in this work, to explore the dissipative effects on a one-dimensional spin-orbit (SO) coupled particle in the presence of a sub-ohmic bath. We…
A range of first-passage percolation type models are believed to demonstrate the related properties of sublinear variance and superdiffusivity. We show that directed last-passage percolation with Gaussian vertex weights has a sublinear…
This review presents various aspects of a mean-field spin glass model known as the p-spin spherical spin glass model, which has raised a lot of interest in the study of spin glasses, and also for its possible links with a mean-field theory…
We present a theoretical model for the evolution of mixture concentrations in a micro-pervaporation device, similar to those recently presented experimentally. The described device makes use of the pervaporation of water through a thin PDMS…
We introduce a Poissonization method to study the coalescent structure of uniform samples from branching processes. This method relies on the simple observation that a uniform sample of size $k$ taken from a random set with positive…
The spin-boson model, involving spins interacting with a bath of quantum harmonic oscillators, is a widely used representation of open quantum systems. Trapped ions present a natural platform for simulating the quantum dynamics of such…
An introduction to spin techniques in particle physics is given. Among the topics covered are: helicity formalism and its applications to the decay and scattering of spin-1/2 and spin-1 particles, techniques for evaluating helicity…