Related papers: Three-Dimensional Quantum Percolation Studied by L…
We study quantum percolation which is described by a tight-binding Hamiltonian containing only off-diagonal hopping terms that are generally in quenched binary disorder (zero or one). In such a system, transmission of a quantum particle is…
In the first paper of this series [S. Torquato, J. Chem. Phys. {\bf 136}, 054106 (2012)], analytical results concerning the continuum percolation of overlapping hyperparticles in $d$-dimensional Euclidean space $\mathbb{R}^d$ were obtained,…
Spatial correlations of occupation probabilities, if their decay is not too fast, can change the critical exponents for classical percolation. From numerical studies of electron dynamics in the lowest Landau level (LLL) we demonstrate the…
Multifractal scaling of critical wave functions at a disorder-driven (Anderson) localization transition is modified near boundaries of a sample. Here this effect is studied for the example of the spin quantum Hall plateau transition using…
Phase transitions are prevalent throughout physics, spanning thermal phenomena like water boiling to magnetic transitions in solids. They encompass cosmological phase transitions in the early universe and the transition into a quark-gluon…
Conditions under which a quantum particle is described using classical quantities are studied. The one-dimensional (1D) and three-dimensional (3D) problems are considered. It is shown that the sum of the contributions from all quantum…
The review is a brief description of the state of problems in percolation theory and their numerous applications, which are analyzed on base of interesting papers published in the last 15-20 years. At the submitted papers are studied both…
The existence of a quantum percolation threshold p_q<1 in the 2D quantum site-percolation problem has been a controversial issue for a long time. By means of a highly efficient Chebyshev expansion technique we investigate numerically the…
Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently…
Percolation plays an important role in fields and phenomena as diverse as the study of social networks, the dynamics of epidemics, the robustness of electricity grids, conduction in disordered media, and geometric properties in statistical…
Scaling theory predicts complete localization in $d=2$ in quantum systems belonging to orthogonal class (i.e. with time-reversal symmetry and spin-rotation symmetry). The conductance $g$ behaves as $g \sim exp(-L/l)$ with system size $L$…
The quantum entangled degrees of entangled states become smaller with the transmission distance increasing, how to keep the purity of quantum entangled states is the puzzle in quantum communication. In the paper, we have designed a new type…
We introduce a simple lattice model in which percolation is constructed on top of critical percolation clusters, and show that it can be repeated recursively any number $n$ of generations. In two dimensions, we determine the percolation…
Our understanding of localization in the integer quantum Hall effect is informed by a combination of semi-classical models and percolation theory. Motivated by the effect of correlations on classical percolation we study numerically…
Quench dynamics is an active area of study encompassing condensed matter physics and quantum information, with applications to cold-atomic gases and pump-probe spectroscopy of materials. Recent theoretical progress in studying quantum…
The quantum metric is a fundamental ingredient of band quantum geometry and has recently at tracted intense interest, with most of its transport signatures appearing in the intrinsic second order nonlinear conductivity. In the clean limit,…
Anderson localization of particles -- the complete halt of wave transport through multiple scattering and phase coherence -- is a paradigmatic manifestation of quantum interference in disordered media. In three dimensions, the scaling…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…
We analyze the out-of-equilibrium dynamics of a quantum particle coupled to local magnetic degrees of freedom that undergo a classical phase transition. Specifically, we consider a two-dimensional tight-binding model that interacts with a…
A triangular triple quantum dot gives various Kondo effects, such as the emergence of an electric polarization accompanied by a complete compensation of spin degrees of freedom. The interplay of spin and charge of electrons in quantum dots…