Related papers: On the critical level-curvature distribution
The prevalence of sparsity in interacting many-body systems motivates an investigation into the spectral statistics of sparse random matrices with on-site disorder. We numerically demonstrate that the Anderson transition can be identified…
We analyze statistical probability distributions of intensities collected by diffraction techniques like Low-Energy Electron Diffraction. A simple theoretical model based in hard-sphere potentials and LEED formalism is investigated for…
We report a careful finite size scaling study of the metal insulator transition in Anderson's model of localisation. We focus on the estimation of the critical exponent $\nu$ that describes the divergence of the localisation length. We…
We establish a general framework to explore parametric statistics of individual energy levels in disordered and chaotic quantum systems of unitary symmetry. The method is applied to the calculation of the universal intra-level parametric…
The quantum kicked rotor (QKR) driven by $d$ incommensurate frequencies realizes the universality class of $d$-dimensional disordered metals. For $d>3$, the system exhibits an Anderson metal-insulator transition which has been observed…
We have examined the behaviour of noninteracting electrons moving on a corner-sharing tetrahedral lattice into which we introduce a uniform (box) distribution, of width W, of random on-site energies. We have used both the relative…
We explore the connections between dissipative quantum phase transitions and non-Hermitian random matrix theory. For this, we work in the framework of the dissipative Dicke model which is archetypal of symmetry-breaking phase transitions in…
For the quantum kicked top we study numerically the distribution of Hilbert-space vectors evolving in the presence of a small random perturbation. For an initial coherent state centered in a chaotic region of the classical dynamics, the…
The (emergent) symmetry of a critical point is one of the most important information to identify the universality class and effective field theory, which is fundamental for various critical theories. However, the underlying symmetry so far…
The localization properties of electron states in the quantum Hall regime are reviewed. The random Landau model, the random matrix model, the tight-binding Peierls model, and the network model of Chalker and Coddington are introduced.…
We present an analytic theory of quantum criticality in quasi one-dimensional topological Anderson insulators. We describe these systems in terms of two parameters $(g,\chi)$ representing localization and topological properties,…
The quantum criticality of the two-lead two-channel pseudogap Anderson model is studied. Based on the non-crossing approximation, we calculate both the linear and nonlinear conductance of the model at finite temperatures with a voltage bias…
Using the Anderson model for disordered systems the fluctuations in electron spectra near the metal--insulator transition were numerically calculated for lattices of sizes up to 28 x 28 x 28 sites. The results show a finite--size scaling of…
Extensive body of work has shown that for the model of a non-interacting electron in a random potential there is a quantum critical point for dimensions greater than two---a metal-insulator transition. This model also plays an important…
We study Anderson localization of a one-dimensional quantum droplet in a speckle-like potential employing the generalized Gross-Pitaevskii equation. We compute the droplet width, density profiles, diffusion exponent and coefficient, and the…
We study whether a generic isolated quantum system initially set out of equilibrium can be considered as localized close to its initial state. Our approach considers the time evolution in the Krylov basis, which maps the dynamics onto that…
We study the relaxation of a non-equilibrium carrier distribution under the influence of the electron-electron interaction in the presence of disorder. Based on the Anderson model, our Hamiltonian is composed from a single particle part…
The nature of the critical point of the Anderson transition in high magnetic fields is discussed with an emphasis on scale invariance and universality of the critical exponent. Special attention is paid to the distribution function of the…
The energy level spacing distribution of a tight-binding hamiltonian is monitored across the mobility edge for a fixed disorder strength. Any mixing of extended and localized levels is avoided in the configurational averages, thus…
Anderson localization is usually understood as a transition between extended and localized phases, with criticality confined to a single mobility edge. Recent advances predict that quasiperiodic systems can instead host a finite critical…