Related papers: Boundary multifractality in critical 1D systems wi…
Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary…
Band structure analysis is central to understanding wave propagation in periodic media; however, it becomes challenging in open systems owing to energy leakage. Photonic crystal (PhC) slabs exemplify such systems, featuring periodicity in…
As opposed to random disorder, which localizes single-particle wave-functions in 1D at arbitrarily small disorder strengths, there is a localization-delocalization transition for quasi-periodic disorder in the 1D Aubry-Andr\'e model at a…
The space of one-dimensional disordered interacting quantum models displaying a Many-Body-Localization Transition seems sufficiently rich to produce critical points with level statistics interpolating continuously between the Poisson…
It is well known that for ordinary one-dimensional (1D) disordered systems, the Anderson localization length $\xi$ diverges as $\lambda^m$ in the long wavelength limit ($\lambda\rightarrow \infty$ ) with a universal exponent $m=2$,…
The random banded matrices (RBM) whose diagonal elements fluctuate much stronger than the off-diagonal ones were introduced recently by Shepelyansky as a convenient model for coherent propagation of two interacting particles in a random…
The parametric motion of energy levels for non-interacting electrons at the Anderson localization critical point is studied by computing the energy level-curvatures for a quasiperiodic ring with twisted boundary conditions. We find a…
We study the critical level statistics at the many-body localization (MBL) transition region in random spin systems. By employing the inter-sample randomness as indicator, we manage to locate the MBL transition point in both orthogonal and…
When an optimal control problem is solved for all possible initial conditions at once, the initial-state space splits into critical regions, each carrying a closed-form control law that can be evaluated online without solving any…
I discuss the quantum dynamics of strongly disordered quantum systems with critically long range interactions, decaying as $1/r^{2d}$ in $d$ spatial dimensions. I argue that, contrary to expectations, localization in such systems is stable…
We study the boundary effects in invasion percolation with and without trapping. We find that the presence of boundaries introduces a new set of surface critical exponents, as in the case of standard percolation. Numerical simulations show…
Restricted Boltzmann machines (RBMs) are a class of neural networks that have been successfully employed as a variational ansatz for quantum many-body wave functions. Here, we develop an analytic method to study quantum many-body spin…
We study the boundary stabilization of one-dimensional cross-diffusion systems in a moving domain. We show first exponential stabilization and then finite-time stabilization in arbitrary small-time of the linearized system around uniform…
The brain criticality hypothesis has largely only characterized brain dynamics in terms of their self-similarity, although experimental evidence suggests that the brain exhibits significant multifractality. To understand how multifractality…
A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that…
The possible paralelism existing between phase transitions and fracture in disordered materials, is discussed using the well-known Fiber Bundle Models and a probabilistic approach suited to smooth fluctuations near the critical point. Two…
We consider highly heterogeneous random networks with symmetric interactions in the limit of high connectivity. A key feature of this system is that the spectral density of the corresponding ensemble exhibits a divergence within the bulk.…
Active matter systems under confinement display persistent surface motion and a strong boundary affinity. However, despite extensive studies of their positional dynamics, much less attention has been given to the corresponding orientational…
An overview of recent advances in the theory of critical phenomena in $d$-dimensional weakly anisotropic systems is given. On the basis of a generalized shear transformation between anisotropic and isotropic systems, exact and approximate…
The localization behavior of the one-dimensional Anderson model with correlated and uncorrelated purely off-diagonal disorder is studied. Using the transfer matrix method, we derive an analytical expression for the localization length at…