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Density functional theory can be extended to excited states by means of a unified variational approach for passive state ensembles. This extension overcomes the restriction of the typical density functional approach to ground states, and…
We investigate how information spreads in three paradigmatic one-dimensional models with spatial disorder. The models we consider are unitarily related to a system of free fermions and are thus manifestly integrable. We demonstrate that…
We consider a tight-binding model on the regular honeycomb lattice with uncorrelated on-site disorder. We use two independent methods (recursive Green's function and self-consistent Born approximation) to extract the scattering mean free…
We study long-range correlation functions of the rectangular Ising lattice with cyclic boundary conditions. Specifically, we consider the situation in which two spins are on the same column, and at least one spin is on or near free…
Motivated by interest in the geometry of high intensity events of turbulent flows, we examine spatial correlation functions of sets where turbulent events are particularly intense. These sets are defined using indicator functions on…
This note illustrates the possibility in simple loaded string models of trapping most of the system energy in a single degree of freedom for very long times, demonstrating in particular that the robustness of the trapping is enhanced by…
This study investigates the entanglement properties of disordered free fermion systems undergoing an Anderson phase transition from a delocalized to a localized phase. The entanglement entropy is employed to quantify the degree of…
A time-dependent approach is used to explore inelastic effects during electron transport through few-level systems. We study a tight-binding chain with one and two sites connected to vibrations. This simple but transparent model gives…
An accurate determination of the electron correlation energy is essential for describing the structure, stability, and function in a wide variety of systems, ranging from gas-phase molecular assemblies to condensed matter and…
We consider the (smoothed) average correlation between the density of energy levels of a disordered system, in which the Hamiltonian is equal to the sum of a deterministic H0 and of a random potential $\varphi$. Remarkably, this correlation…
We study the tail of the spectrum for non-interacting bosons in a blue-detuned random speckle potential. Using an instanton approach we derive the asymptotic behavior of the density of states in d dimensions. The leading corrections…
Using the method of energy-level statistics, the localization properties of electrons moving in two dimensions in the presence of a perpendicular random magnetic field and additional random disorder potentials are investigated. For this…
Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…
We investigate two-proton correlation functions for reactions in which fast dynamical and slow evaporative proton emission are both present. In such cases, the width of the correlation peak provides the most reliable information about the…
Gene expression estimation from pathology images has the potential to reduce the RNA sequencing cost. Point-wise loss functions have been widely used to minimize the discrepancy between predicted and absolute gene expression values.…
Sophisticated high-energy and large momentum-transfer scattering experiments combined with ab-initio calculations can reveal the short-distance behavior of nucleon pairs in nuclei. On an opposite energy and resolution scale, elastic…
For deterministic continuous time nonlinear control systems, epsilon-practical stabilization entropy and practical stabilization entropy are introduced. Here the rate of attraction is specified by a KL-function. Upper and lower bounds for…
We analyze the effects of intersite energy correlations on the linear optical properties of one-dimensional disordered Frenkel exciton systems. The absorption line width and the factor of radiative rate enhancement are studied as a function…
We derive an exact representation of the exchange-correlation energy within density functional theory (DFT) which spawns a class of approximations leading to correct long-range asymptotic behavior. In what amounts to be the simplest…
The amount of randomness in a signal generated by physical or non-physical process can reveal important information about that process. For example, the presence of randomness in ECG signals may indicate a cardiac disease. On the hand, the…