Related papers: Universal correlations for deterministic plus rand…
We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in…
We study small oscillations of highly connected systems, which represent a limit opposite to the more familiar case of disordered crystals. As a concrete example we analyze the vibrational spectra of composite pendula. Remarkably, these…
We explore the relation between the entanglement of a pure state and its energy variance for a local one dimensional Hamiltonian, as the system size increases. In particular, we introduce a construction which creates a matrix product state…
We consider environment induced decoherence of quantum superpositions to mixtures in the limit in which that process is much faster than any competing one generated by the Hamiltonian $H_{\rm sys}$ of the isolated system. This interaction…
We study the level statistics of a non-integrable one dimensional interacting fermionic system characterized by the GOE distribution. We calculate numerically on a finite size system the level spacing distribution $P(s)$ and the Dyson-Mehta…
Models of disorder with a direction (constant imaginary vector-potential) are considered. These non-Hermitian models can appear as a result of computation for models of statistical physics using transfer matrix technique or describe…
Measuring strength or degree of statistical dependence between two random variables is a common problem in many domains. Pearson's correlation coefficient $\rho$ is an accurate measure of linear dependence. We show that $\rho$ is a…
An explicit expression is derived for the statistical description of small quantum systems, which are relatively-weakly and directly coupled to only small parts of their environments. The derived expression has a canonical form, but is…
We present a universal characterization of stress correlations in athermal systems, across crystalline to amorphous packings. Via numerical analysis of static configurations of particles interacting through harmonic as well as Lennard-Jones…
The explicit analytical expression for the distribution function of parametric derivatives of energy levels ("level velocities") with respect to a random change of scattering potential is derived for the chaotic quantum systems belonging to…
We develop a very general perturbative theory of time-dependent transport in a weak tunneling junction which is independent of experimental details and on many-body correlated states in the coupled conductors. These can be similar or…
Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for…
Hyperuniformity refers to the suppression of density fluctuations at large scales. Typical for ordered systems, this property also emerges in several disordered physical and biological systems, where it is particularly relevant to…
We consider the homogenization of parabolic equations with large spatially-dependent potentials modeled as Gaussian random fields. We derive the homogenized equations in the limit of vanishing correlation length of the random potential. We…
We derive a universal form for the correlation function of general n component systems in the limit of high temperatures or weak coupling. This enables the extraction of effective microscopic interactions from measured high temperature…
We study the entanglement entropy and particle number cumulants for a system of disordered noninteracting fermions in $d$ dimensions. We show, both analytically and numerically, that for a weak disorder the entanglement entropy and the…
A recursive method is derived to calculate all eigenvalue correlation functions of a random hermitian matrix in the large size limit, and after smoothing of the short scale oscillations. The property that the two-point function is…
The covariance of two random variables measures the average joint deviations from their respective means. We generalise this well-known measure by replacing the means with other statistical functionals such as quantiles, expectiles, or…
We calculate the correlator of the local density of states <\rho_{E}(r_1)\rho_{E+\omega}(r_2)> in quasi-one-dimensional disordered wires in a magnetic field, assuming that |r_1-r_2| is much smaller than the localization length. This amounts…
.Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments…