Related papers: Various complexity measures in confined hydrogen a…
The definition of complexity through Statistical Complexity Measures (SCM) has recently seen major improvements. Mostly, effort is concentrated in measures on time series. We propose a SCM definition for spatial dynamical systems. Our…
We study the compact embedding between smoothness Morrey spaces on bounded domains and characterise its entropy numbers. Here we discover a new phenomenon when the difference of smoothness parameters in the source and target spaces is…
We study a modified Ramsey spectroscopy technique employing slowly decaying states for quantum metrology applications using dense ensembles. While closely positioned atoms exhibit superradiant collective decay and dipole-dipole induced…
Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in $d$-dimensional Euclidean space $\mathbb{R}^d$ across length scales is an outstanding challenge in physics, chemistry, and…
The scaling of entanglement with subsystem size encodes key information about phases and criticality, but the von Neumann entropy is costly to access in experiments and simulations, often requiring full state tomography. The second R\'enyi…
We present extensive molecular dynamics (MD) simulations investigating numerous candidate crystal structures for hydrogen in conditions around the present experimental frontier (400GPa). Spontaneous phase transitions in the simulations…
We analyze the subsystem size scaling of the entanglement entropy of a non-ergodic pure state that can be described by a multi-parametric Gaussian ensemble of complex matrices in a bipartite basis. Our analysis indicates, for a given set of…
Estimation of Shannon and R\'enyi entropies of unknown discrete distributions is a fundamental problem in statistical property testing and an active research topic in both theoretical computer science and information theory. Tight bounds on…
Nontrivial symmetry of order parameters is crucial in some of the most interesting quantum many-body states of ultracold atoms and condensed matter systems. Examples in cold atoms include p-wave Feshbach molecules and d-wave paired states…
We present a comprehensive study of the discretized modes of an atomic gas in different conditions of confinement. Starting from the equations of hydrodynamics we derive a closed equation for the velocity field, depending on the adiabatic…
This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…
We apply the statistical measure of complexity, introduced by L\'{o}pez-Ruiz, Mancini and Calbet to a hard-sphere dilute Fermi gas whose particles interact via a repulsive hard-core potential. We employ the momentum distribution of this…
We numerically study the measurement-driven quantum phase transition of Haar-random quantum circuits in $1+1$ dimensions. By analyzing the tripartite mutual information we are able to make a precise estimate of the critical measurement rate…
The partial scaling transform of the density matrix for multiqubit states is introduced to detect entanglement of quantum states. The transform contains partial transposition as a special case. The scaling transform corresponds to partial…
In this paper, we introduce and study unified $(r,s)$-relative entropy and quantum unified $(r,s)$-relative entropy, in particular, our main results of quantum unified $(r,s)$-relative entropy are established on the separable complex…
Scalar, baryon and vector--current densities in coordinate and momentum space are calculated within a relativistic mean--field model. The role of the low components of the bound nucleon wave function is investigated in detail for different…
A quasi two-dimensional colloidal suspension is studied under the influence of immobilisation (pinning) of a random fraction of its particles. We introduce a novel experimental method to perform random pinning and, with the support of…
The asymptotics of the weighted $L_{p}$-norms of Hermite polynomials, which describes the R\'enyi entropy of order $p$ of the associated quantum oscillator probability density, is determined for $n\to\infty$ and $p>0$. Then, it is applied…
The time evolution of complex systems usually can be described through stochastic processes. These processes are measured at finite resolution, what necessarily reduces them to finite sequences of real numbers. In order to relate these data…
Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…