Related papers: Hemaka's constant
\emph{Probabilistic hysteresis} is a manifestation of irreversibility in a small, isolated classical system [Sci. Rep. 9, 14169]: after a slow cyclic sweep of a control parameter, the probability that a microcanonical ensemble returns to…
We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables to directly compare different atomic environments with an arbitrary number of…
The strict connection between Lie point-symmetries of a dynamical system and its constants of motion is discussed and emphasized, through old and new results. It is shown in particular how the knowledge of a symmetry of a dynamical system…
We study a particle on a ring in presence of a dissipative Caldeira-Leggett environment and derive its response to a DC field. We show how this non-equilibrium response is related to a flux averaged equilibrium response. We find, through a…
Asymmetrical features in disks provide indirect evidences of embedded objects, such as planets. Observed with the Atacama Large Millimeter/submillimeter Array (ALMA), the circumstellar disk in MWC 758 traced with thermal dust continuum…
We investigate the dependence of Poincar\'e recurrence-times statistics on the choice of recurrence-set, by sampling the dynamics of two- and four-dimensional Hamiltonian maps. We derive a method that allows us to visualize the direct…
The density matrix yields probabilistic information about the outcome of measurements on a quantum system, but it does not distinguish between classical randomness in the preparation of the system and entanglement with its environment.…
Dependent symmetries, symmetries that depend on the situation of the subsystem in a larger closed system, are explored by looking at simple examples. This is a new kind of symmetry in the open quantum dynamics of a subsystem Each symmetry…
Recently, Rindler and Ishak have argued that the bending of light is, in principle, changed by the presence of a cosmological constant since one must consider not only the null geodesic equation, but also the process of measurement. I agree…
The data on the astronomical orientation of the IV dynasty Egyptian pyramids are re-analyzed and it is shown that such data suggest an inverse chronology between the `first` and the `second` Giza pyramid.
We study the first detected recurrence time problem of continuous-time quantum walks on graphs. While previous works have employed projective measurements to determine the first return time, we implement a protocol based on weak…
Persistent homology is currently one of the more widely known tools from computational topology and topological data analysis. We present in this note a brief survey on the evolution of the subject. The goal is to highlight the main ideas,…
For a universe presently dominated by static or dynamic vacuum energy, cosmological constant (LCDM) or quintessence (QCDM), we calculate the asymptotic collapsed mass fraction as function of the present ratio of vacuum energy to clustered…
\noindent In our contribution to this volume we deal with \emph{discrete} symmetries: these are symmetries based upon groups with a discrete set of elements (generally a set of elements that can be enumerated by the positive integers). In…
We use persistent homology in order to define a family of fractal dimensions, denoted $\mathrm{dim}_{\mathrm{PH}}^i(\mu)$ for each homological dimension $i\ge 0$, assigned to a probability measure $\mu$ on a metric space. The case of…
Investigation of states with a periodic time dependence of physical quantities attracts a considerable interest now. Although it has been proposed initially that such states (coined Quantum Time Crystals) might be macroscopic and…
Ozawa and Shioya proposed the limit formula for observable diameters of pyramids under weak convergence. However, we find a constructive counterexample to an inequality used in their proof. In this paper, we correct the inequality and…
Extending results of Linial (1984) and Aigner (1985), we prove a uniform lower bound on the balance constant of a poset $P$ of width $2$. This constant is defined as $\delta(P) = \max_{(x, y)\in P^2}\min\{\mathbb{P}(x\prec y),…
The particle dynamics of the recently observed ring around dwarf planet Haumea is numerically investigated. The point mass gravitational force, a second degree and order gravity field, and the solar radiation pressure as the main…
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are…