Related papers: Emergence via non-existence of averages
In open, driven systems where parity-time symmetry is preserved, phenomena that defy conventional wisdom emerge near exceptional points, promising advances in photonics. While most studies focus on two-level systems of a conventional…
Recently we pointed out the so-called Local Time Scheme as a novel approach to quantum foundations that solves the preferred pointer-basis problem. In this paper we introduce and analyze in depth a rather non-standard dynamical map that is…
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations (PDEs), these emergent patterns sometimes appear as local minimisers of a…
The phenomenon of superconvergence is proved for all freely infinitely divisible distributions. Precisely, suppose that the partial sums of a sequence of free identically distributed, infinitesimal random variables converge in distribution…
Dense suspensions of self-propelled rod-like particles exhibit a fascinating variety of non-equilibrium phenomena. By means of computer simulations of a minimal model for rigid self-propelled colloidal rods with variable shape we explore…
A network as a substrate for dynamic processes may have its own dynamics. We propose a model for networks which evolve together with diffusing particles through a coupled dynamics, and investigate emerging structural property. The model…
Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…
A new sufficient condition is proved for the existence of stochastic semigroups generated by the sum of two unbounded operators. It is applied to one-dimensional piecewise deterministic Markov processes, where we also discuss the existence…
Change-point detection has been a classical problem in statistics and econometrics. This work focuses on the problem of detecting abrupt distributional changes in the data-generating distribution of a sequence of high-dimensional…
For a sequence of sub-additive potentials, Dai [Optimal state points of the sub-additive ergodic theorem, Nonlinearity, 24 (2011), 1565-1573] gave a method of choosing state points with negative growth rates for an ergodic dynamical system.…
Ensemble averages are an approximation technique for connecting macroscopic and microscopic properties of a system. For systems open with respect to exchange of particles with a bath, the microscopic states are those with integer numbers of…
We define polygonal dynamics as a family of dynamical systems acting on points in projective spaces. The most famous example is the pentagram map. Similar collapsing phenomena seem to occur in most of these systems. We prove it in some…
We give a probabilistic introduction to determinantal and permanental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatorics (nonintersecting paths, random spanning trees).…
A new class of critical points, termed as perpetual points, where acceleration becomes zero but the velocity remains non-zero, are observed in dynamical systems. The velocity at these points is either maximum or minimum or of inflection…
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
The optical interference constitutes a paramount resource in modern physics. At the scale of individual atoms and photons, it is a diverse concept that causes different coherent phenomena. We present the experimental characterization of…
Active matter is not only indispensable to our understanding of diverse biological processes, but also provides a fertile ground for discovering novel physics. Many emergent properties impossible for equilibrium systems have been…
We propose mechanical systems, described by Newton's equation of motion, as suited platforms for symmetry protection of non-Hermitian topological degeneracies. We point out that systems possess emergent symmetry, which is a unique…
The past decade has witnessed a surge of interest in exploring emergent particles in condensed matter systems. Novel particles, emerged as excitations around exotic band degeneracy points, continue to be reported in real materials and…
Exceptional points, resulting from non-Hermitian degeneracies, have the potential to enhance the capabilities of quantum sensing. Thus, finding exceptional points in different quantum systems is vital for developing such future sensing…