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If the quantum mechanical description of reality is not complete and a hidden variable theory is possible, what arises is the problem to explain where the rates of the outcomes of statistical experiments come from, as already noticed by…
We propose a new method to define anomaly scores and apply this to particle physics collider events. Anomalies can be either rare, meaning that these events are a minority in the normal dataset, or different, meaning they have values that…
We present an analysis of the stationary distributions of run-and-tumble particles trapped in external potentials in terms of a thermophoretic potential, that emerges when trapped active motion is mapped to trapped passive Brownian motion…
We consider nonequilibrium systems with complex dynamics in stationary states with large fluctuations of intensive quantities (e.g. the temperature, chemical potential, or energy dissipation) on long time scales. Depending on the…
Parametric inference posits a statistical model that is a specified family of probability distributions. Restricted inference, e.g., restricted likelihood ratio testing, attempts to exploit the structure of a statistical submodel that is a…
Recent advances in differential topology single out four-dimensions as being special, allowing for vast varieties of exotic smoothness (differential) structures, distinguished by their handlebody decompositions, even as the coarser…
Since Newton, all classical and quantum physics depends upon the "Newtonian Paradigm". Here the relevant variables of the system are identified. The boundary conditions creating the phase space of all possible values of the variables are…
We study the exotic quantum statistical behavior of composite particle of double-spin cluster and quasiparticle of triple-spin cluster in a four-spin quantum model. We constructed a four spin-1/2 model on a triangular star lattice but added…
In this work we explore experimental signatures of fractional topological insulators in three dimensions. These are states of matter with a fully gapped bulk that host exotic gapless surface states and fractionally charged quasiparticles.…
These lecture notes present an overview of equilibrium statistical mechanics of classical fluids, with special applications to the structural and thermodynamic properties of systems made of particles interacting via the hard-sphere…
Recently, it has been proposed that exotic one-dimensional phases can be realized by gapping out the edge states of a fractional topological insulator. The low-energy edge degrees of freedom are described by a chain of coupled parafermions.…
Trove of exotic topoloid structures has recently been predicted by searching for compounds whose calculated band structure crossing points fulfill specific symmetry requirements. Discovery of exciting physical phenomena by experimental…
Superstatistics describes nonequilibrium steady states as superpositions of canonical ensembles with a probability distribution of temperatures. Rather than assume a certain distribution of temperature, recently [J. Phys. A: Math. Theor.…
An exact solution to the problem of parametric level statistics in non-Gaussian ensembles of N by N Hermitian random matrices with either soft or strong level confinement is formulated within the framework of the orthogonal polynomial…
Complex systems are difficult to study not only because they are nonlinear, multiscale, and often nonstationary, but because their scientifically relevant organization is often invisible at the level of individual components, pairwise…
As one of the main subjects of investigation in data science, network science has been demonstrated a wide range of applications to real-world networks analysis and modeling. For example, the pervasive presence of structural or topological…
Topological orders and associated topological protected excitations satisfying non-Abelian statistics have been widely explored in various platforms. The $\mathbb{Z}_3$ parafermions are regarded as the most natural generation of the…
We discuss counterintuitive aspects of probabilities for systems of identical particles obeying quantum statistics. Quantum coins and children (two level systems) and quantum dice (many level systems) are used as examples. It is emphasized…
We study a random matrix model for the statistical properties of the purity of a bipartite quantum system at a finite (fictitious) temperature. This enables us to write the generating function for the cumulants, for both balanced and…
We introduce a construction to embed a quasiperiodic lattice of obstacles into a single unit cell of a higher-dimensional space, with periodic boundary conditions. This construction transparently shows the existence of channels in these…