Related papers: Topological Exchange Statistics in One Dimension
Statistical mechanics and thermodynamics for ideal fractional exclusion statistics with mutual statistical interactions is studied systematically. We discuss properties of the single-state partition functions and derive the general form of…
Studies of free particles in low-dimensional quantum systems such as two-leg ladders provide insight into the influence of statistics on collective behaviour. The behaviours of bosons and fermions are well understood, but two-dimensional…
Motivated by new capabilities to realise artificial gauge fields in ultracold atomic systems, and by their potential to access correlated topological phases in lattice systems, we present a new strategy for designing topologically…
A new theoretical approach to non-equilibrium statistical systems has recently been proposed by the author, a co-author and others. It is based on a variational principle which is associated with the discrepancy of a path through…
Multi-connected universe models with space identification scales smaller than the size of the observable universe produce topological images of cosmic sources. We generalise to locally hyperbolic spaces the crystallographic method, aimed to…
Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear…
It is known that three-body contact interactions in one-dimensional $n(\geq3)$-body problems of nonidentical particles can be topologically nontrivial: they are all classified by unitary irreducible representations of the pure twin group…
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…
The methods of Information geometry have been glowing up to develop various subjects of theoretical physics, including quantum information systems. The present article has two purposes. The first one is to develop general theory of…
Non-relativistic charged particles and strings coupled with abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. We consider three models: the string in self-interaction through a…
We describe the mathematical theory of topological quantum computing with symmetry defects in the language of fusion categories and unitary representations. Symmetry defects together with anyons are modeled by G-crossed braided extensions…
A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…
The leapfrogging motion of smoke rings is a three dimensional version of the motion that in two dimensions leads to exotic exchange statistics. The statistical phase factor can be computed using the hydrodynamical Euler equation, which is a…
Many physical situations are characterized by interfaces with a non trivial shape so that relevant geometric features, such as interfacial area, curvature or unit normal vector, can be used as main indicators of the topology of the…
We demonstrate the identification and classification of topological phase transitions from experimental data using Diffusion Maps: a nonlocal unsupervised machine learning method. We analyze experimental data from an optical system…
Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…
Anyons are quasiparticles with fractional statistics, bridging between fermions and bosons. We propose an experimental setup to measure the statistical angle of topological anyons emitted from a quantum point contact (QPC) source. The setup…
Single-parameter persistent homology, a key tool in topological data analysis, has been widely applied to data problems along with statistical techniques that quantify the significance of the results. In contrast, statistical techniques for…
A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their…
We discuss the conditions under which identical particles may yet be distinguishable and the relationship between particle permutation and exchange. We show that we can always define permutation-symmetric state vectors. When the particles…