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A basic statistical mechanics analysis of many-body systems with non-reciprocal pair interactions is presented. Different non-reciprocity classes in two- and three-dimensional binary systems (relevant to real experimental situations) are…
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…
The unrelated discoveries of quasicrystals and topological insulators have in turn challenged prevailing paradigms in condensed-matter physics. We find a surprising connection between quasicrystals and topological phases of matter: (i)…
We show that quasiparticle excitations with irrational charge and irrational exchange statistics exist in tight-biding systems described, in the continuum approximation, by the Dirac equation in (2+1)-dimensional space and time. These…
A new class of random partial differential equations of parabolic type is considered, where the stochastic term consists of an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing…
The most complicated phenomena of equilibrium statistics, phase separations and transitions of various order and critical phenomena, can clearly and sharply be seen even for small systems in the topology of the curvature of the…
We study the behaviour of linear and nonlinear spectroscopic quantities in two-dimensional topologically ordered systems, which host anyonic excitations exhibiting fractional statistics. We highlight the role that braiding phases between…
Quantum statistics have a profound impact on the properties of systems composed of identical particles. In this Letter, we demonstrate that the quantum statistics of a pair of identical massive particles can be probed by a direct…
Superstatistics are superpositions of different statistics relevant for driven nonequilibrium systems with spatiotemporal inhomogeneities of an intensive variable (e.g., the inverse temperature). They contain Tsallis statistics as a special…
An anyon exclusion statistics, which generalizes the Bose-Einstein and Fermi-Dirac statistics of bosons and fermions, was proposed by Haldane[1]. The relevant past studies had considered only anyon systems without any physical boundary but…
Statistical thermodynamics is valuable as a conceptual structure that shapes our thinking about equilibrium thermodynamic states. A cloud of unresolved questions surrounding the foundations of the theory could lead an impartial observer to…
Plasmas and other systems with long-range interactions are commonly found in non-equilibrium steady states that are outside traditional Boltzmann-Gibbs statistics, but can be described using generalized statistical mechanics frameworks such…
Semidefinite programming can be considered over any real closed field, including fields of Puiseux series equipped with their nonarchimedean valuation. Nonarchimedean semidefinite programs encode parametric families of classical…
Traditional statistical mechanics is constrained by the binary paradigms of identical/distinguishable and bosonic/fermionic particle statistics, leading to a fundamental logical gap in describing systems with partial distinguishability. We…
In the present paper, first the mathematical basic properties of the exceptional points are discussed. Then, their role in the description of real physical quantum systems is considered. Most interesting value is the phase rigidity of the…
We review some recent developments which make use of the concept of `superstatistics', an effective description for nonequilibrium systems with a varying intensive parameter such as the inverse temperature. We describe how the asymptotic…
Anyons are quasiparticles in two-dimensional systems that show statistical properties very distinct from those of bosons or fermions. While their isolated observation has not yet been achieved, here we perform a quantum simulation of anyons…
Particle statistics impose fundamental constraints on nonequilibrium quantum dynamics, yet it remains an open question whether anyonic statistics can lead to emergent dynamical scaling beyond the conventional Bose-Fermi paradigm. Here we…
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…
Search for parafermions and Fibonacci anyons, which are excitations obeying non-Abelian statistics, is driven both by the quest for deeper understanding of nature and prospects for universal topological quantum computation. However,…