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The behavior of a collection of identical particles is intimately linked to the symmetries of their wavefunction under particle exchange. Topological anyons, arising as quasiparticles in low-dimensional systems, interpolate between bosons…
An exposition of the different definitions and approaches to quantum statistics is given, with emphasis in one-dimensional situations. Permutation statistics, scattering statistics and exclusion statistics are analyzed. The Calogero model,…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…
Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to…
We show that the thermodynamic Bethe ansatz equations for one-dimensional integrable many-body systems can be reinterpreted in such a way that they only code the statistical interactions, in the sense of Haldane, between particles of…
We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two…
A quantum statistical model of nuclear multifragmentation is proposed. The recurrence equation method used within the canonical ensemble makes the model solvable and transparent to physical assumptions and allows to get results without…
We revisit the problem of full counting statistics of particles on a segment of a one-dimensional gas of free fermions. Using a combination of analytical and numerical methods, we study the crossover between the counting of discrete…
How and why may an interacting system of many particles be described assuming that all particles are independent and identically distributed ? This question is at least as old as statistical mechanics itself. Its quantum version has been…
Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on…
Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations (PDEs) are a popular tool for modelling such phenomena deterministically, but it is often necessary to use…
I describe in these notes the physical properties of one dimensional interacting quantum particles. In one dimension the combined effects of interactions and quantum fluctuations lead to a radically new physics quite different from the one…
Recursion formulae of the N-particle partition function, the occupation numbers and its fluctuations are given using the single-particle partition function. Exact results are presented for fermions and bosons in a common one-dimensional…
We show that model-based Bayesian clustering, the probabilistically most systematic approach to the partitioning of data, can be mapped into a statistical physics problem for a gas of particles, and as a result becomes amenable to a…
The standard topological approach to indistinguishable particles formulates exchange statistics by using the fundamental group to analyze the connectedness of the configuration space. Although successful in two and more dimensions, this…
The clustering of galaxies in ongoing and upcoming galaxy surveys contains a wealth of cosmological information, but extracting this information is a non-trivial task since galaxies and their host haloes are stochastic tracers of the matter…
We present a theoretical study of entanglement in ensembles consisting of an arbitrary number of particles. Multipartite entanglement criteria in terms of observables are formulated for a fixed number of particles as well as for systems…
Statistical models on infinite graphs may exhibit inhomogeneous thermodynamic behaviour at macroscopic scales. This phenomenon is of geometrical origin and may be properly described in terms of spectral partitions into subgraphs with well…
When the dynamics of a spin ensemble are expressible solely in terms of symmetric processes and collective spin operators, the symmetric collective states of the ensemble are preserved. These many-body states, which are invariant under…
Indistinguishability of particles is normally considered to be an inherently quantum property which cannot be possessed by a classical theory. However, Saunders has argued that this is incorrect, and that classically indistinguishable…