Related papers: Microscopic and macroscopic properties of A-supers…
We show that Calogero-Sutherland models for interacting particles have a natural supersymmetric extension. For the construction, we use Jacobians which appear in certain superspaces. Some of the resulting Hamiltonians have a direct physics…
Statistical mechanics explains the properties of macroscopic phenomena based on the movements of microscopic particles such as atoms and molecules. Movements of microscopic particles can be represented by large-scale interacting systems. In…
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…
The thermodynamic distribution function for exclusion statistics is derived. Creation and annihilation operators for particles obeying such statistics are discussed. A connection with anyons is pointed out.
At the core of equilibrium statistical mechanics lies the notion of statistical ensembles: a collection of microstates, each occurring with a given a priori probability that depends only on a few macroscopic parameters such as temperature,…
A general statistical thermodynamic theory that considers given sequences of x-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability…
The generalization of $A_r$ statistics, including bosonic and fermionic sectors, is performed by means of the so-called Jacobson generators. The corresponding Fock spaces are constructed. The Bargmann representations are also considered.…
It has been conjectured that the Pauli exclusion principle alone may be responsible for a particular geometric arrangement of confined systems of identical fermions even when there is no interaction between them. These geometric structures,…
We provide an update of the overview of imprints of Tsallis nonextensive statistics seen in a multiparticle production processes. They reveal an ubiquitous presence of power law distributions of different variables characterized by the…
The aim of the present paper is to provide a preliminary investigation of the thermodynamics of particles obeying monotone statistics. To render the potential physical applications realistic, we propose a modified scheme called…
The basic idea of a microscopic understanding of Thermodynamics is to derive its main features from a microscopic probability distribution. In such a vein, we investigate the thermal statistics of quasi-probabilities's semi-classical…
Description of adjoint invariants of general Linear Lie superalgebras $\mathfrak{gl}(m|n)$ by Kantor and Trishin is given in terms of supersymmetric polynomials. Later, generators of invariants of the adjoint action of the general linear…
We construct Fock and MacMahon modules for the quantum toroidal superalgebra $\mathcal{E}_\mathbf{s}$ associated with the Lie superalgebra $\mathfrak{gl}_{m|n}$ and parity $\mathbf{s}$. The bases of the Fock and MacMahon modules are labeled…
These Lecture Notes are devoted to an introductory description of some of the most widely applied statistical methods for the analysis of the Large-Scale Structure (LSS) of the Universe. Rather than providing technical details about the…
Thermodynamics provides powerful constraints on physical and chemical systems in equilibrium. However, non-equilibrium dynamics depends explicitly on microscopic properties, requiring an understanding beyond thermodynamics. Remarkably, in…
The new mathematical framework based on the free energy of pure classical fluids presented in [R. D. Rohrmann, Physica A 347, 221 (2005)] is extended to multi-component systems to determine thermodynamic and structural properties of…
Previous and present "academic" research aiming at atomic scale understanding is mainly concerned with the study of individual molecular processes possibly underlying materials science applications. Appealing properties of an individual…
Superstatistics describes statistical systems that behave like superpositions of different inverse temperatures $\beta$, so that the probability distribution is $p(\epsilon_i) \propto \int_{0}^{\infty} f(\beta) e^{-\beta \epsilon_i}d\beta$,…
Inspired by the concept of complementarity, we present a illustrative model for the weak interactions with unbroken gauge symmetry and unbroken supersymmetry. The observable particles are bound states of some more fundamental particles.…
We made use of supersymmetric (SUSY) quantum mechanics to find a condition under which the Stark effect problem for a polar and polarizable closed-shell diatomic molecule subject to collinear electrostatic and nonresonant radiative fields…