Related papers: Haldane-Wu statistics and Rogers dilogarithm
We point out a formal analogy between lattice kinetic propagators and Haldane-Wu fractional statistics. The analogy could be used to compute the partition function of fractional quantum systems by solving a corresponding lattice kinetic…
Gapped periodic quantum systems exhibit an interesting Localization Dichotomy, which emerges when one looks at the localization of the optimally localized Wannier functions associated to the Bloch bands below the gap. As recently proved,…
In the paper, two-parametric models of fractional statistics are proposed in order to determine the functional form of the distribution function of free anyons. From the expressions of the second and third virial coefficients, an…
The large-deviation method allows to characterize an ergodic counting process in terms of a thermodynamic frame where a free energy function determines the asymptotic non-stationary statistical properties of its fluctuations. Here, we study…
The low energy properties of the one-dimensional anyon gas with $\delta$-function interaction are discussed in the context of its Bethe ansatz solution. It is found that the anyonic statistical parameter and the dynamical coupling constant…
We introduce a generalized approach to one-dimensional (1D) conduction based on Haldane's concept of fractional statistics (FES) and the Landauer formulation of transport theory. We show that the 1D ballistic thermal conductance is…
In the first part, we introduce the notion of fractional statistics in the sense of Haldane. We illustrate it on simple models related to anyon physics and to integrable models solvable by the Bethe ansatz. In the second part, we describe…
We show that Haldanes new definition of statistics, when generalised to infinite dimensional Hilbert spaces, is equal to the high temperature limit of the second virial coefficient. We thus show that this exclusion statistics parameter, g ,…
We discuss the thermodynamics of a gas of free particles obeying Haldane's exclusion statistics, deriving low temperature and low density expansions. For gases with a constant density of states, we derive an exact equation of state and find…
In this paper we compute the scaling functions of the effective central charges for various quantum integrable models in a deep ultraviolet region $R\to 0$ using two independent methods. One is based on the ``reflection amplitudes'' of the…
We formulate and study the microscopic statistical mechanics of systems of particles with exclusion statistics in a discrete one-body spectrum. The statistical mechanics of these systems can be expressed in terms of effective single-level…
We introduce innovative inference procedures for analyzing time series data. Our methodology enables density approximation and composite hypothesis testing based on Whittle's estimator, a widely applied M-estimator in the frequency domain.…
We show how statistical thermodynamics can be formulated in situations in which thermodynamics applies, while equilibrium statistical mechanics does not. A typical case is, in the words of Landau and Lifshitz, that of partial (or…
Many continuous reaction-diffusion models on $\mathbb{Z}$ (annihilating or coalescing random walks, exclusion processes, voter models) admit a rich set of Markov duality functions which determine the single time distribution. A common…
We show that the particles in the Calogero-Sutherland Model obey fractional exclusion statistics as defined by Haldane. We construct anyon number densities and derive the energy distribution function. We show that the partition function…
We brief{}ly review the connection between statistical mechanics and thermodynamics. We show that, in order to satisfy thermodynamics and its Legendre transformation mathematical frame, the celebrated Boltzmann-Gibbs~(BG) statistical…
After a brief discussion of the concepts of fractional exchange and fractional exclusion statistics, we report partly analytical and partly numerical results on thermodynamic properties of assemblies of particles obeying fractional…
We develop a finite temperature field theory formalism in any dimension that has the filling fractions as the basic dynamical variables. The formalism efficiently decouples zero temperature dynamics from the quantum statistical sums. The…
The GUE Hypothesis, which concerns the distribution of zeros of the Riemann zeta-function, is used to evaluate some integrals involving the logarithmic derivative of the zeta-function. Some connections are shown between the GUE Hypothesis…
We develop the full counting statistics of dissipated heat to explore the relation with Landauer's principle. Combining the two-time measurement protocol for the reconstruction of the statistics of heat with the minimal set of assumptions…