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We analytically evaluate the large deviation function in a simple model of classical particle transfer between two reservoirs. We illustrate how the asymptotic large time regime is reached starting from a special propagating initial…
The correlation function of two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor representation are…
We study a fine hierarchy of Borel-piecewise continuous functions, especially, between closed-piecewise continuity and $G_\delta$-piecewise continuity. Our aim is to understand how a priority argument in computability theory is connected to…
We determine the pair correlations of countable sets $T \subset \mathbb{R}^n$ satisfying natural equidistribution conditions. The pair correlations are computed as the volume of a certain region in $\mathbb{R}^{2n}$, which can be expressed…
A dynamical pair breaking effect is evidenced at very low excitation energies. For this purpose, a new set of time-dependent coupled channel equations for pair-breaking in superfluid systems are deduced from the variational principle. These…
We suggest a duality between the standard (dynamical) and statistical distributions of partons in the nucleons. The temperature parameter entering into the statistical form for the quark distributions is estimated. It is found that this…
In this note we prove the strong Feller property of a strong Markov quasi diffusion process corresponding to an elliptic operator with merely bounded measurable coefficients. We also prove H\"older continuity of harmonic functions…
An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are…
A problem of the equivalence of statistical ensembles is critically analyzed. It is shown, that although different probability distributions of statistical physics have the same behavior in the thermodynamic limit, there are physical…
We prove equivalence between nonnegative distributional solutions of the fractional heat equation and caloric functions, i.e., functions satisfying the mean value property with respect to the space-time isotropic $\alpha$-stable process. We…
Finite volume corrections to higher moments are important observable quantities. They make possible to differentiate between different statistical ensembles even in the thermodynamic limit. It is shown that this property is a universal one.…
We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref. [1] by combining the…
The formalism developed in the first paper of the series [arXiv:0901.1060] is applied to two thermodynamic systems: (i) of three global observables (the energy, the total electron number and the spin number), (ii) of one global observable…
In this work, we study the fractional power series solutions around regular singular point x=0 of conformable fractional Bessel differential equation and fractional Bessel functions. Then, we compare fractional solutions with ordinary…
We consider an isothermal machine composed of two Brownian particles (say particle A and B) connected by a harmonic spring. A constant load is attached to particle A, and the particle B is trapped in a harmonic confinement whose minimum is…
We characterize the region of meromorphic continuation of an analytic function $f$ in terms of the geometric rate of convergence on a compact set of sequences of multi-point rational interpolants of $f$. The rational approximants have a…
In this work, I derive the time-dependent probability density function of classical observables using the Hamiltonian mechanics approach, extending the notion of fluctuation theorems for any observables. In particular, the time-dependent…
Thermodynamic uncertainty principles make up one of the few rare anchors in the largely uncharted waters of nonequilibrium systems, the fluctuation theorems being the more familiar. In this work we aim to trace the uncertainties of…
We extend the form-factors approach to the quantum Ising model at finite temperature. The two point function of the energy is obtained in closed form, while the two point function of the spin is written as a Fredholm determinant. Using the…
We review the role of dual pairs in mechanics and use them to derive particle-like solutions to regularized incompressible fluid systems. In our case we have a dual pair resulting from the action of diffeomorphisms on point particles…