Related papers: Appell Transformation and Canonical Transforms
Enforcing exact conservation laws instead of average ones in statistical thermal models for relativistic heavy ion reactions gives raise to so called canonical effect, which can be used to explain some enhancement effects when going from…
Continuing our investigation into the Hierarchical Reference Theory of fluids for thermodynamic states of infinite isothermal compressibility kappa[T] we now turn to the available numerical evidence to elucidate the character of the partial…
Hermite polynomials, which are associated to a Gaussian weight and solve the Laplace equation with a drift term of linear growth, are classical in analysis and well-understood via ODE techniques. Our main contribution is to give explicit…
Taking the formal analogies between black holes and classical thermodynamics seriously seems to first require that classical thermodynamics applies to relativistic regimes. Yet, by scrutinizing how classical temperature is extended into…
The Hankel transform of an integer sequence is a much studied and much applied mathematical operation. In this note, we extend the notion in a natural way to sequences of $d$ integer sequences. We explore links to generalized continued…
For 1D Hamiltonian systems with periodic solutions, Helmholtz formalism provides a tantalizing interpretation of classical thermodynamics, based on time integrals of purely mechanical quantities and without need of statistical description.…
The Fourier transform operation is an important conceptual as well as computational tool in the arsenal of every practitioner of physical and mathematical sciences. We discuss some of its applications in optical science and engineering,…
In this paper, we extend the iterative expression for the generalized spherical functions associated to the root systems of type $A$ previously obtained beyond regular elements. We also provide the corresponding expression in the flat case.…
The historical development of the Carnot cycle necessitated the construction of isothermal and adiabatic pathways within the cycle that were also mechanically "reversible" which lead eventually to the Kelvin-Clausius development of the…
We compute thermal and quantum fluctuations in the background of a domain wall in a scalar field theory at finite temperature using the exact scalar propagator in the subspace orthogonal to the wall's translational mode. The propagator…
Legendre transform between thermodynamic quantities such as the Helmholtz free energy and entropy plays a key role in the formulation of the canonical ensemble. In the standard treatment, the transform exchanges the independent variable…
A compactly supported distribution is called invertible in the sense of Ehrenpreis-H\"ormander if the convolution with it induces a surjection from $\mathcal{C}^{\infty}(\mathbb{R}^{n})$ to itself. We give sufficient conditions for radial…
We define a finite-field version of Appell-Lauricella hypergeometric functions built from period functions in several variables, paralleling the development by Fuselier, et. al in the single variable case. We develop geometric connections…
We present a formalism able to predict the transformation of light beams passing through biaxial crystals. We use this formalism to show both theoretically and experimentally the transition from double refraction to conical refraction,…
We investigate the radiation of energy and angular momentum from 2D topological systems with broken inversion symmetry and time reversal symmetry. A general theory of far-field radiation is developed using the linear response of 2D…
In d-dimensional lattices of coupled quantum harmonic oscillators, we analyze the heat current caused by two thermal baths of different temperature, which are coupled to opposite ends of the lattice, with focus on the validity of Fourier's…
Univariate specializations of Appell's hypergeometric functions F1, F2, F3, F4 satisfy ordinary Fuchsian equations of order at most 4. In special cases, these differential equations are of order 2, and could be simple (pullback)…
de Haas-van Alphen oscillation spectrum of two-dimensional systems is studied for general power law energy dispersion, yielding a Fermi surface area of the form $S(E)\propto E^\alpha$ for a given energy $E$. The case $\alpha=1$ stands for…
The main purpose of this paper is to study generalized (self-) reciprocal Appell polynomials, which play a certain role in connection with Faulhaber-type polynomials. More precisely, we show for any Appell sequence when satisfying a…
In this paper, we formulate the relativistic heat equation and the relativistic kinetic Fokker-Planck equations into the GENERIC (General Equation for Non-Equilibrium Reversible-Irreversible Coupling) framework. We also show that the…