Related papers: Some applications of the Lambert W function to cla…
We study the classical limit of quantum mechanics on graphs by introducing a Wigner function for graphs. The classical dynamics is compared to the quantum dynamics obtained from the propagator. In particular we consider extended open graphs…
The Wright function arises in the theory of the fractional differential equations. It is a very general mathematical object having diverse connections with other special and elementary functions. The Wright function provides a unified…
We derive several new transformations relating WP-Bailey pairs. We also consider the corresponding transformations relating standard Bailey pairs, and as a consequence, derive some quite general expansions for products of theta functions…
The new scheme employed (throughout the thermodynamic phase space), in the statistical thermodynamic investigation of classical systems, is extended to quantum systems. Quantum Nearest Neighbor Probability Density Functions are formulated…
A technique is presented for finding the classical Lagrange function corresponding to a given dispersion relation. This allows us to study the classical analogue of the Standard-Model Extension. Developments are discussed.
We study a class of one-dimensional classical fluids with penetrable particles interacting through positive, purely repulsive, pair-potentials. Starting from some lower bounds to the total potential energy, we draw results on the…
We present and discuss a selected set of problems of classical mechanics and thermodynamics. The discussion is based on the use of the impulse-momentum equation simultaneously with the centre-of-mass (pseudo-work) equation or with the first…
We study the formulation of statistical mechanics on noncommutative classical phase space, and construct the corresponding canonical ensemble theory. For illustration, some basic and important examples are considered in the framework of…
Some connections between quantum mechanics and classical physics are explored. The Planck-Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the Canonical Commutation Relations and the Maxwell--Lorentz…
A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables…
A probabilistic interpretation of one-particle relativistic quantum mechanics is proposed. Quantum Action Principle formulated earlier is used for to make the dynamics of the Minkowsky time variable of a particle to be classical. After…
A very brief introduction to tropical and idempotent mathematics is presented. Applications to classical mechanics and geometry are especially examined.
Several distributions and families of distributions are proposed to model skewed data, think, e.g., of skew-normal and related distributions. Lambert W random variables offer an alternative approach where, instead of constructing a new…
We consider the Lorenz equations, a system of three dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been…
We study the statistical mechanics of classical and quantum systems in non-equilibrium steady states. Emphasis is placed on systems in strong thermal gradients. Various measures and functional forms of observables are presented. The quantum…
The model under consideration is a classical 2D Coulomb gas of pointlike positive and negative unit charges, interacting via a logarithmic potential. In the whole stability range of temperatures, the equilibrium statistical mechanics of…
Integral Mittag-Leffler, Whittaker and Wright functions with integrands similar to those which already exist in mathematical literature are introduced for the first time. For particular values of parameters, they can be presented in…
We discuss a new type of delay differential equation that exhibits resonating transient oscillations. The power spectrum peak of the dynamical trajectory reaches its maximum height when the delay is suitably tuned. Furthermore, our analysis…
In these four lectures, aiming at senior undergraduate and junior graduate Physics and Mathematics students, basic elements of the theory of elliptic functions are presented. Simple applications in classical mechanics are discussed,…
Assuming a classical statistical system of point particles the fundamental equations of continuum thermomechanics (continuity equation, equation of motion, and energy equation) shall be derived exactly. The macroscopic state functions…