Related papers: On the Derivation of Conserved Quantities in Class…
An example of mechanical system whose configuration space is direct product of a curved space and the local group of rotations, is presented. The system is considered as a model of spinning particle moving in the space. The Hamiltonian…
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
We discuss the principles to be used in the construction of discrete time classical and quantum mechanics as applied to point particle systems. In the classical theory this includes the concept of virtual path and the construction of system…
We consider a fractional generalization of Hamiltonian and gradient systems. We use differential forms and exterior derivatives of fractional orders. We derive fractional generalization of Helmholtz conditions for phase space. Examples of…
We give a systematic method for discretizing Hamiltonian partial differential equations (PDEs) with constant symplectic structure, while preserving their energy exactly. The same method, applied to PDEs with constant dissipative structure,…
We consider the problem of learning an interpretable potential energy function from a Hamiltonian system's trajectories. We address this problem for classical, separable Hamiltonian systems. Our approach first constructs a neural network…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
We study mathematically a system of partial differential equations arising in the modelling of an aging fluid, a particular class of non Newtonian fluids. We prove well-posedness of the equations in appropriate functional spaces and…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…
We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…
A conceptually simple physical interpretation of a conserved Hamiltonian $\mathcal{H}$ for a mechanical system with a time-dependent constraint is given. For the case of a bead on a vertical hoop forced to rotate with constant angular…
We explore the possibility of using the method of classical integral transforms to solve a class of $q$-difference-differential equations. The Laplace and the Mellin transform of $q$-derivatives are derived. The results show that the Mellin…
Products and tensor products are linked by a universal property. Imposing the invariance of the laws of Nature under tensor composition along with Leibniz identity determines quantum and classical mechanics algebraic structure through the…
In recent publications in physics and mathematics, concerns have been raised about the use of real numbers to describe quantities in physics, and in particular about the usual assumption that physical quantities are infinitely precise. In…
In this paper we develop a fractional Hamilton-Jacobi formulation for discrete systems in terms of fractional Caputo derivatives. The fractional action function is obtained and the solutions of the equations of motion are recovered. An…
We argue here that, as it happens in Classical and Quantum Mechanics, where it has been proven that alternative Hamiltonian descriptions can be compatible with a given set of equations of motion, the same holds true in the realm of…
Generalising a result of classical mechanics an infinite set of conserved quantities can be found for the bare equations of motion describing the evolution of a scalar field in out of equilibrium quantum field theory, in the large N…