Related papers: Lagrange's planetary equations with time-dependent…
Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes like star formation and merging events. Recent studies show…
The short-time behavior of the survival probability of a system governed by a time-dependent non-Hermitian Hamiltonian is derived using to the second order perturbative approach. The resulting expression allows for the analysis of some…
The influence of multiplicative stochastic perturbations on the class of asymptotically Hamiltonian systems on the plane is investigated. It is assumed that disturbances do not preserve the equilibrium of the corresponding limiting system…
We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar…
This paper outlines astrophysical issues related to the long term fate of the universe. We consider the evolution of planets, stars, stellar populations, galaxies, and the universe itself over time scales which greatly exceed the current…
The dynamics of expansion of the Universe and evolution of scalar perturbations are studied for the quintessential scalar fields $Q$ with the classical Lagrangian satisfying the additional condition $w=const$ or $c^2_a=0$. Both…
The temporal evolution of the entanglement between two qubits evolving by random interactions is studied analytically and numerically. Two different types of randomness are investigated. Firstly we analyze an ensemble of systems with…
The dynamics of galaxies in an expanding universe is often determined for gravitational and dark matter in an Einstein-de Sitter universe, or alternatively by modifying the gravitational long-range attractions in the Newtonian dynamics…
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
We consider a slowly rotating rectangular billiard with moving boundaries and use the canonical perturbation theory to describe the dynamics of a billiard particle. In the process of slow evolution certain resonance conditions can be…
We analyze the secular evolution of hierarchical triple systems to second-order in the quadrupolar perturbation induced on the inner binary by the distant third body. The Newtonian three-body equations of motion, expanded in powers of the…
A novel expansion of the evolution operator associated with a -- in general, time-dependent -- perturbed quantum Hamiltonian is presented. It is shown that it has a wide range of possible realizations that can be fitted according to…
In recent works we have used quantum tools in the analysis of the time evolution of several macroscopic systems. The main ingredient in our approach is the self-adjoint Hamiltonian $H$ of the system $\Sc$. This Hamiltonian quite often, and…
An approximate strategy for studying the evolution of binary systems of extended objects is introduced. The stars are assumed to be polytropic ellipsoids. The surfaces of constant density maintain their ellipsoidal shape during the time…
There are a number of mathematical theorems in the literature on the dynamics of cosmological models with accelerated expansion driven by a positive cosmological constant $\Lambda$ or a nonlinear scalar field with potential $V$…
We derive the Hamilton equations of motion for a constrained system in the form given by Dirac, by a limiting procedure, starting from the Lagrangean for an unconstrained system. We thereby ellucidate the role played by the primary…
The irreversibility of the equations of classical dynamics (the Hamilton equations and the Liouville equation) in the space with multifractal time is demonstrated. The time is given on multifractal sets with fractional dimensions. The last…
We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new…
A mathematical model of the evolution of plane perturbations in the cosmological statistical system of completely degenerated scalar-charged fermions with the Higgs scalar interaction is formulated. A complete closed system of differential…
Using well known Lagrangean techniques for uncovering the gauge symmetries of a Lagrangean, we derive the transformation laws for the phase space variables corresponding to local symmetries of the Hamilton equations of motion. These…