Related papers: Instantons for the destabilization of the inner So…
Several properties of the Solar System, including the wide radial spacing and orbital eccentricities of giant planets, can be explained if the early Solar System evolved through a dynamical instability followed by migration of planets in…
We consider a physical system comprising discrete massive particles on the real line whose trajectories interact via perfectly inelastic collision, also known as sticky particles. It turns out that polygons formed in a convex "cumulative…
Instantons play a crucial role in understanding non-perturbative dynamics in quantum field theories, including those with spontaneously broken gauge symmetries. In the broken phase, finite-size instanton-like configurations are no longer…
The decay of unstable states when several metastable states are available for occupation is investigated using path-integral techniques. Specifically, a method is described which allows the probabilities with which the metastable states are…
In this paper we consider a random motion of magnetic bright points (MBP) associated with magnetic fields at the solar photosphere. The MBP transport in the short time range [0-20 minutes] has a subdiffusive character as the magnetic flux…
Instanton analysis is applied to models B--H of critical dynamics. It is shown that the static instanton of the massless $\phi^{4}$ model determines the large-order asymptotes of the perturbation expansion of these near-equilibrium dynamic…
Ensembles of in-plane and inclined orbits in the vicinity of the Lagrange points of the terrestrial planets are integrated for up to 100 million years. The integrations incorporate the gravitational effects of Sun and the eight planets…
Fermi's golden rule defines the transition rate between weakly coupled states and can thus be used to describe a multitude of molecular processes including electron-transfer reactions and light-matter interaction. However, it can only be…
While there does not at this time exist a complete canonical theory of full 3+1 quantum gravity, there does appear to be a satisfactory canonical quantization of minisuperspace models. The method requires no `choice of time variable' and…
This work is an analytical calculation of the path probability for random dynamics of mechanical system described by Langevin equation with Gaussian noise. The result shows an exponential dependence of the probability on the action. In the…
The evolution of a system of chemical reactions can be studied, in the eikonal approximation, by means of a Hamiltonian dynamical system. The fixed points of this dynamical system represent the different states in which the chemical system…
Young stars are mostly found in dense stellar environments, and even our own Solar system may have formed in a star cluster. Here, we numerically explore the evolution of planetary systems similar to our own Solar system in star clusters.…
A path information is defined in connection with the different possible paths of chaotic system moving in its phase space between two cells. On the basis of the assumption that the paths are differentiated by their actions, we show that the…
We describe in detail a physical situation in which instantons are necessarily complex, not just Wick rotations of classical solutions to Euclidean spacetime. These complex instantons arise in the semiclassical evaluation of vacuum pair…
We calculate the interplanetary magnetic field path lengths traveled by electrons in solar electron events detected by the WIND 3DP instrument from $1994$ to $2016$. The velocity dispersion analysis method is applied for electrons at…
The physical basis of chaos in the solar system is now better understood: in all cases investigated so far, chaotic orbits result from overlapping resonances. Perhaps the clearest examples are found in the asteroid belt. Overlapping…
To improve our understanding of orbital instabilities in compact planetary systems, we compare suites of $N$-body simulations against numerical integrations of simplified dynamical models. We show that, surprisingly, dynamical models that…
Unexpected dynamic phenomena have surprised solar system observers in the past and have led to important discoveries about solar system workings. Observations at the initial stages of these events provide crucial information on the physical…
Coherent state path integrals are shown in general to contain instantons with jumps at the boundaries, i.e., with boundary points lying outside classical parameter or phase space. As an example, the magnetic molecule Fe_8 is studied using a…
Most stars form in star clusters and stellar associated. To understand the roles of star cluster environments in shaping the dynamical evolution of planetary systems, we carry out direct $N$-body simulations of four planetary systems models…