Related papers: Instantons for the destabilization of the inner So…
We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…
For many non-equilibrium dynamics driven by small noise, in physics, chemistry, biology, or economy, rare events do matter. Large deviation theory then explains that the leading order term of the main statistical quantities have an…
We use semiclassical methods to calculate the probability of inducing a change of topology via a high-energy collision in the SU(2)-Higgs theory. This probability is determined by a complex solution to a classical boundary value problem on…
Numerical minimization of the Euclidean action of the two-dimensional Abelian Higgs model is used to construct periodic instantons, the euclidean field configurations with two turning points describing transitions between the vicinities of…
If a dynamical system is long-lived and non-resonant (that is, if there is a set of tracers that have evolved independently through many orbital times), and if the system is observed at any non-special time, it is possible to infer the…
Instanton theory has arisen as a practical tool for calculating tunneling splittings in molecular systems. Unfortunately, the original formulation of instanton theory fundamentally breaks down when trying to calculate the level splitting in…
The long-term stability of the Solar System is an issue of significant scientific and philosophical interest. The mechanism leading to instability is Mercury's eccentricity being pumped up so high that Mercury either collides with Venus or…
Some models allowing explicit calculation of periodic instantons and evaluation of their action are studied with regard to transitions from classical to quantum behaviour as the temperature is lowered and tunneling sets in. It is shown that…
The formation of the solar system's giant planets predated the ultimate epoch of massive impacts that concluded the process of terrestrial planet formation. Following their formation, the giant planets' orbits evolved through an episode of…
The discovery of the chaotic motion of the planets in the Solar System dates back more than 30 years. Still, no analytical theory has satisfactorily addressed the origin of chaos so far. Implementing canonical perturbation theory in the…
We examine the accuracy of a common technique for estimating the start time of solar energetic particle injection based on a linear fit to the observed onset time versus 1/(particle velocity). This is based on a concept that the first…
Extinction appears ubiquitously in many fields, including chemical reactions, population biology, evolution, and epidemiology. Even though extinction as a random process is a rare event, its occurrence is observed in large finite…
Estimating the probability of failures or accidents with aerospace systems is often necessary when new concepts or designs are introduced, as it is being done for Autonomous Aircraft. If the design is safe, as it is supposed to be, accident…
Many out-of-equilibrium flows present non-Gaussian fluctuations in physically relevant observables, such as energy dissipation rate. This implies extreme fluctuations that, although rarely observed, have a significant phenomenology.…
Orbital resonances are ubiquitous in the Solar system. They play a decisive role in the long term dynamics, and in some cases the physical evolution, of the planets and of their natural satellites, as well as the evolution of small bodies…
We study the path-integral formalism in the imaginary-time to show its validity in a case with a metastable ground state. The well-known method based on the bounce solution leads to the imaginary part of the energy even for a state that is…
We perform time-dependent analysis of quantum dynamics of dark matter particles in the Solar System. It is shown that this problem has similarities with a microwave ionization of Rydberg atoms studied previously experimentally and…
A planetary system can undergo multiple episodes of intense dynamical activities throughout its life, resulting in the production of star-grazing planetesimals (or exocomets) and pollution of the host star. Such activity is especially…
We propose currently feasible experiments using small, isolated systems of ultracold atoms to investigate the effects of dynamical chaos in the microscopic onset of irreversibility. A control parameter is tuned past a critical value, then…
Instanton calculations are performed in the context of stationary Burgers turbulence to estimate the tails of the probability density function (PDF) of velocity gradients. These results are then compared to those obtained from massive…