Related papers: Many Body Symmetrical Dynamical Systems
Disordered quantum many-body systems pose one of the central challenges in condensed matter physics and quantum information science, as their dynamics are generally intractable for classical computation. Many-body localization (MBL),…
We study the rhomboidal symmetric-mass 4-body problem in both a two-degree-of-freedom and a four-degree-of-freedom setting. Under suitable changes of variables in both settings, isolated binary collisions at the origin are regularizable.…
About half of all known stellar systems with Sun-like stars consist of two or more stars, significantly affecting the orbital stability of any planet in these systems. This observational evidence has prompted a large array of theoretical…
In this paper, we give a summary of stability criteria that have been derived for hierarchical triple systems over the past few decades. We give a brief description and we discuss the criteria that are based on the generalisation of the…
We construct a smooth nontrivial mixed partially hyperbolic system and explicitly identify its skeleton. This example shares characteristics with the classical examples. Moreover, the support of each physical measure contains three fixed…
This paper presents a study of the use of numerical simulation and Bayesian optimisation techniques to investigate the dynamics of celestial systems. Initially, the study focuses on Lagrange points in restricted three-body systems where a…
Many-body localized (MBL) systems do not approach thermal equilibrium under their intrinsic dynamics; MBL and conventional thermalizing systems form distinct dynamical phases of matter, separated by a phase transition at which equilibrium…
In this work, we revisit the planar restricted four-body problem to study the dynamics of an infinitesimal mass under the gravitational force produced by three heavy bodies with unequal masses, forming an equilateral triangle configuration.…
A field-theoretic description of the critical behaviour of the weakly disordered systems is given. Directly, for three- and two-dimensional systems a renormalization analysis of the effective Hamiltonian of model with replica symmetry…
Central configurations are fundamental equilibrium solutions of the Newtonian $n$-body problem and play a key role in understanding the structure and dynamics of gravitational systems. However, the classification and enumeration of such…
This manuscript considers the main features of the nonlinear dynamics of multiple irregular celestial body systems. The gravitational potential, static electric potential, and magnetic potential are considered. Based on the three…
A detailed analysis of necessary conditions on a family of many-body potentials, which ensure stability, superstability or strong superstability of a statistical system is given in present work.There has been given also an example of…
In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the…
This work is devoted to the study of some exactly solvable quantum problems of four, five and six bodies moving on the line. We solve completely the corresponding stationary Schr\"odinger equation for these systems confined in an harmonic…
For the 5-components Maxwell-Bloch system the stability problem for the isolated equilibria is completely solved. Using the geometry of the symplectic leaves, a detailed construction of the homoclinic orbits is given. Studying the problem…
Stability is one of the most fundamental aspects regarding planetary systems. It plays an important role in our understanding on the formation channel of the planetary systems, as well as their habitability. Many approaches have been…
Closed quantum many-body systems out of equilibrium pose several long-standing problems in physics. Recent years have seen a tremendous progress in approaching these questions, not least due to experiments with cold atoms and trapped ions…
Multibody dynamics simulations are currently widely accepted as valuable means for dynamic performance analysis of mechanical systems. The evolution of theoretical and computational aspects of the multibody dynamics discipline make it…
Stability of equilibrium states in mechanical systems with multiple unilateral frictional contacts is an important practical requirement, with high relevance for robotic applications. In our previous work, we theoretically analyzed…
The problem of the dynamical stability of anistropic systems is studied, by proposing a criterion in terms of the adiabatic local index $\gamma$. The result has general validity and can be applied to several physical situations.…