Related papers: The characteristic exponents of the falling ball m…
There are two main approaches to non-equlibrium statistical mechanics: one using stochastic processes and the other using dynamical systems. To model the dynamics during inflation one usually adopts a stochastic description, which is known…
We study the dynamics of particles coupled to gravity in (2 + 1) dimensions. Using the ADM formalism, we derive the general Hamiltonian for an N-body system and analyze the dynamics of a two-particle system. Non-linear terms are found up to…
This review work addresses the recent advances in solving more comprehensive Hamiltonians. The generalized tight-binding model is developed to investigate the feature-rich quantization phenomena in emergent 2D materials. The mutli-orbital…
We observe that the fully nonlinear evolution equations of Rosenau and Hymann, often abbreviated as $K(n,\,m)$ equations, can be reduced to Hamiltonian form only on a zero-energy hypersurface belonging to some potential function associated…
The foundations of Statistical Mechanics can be recovered almost in their entirety from the Principle of Maximum Entropy. In this work we show that its non-equilibrium generalization, the Principle of Maximum Caliber (Jaynes, 1980), when…
We calculate the Lyapunov exponents in a classical molecular dynamics framework. The system is composed of few hundreds particles interacting either through Yukawa (Nuclear) or Slater-Kirkwood (Atomic) forces. The forces are chosen to give…
We show that recent observations of fractal dimensions in the $\mu$-space of $N$-body Hamiltonian systems with long-range interactions are due to finite $N$ and finite resolution effects. We provide strong numerical evidence that, in the…
We study the dynamical properties of the canonical ordered phase of the Hamiltonian mean-field (HMF) model, in which $N$ particles, globally-coupled via pairwise attractive interactions, form a rotating cluster. Using a combination of…
For a one-dimensional conservative systems with position depending mass, one deduces consistently a constant of motion, a Lagrangian, and a Hamiltonian for the non relativistic case. With these functions, one shows the trajectories on the…
We show that the Lyapunov exponent (LE) of periodic orbits with Lebesgue measure zero from the Gauss map can be used to determine the main qualitative behavior of the LE of a Hamiltonian system. The Hamiltonian system is a one-dimensional…
We introduce and study the mechanical system which describes the dynamics and statics of rigid bodies of constant density floating in a calm incompressible fluid. Since much of the standard equilibrium theory, starting with Archimedes,…
It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…
An argument by Hassell proving the existence of a Bunimovich stadium for which there are semiclassical measures giving positive mass to the submanifold of bouncing ball trajectories uses a notion of non-gliding points. However, this notion…
We study the scattering equations recently proposed by Cachazo, He and Yuan in the special kinematics where their solutions can be identified with the zeros of the Jacobi polynomials. This allows for a non-trivial two parameter family of…
We investigate the dependence of the largest Lyapunov exponent of a $N$-particle self-gravitating ring model at equilibrium with respect to the number of particles and its dependence on energy. This model has a continuous phase-transition…
Mass segregation problem is thought to be entangled with the dynamical evolution of young stellar clusters \cite{olczak}. This is a common sense in the astrophysical community. In this work, the Hamiltonian Mean Field (HMF) model with…
This paper provides an introduction to some stochastic models of lattice gases out of equilibrium and a discussion of results of various kinds obtained in recent years. Although these models are different in their microscopic features, a…
I formulate the theory of three dimensional "Malthusian flocks" -- i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being "born" and "dying" during their motion -- whose constituents all…
Correct quantum Hamiltonians of a few exactly solvable models in two space-time dimensions are derived by taking into account operator solutions of the field equations. While two versions of the model with derivative coupling are found to…
The 1:1:2 resonant elastic pendulum is a simple classical system that displays the phenomenon known as Hamiltonian monodromy. With suitable initial conditions, the system oscillates between nearly pure springing and nearly pure…