Related papers: The dynamics around stable and unstable Hamiltonia…
With perfectly balanced gain and loss, dynamical systems with indefinite damping can obey the exact PT-symmetry being marginally stable with a pure imaginary spectrum. At an exceptional point where the symmetry is spontaneously broken, the…
When an integrable two-degrees-of-freedom Hamiltonian system possessing a circle of parabolic fixed points is perturbed, a parabolic resonance occurs. It is proved that its occurrence is generic for one parameter families (co-dimension one…
In this paper we analyze the stability of equilibrium manifolds of hyperbolic shallow water moment equations. Shallow water moment equations describe shallow flows for complex velocity profiles which vary in vertical direction and the…
We show that the physical mechanism for the equilibration of closed quantum systems is dephasing, and identify the energy scales that determine the equilibration timescale of a given observable. For realistic physical systems (e.g those…
Highlights: \begin{itemize} \item Relativistic effect of crystal dynamics "freezing". \item Non-statistical model of thermodynamic equilibration. \end{itemize} The dynamics of oscillations of a one-dimensional atomic chain is investigated…
Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular, the selection of control parameters and their minimal number are…
We study the dynamics of an inertial particle coupled to forcing, dissipation, and noise in the small mass limit. We derive an expression for the limiting (homogenized) joint distribution of the position and (scaled) velocity degrees of…
We study the process by which quantum correlations are created when an interaction Hamiltonian is repeatedly applied to a system of two harmonic oscillators for some characteristic time interval. We show that, for the case where the…
We solve the nonequilibrium dynamics of qubits or quantum spin chains (s=1/2) modeled by an anisotropic XY Hamiltonian, when the initial condition is prepared as a spatially inhomogeneous state of the magnetization. Infinite systems are…
The dynamics of the spin-boson Hamiltonian is considered in the stochastic approximation. The Hamiltonian describes a two-level system coupled to an environment and is widely used in physics, chemistry and the theory of quantum measurement.…
The linear stability of the homogeneous equilibrium of non-relativistic fluids with mass flux and special relativistic fluids with the absolute value of the energy vector as internal energy is investigated. It is proved that the equilibrium…
A stationary physical system satisfies peculiar balance conditions involving mean values of appropriate observables. In this paper we show how to deduce such quantitative links, named balance equations, demonstrating as well their…
Physical systems with symmetry arise abundantly in applications, and are endowed with interesting mathematical structures. The present paper focusses on linear reciprocal and input-output Hamiltonian systems. Their characterization is…
For simple mechanical systems, bifurcating branches of relative equilibria with trivial symmetry from a given set of relative equilibria with toral symmetry are found. Lyapunov stability conditions along these branches are given.
Let $\mathcal{F}$ be a $C^2$ random partially hyperbolic dynamical system. For the unstable foliation, the corresponding unstable metric entropy, unstable topological entropy and unstable pressure via the dynamics of $\mathcal{F}$ on the…
We address a simple connection between results of Hamiltonian nonlinear dynamical theory and thermostatistics. Using a properly defined dynamical temperature in low-dimensional symplectic maps, we display and characterize long-standing…
This paper is concerned with stochastic Hamiltonian systems which model a class of open dynamical systems subject to random external forces. Their dynamics are governed by Ito stochastic differential equations whose structure is specified…
The Fluctuation Theorems are a group of exact relations that remain valid irrespective of how far the system has been driven away from equilibrium. Other than having practical applications, like determination of equilibrium free energy…
Nuclear dynamics of mass asymmetric systems at balance energy.
We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique…