Related papers: The dynamics around stable and unstable Hamiltonia…
We review in detail the Hamiltonian dynamics for constrained systems. Emphasis is put on the total Hamiltonian system rather than on the extended Hamiltonian system. We provide a systematic analysis of (global and local) symmetries in total…
Numerous pivotal concepts have been introduced to clarify the puzzle of relaxation and/or equilibration in closed quantum systems. All of these concepts rely in some way on specific conditions on Hamiltonians $H$, observables $A$, and…
The dynamics of a three-dimensional Hamilton-Poisson system is closely related to its constants of motion, the energy or Hamiltonian function $H$ and a Casimir $C$ of the corresponding Lie algebra. The orbits of the system are included in…
Numerous works have shown that under mild assumptions unitary dynamics inevitably leads to equilibration of physical expectation values if many energy eigenstates contribute to the initial state. Here, we consider systems driven by…
This is an expository paper on Lyapunov stability of equilibria of autonomous Hamiltonian systems. Our aim is to clarify the concept of weak instability, namely instability without non-constant motions which have the equilibrium as limit…
The physics of many closed, conservative systems can be described by both classical and quantum theories. The dynamics according to classical theory is symplectic and admits linear instabilities which would initially seem at odds with a…
A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results…
We establish a general framework to explore parametric statistics of individual energy levels in disordered and chaotic quantum systems of unitary symmetry. The method is applied to the calculation of the universal intra-level parametric…
It has recently been shown that small quantum subsystems generically equilibrate, in the sense that they spend most of the time close to a fixed equilibrium state. This relies on just two assumptions: that the state is spread over many…
The planar quantum dynamics of a neutral particle with a magnetic dipole moment in the presence of electric and magnetic fields is considered. The criteria to establish the planar dynamics reveal that the resulting nonrelativistic…
Various notions of fluctuations exist depending on the way one chooses to measure them. We discuss two extreme cases (continuous measurement versus long inter-measurement times) and we see their relation with entropy production and with…
Equations describing plasma equilibria are derived from the total energy of the system. The MHD equilibrium is shown to hold even for systems where the magnetic field may locally vanish. Through conservation of helicity, confinement is…
Usually, the relaxation times of a gas are estimated in the frame of the Boltzmann equation. In this paper, instead, we deal with the relaxation problem in the frame of the dynamical theory of Hamiltonian systems, in which the definition…
An interesting situation occurs when the linearized dynamics of the shape of a formally stable Hamiltonian relative equilibrium at nongeneric momentum 1:1 resonates with a frequency of the relative equilibrium's generator. In this case some…
The stability of the orbital motion of two long cylindrical magnets interacting exclusively with magnetic forces is described. To carry out analytical studies a model of magnetically interacting symmetric tops [1] is used. The model was…
The coupling of non-Hermitian PT-symmetric Hamiltonians to standard Hermitian Hamiltonians, each of which individually has a real energy spectrum, is explored by means of a number of soluble models. It is found that in all cases the energy…
The problem of proper symmetry definition for constraint dynamical systems with Hamiltonians is considered. Finally, we choose a definition of symmetry which agrees with the analogous definition used for the non-constraint dynamical systems…
The eigenvalue of the hermitic Hamiltonian is real undoubtedly. Actually, The reality can also be guaranteed by the $PT$-symmetry. The hermiticity and the $PT$-symmetric quantum theory both have requirements regarding the boundary…
Gravitational and electromagnetic interactions are Hamiltonian systems with forces between pairs of particles. We propose an alternative: Hamiltonian dynamics with triplet interactions between point particles. Our system has a potential…
Transient stability is crucial to the reliable operation of power systems. Existing theories rely on the simplified electromechanical models, substituting the detailed electromagnetic dynamics of inductor and capacitor with their impedance…