Related papers: Stability, complex modes and non-separability in r…
The dynamics of the oscillator system is investigated. The conditions under which this dynamics becomes unstable are determined. In particular, it is shown that plasma in constant magnetic field becomes unstable if its density exceeds a…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
We show how the state of an unstable particle can be defined in terms of stable asymptotic states. This general definition is used to discuss and to solve some old problems connected with the short-time and large-time behaviour of the…
We study the dynamics of a quantum or classical particle in a two-dimensional rotating anisotropic harmonic potential. By a sequence of symplectic transformations for constant rotation velocity we find uncoupled normal generalized…
We consider model of a complex particle that consists of a rigid shell and a nucleus with spatial asymmetric interaction. The particle's dynamics with the nucleus driven by a periodic excitation is considered. It is shown that…
We present a novel geometric approach for determining the unique structure of a Hamiltonian and establishing an instability criterion for quantum quadratic systems. Our geometric criterion provides insights into the underlying geometric…
We present a detailed non-perturbative analysis of the time-evolution of a well-known quantum-mechanical system - a particle between potential walls - describing the decay of unstable states. For sufficiently high barriers, corresponding to…
Based on the spectral decomposition technique, we introduce a simple and universal numerical method to analyze the stability of solitons. Adopting this method, the linear dynamical properties of $Q$-balls are systematically revealed, from…
We study a class of dynamical systems for which the motions can be described in terms of geodesics on a manifold (ordinary potential models can be cast into this form by means of a conformal map). It is rigorously proven that the geodesic…
Particles confined in droplets are called compound particles. They are encountered in various biological and soft matter systems. Hydrodynamics can play a decisive role in determining the configuration and stability of these multiphase…
We investigate the evolution of phase space close to complex unstable periodic orbits in two galactic type potentials. They represent characteristic morphological types of disc galaxies, namely barred and normal (non-barred) spiral…
We introduce a class of convex, higher-dimensional billiard models which generalise stadium billiards. These models correspond to the free motion of a point-particle in a region bounded by cylinders cut by planes. They are motivated by…
Evolution of coherent states is considered for a particle confined to a cylinder moving in a harmonic oscillator potential. Because of the discontinuous changes as time goes by of the phase representing the position of a particle on a…
We show how the stability conditions for a system of interacting fermions that conventionally involve variations of thermodynamic potentials can be rewritten in terms of one- and two-particle correlators. We illustrate the applicability of…
The stability of charged particle motion in a uniform magnetic field with an added spatially uniform transverse rotating magnetic field (RMF) is studied analytically. It is found that the stability diagram of a single-particle's orbit…
We study the oscillations and stability of self-gravitating cylindrically symmetric fluid systems and collisionless systems. This is done by studying small perturbations to the equilibrium system and finding the normal modes, using methods…
We study the non relativistic motions of a charged particle in the electromagnetic field generated by two parallel electrically neutral vertical wires carrying time depends currents. Under quantitative conditions on the currents we prove…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
It is shown that the total energy of the static "field + particle" system, defined in the framework of classical, renormalized electrodynamics of particles and fields, depends in an unstable way upon the field boundary data. It is argued…
Complete description of the classical and quantum dynamics of a particle in an anisotropic, rotating, harmonic trap is given. The problem is studied in three dimensions and no restrictions on the geometry are imposed. In the generic case,…