Related papers: The Henon-Heiles system defined on canonically def…
A reflection-asymmetric deformed oscillator potential is analysed from the classical and quantum mechanical point of view. The connection between occurrence of shell structures and classical periodic orbits is studied using the ''removal of…
We analyze seemingly contradictory claims in the literature about the role played by decoherence in ensuring classical behavior for the chaotically tumbling satellite Hyperion. We show that the controversy is resolved once the very…
We study in detail the time behavior of classical fidelity for chaotic systems. We show in particular that the asymptotic decay, depending on system dynamical properties, can be either exponential, with a rate determined by the gap in the…
We use Moser's normal forms to study chaotic motion in two-degree hamiltonian systems near a saddle point. Besides being convergent, they provide a suitable description of the cylindrical topology of the chaotic flow in that vicinity. Both…
We relate analytically defined deformations of modular curves and modular forms from the literature to motivic periods via cohomological descriptions of deformation theory. Leveraging cohomological vanishing results, we prove the existence…
Classical and quantum mechanical results are reported for the single particle motion in a harmonic oscillator potential which is characterized by a quadrupole deformation and an additional octupole deformation. The chaotic character of the…
We investigate the decay process from a time dependent potential well in the semiclassical regime. The classical dynamics is chaotic and the decay rate shows an irregular behavior as a function of the system parameters. By studying the…
We consider a canonical transformation of parabolic coordinates on the plain and suppose that this transformation together with some additional relations may be considered as a counterpart of the auto and hetero B\"acklund transformations…
We use the integrable deformations method for a three-dimensional system of differential equations to obtain deformations of the T system. We analyze a deformation given by particular deformation functions. We point out that the obtained…
A widely accepted definition of ``quantum chaos'' is ``the behavior of a quantum system whose \emph{classical} \emph{limit is chaotic}''. The dynamics of quantum-chaotic systems is nevertheless very different from that of their classical…
It is argued that, if a regular Hamiltonian is perturbed by a term that produces chaos, the onset of chaos is shifted towards larger values of the perturbation parameter if the unperturbed spectrum is degenerate and the lifting of the…
Several recent studies have concerned the faith of classical symmetries in quantum space-time. In particular, it appears likely that quantum (discretized, noncommutative,...) versions of Minkowski space-time would not enjoy the classical…
We describe a method for determining the transient process duration in a standard two-dimensionaldynamic system with discrete time (Henon map), occurring in the regime of chaotic oscillations
We give an approach to open quantum systems based on formal deformation quantization. It is shown that classical open systems of a certain type can be systematically quantized into quantum open systems preserving the complete positivity of…
A simple semiclassical H\'enon-Heiles model is constructed based on Dirac's time-dependent variational principle. We obtain an effective semiclassical Hamiltonian using a Hatree-type two-body trial wavefunction in the Jackiw-Kerman form.…
We described the $q$-deformed phase space. The $q$-deformed Hamilton eqations of motion are derived and discussed. Some simple models are considered.
The H\'enon-Heiles potential was first proposed as a simplified version of the gravitational potential experimented by a star in the presence of a galactic center. Currently, this system is considered a paradigm in dynamical systems because…
Using the decoherence formalism of Gell-Mann and Hartle, a quantum system is found which is the equivalent of the classical chaotic Duffing oscillator. The similarities and the differences from the classical oscillator are examined; in…
The competition between strength and correlation of coupling terms in a Hamiltonian defines numerous phenomenological models exhibiting spectral properties interpolating between those of Poisson (integrable) and Wigner-Dyson (chaotic)…
Here we study the relaxation of a chain consisting of 3 masses joined by non-linear springs and periodic conditions when the stiffness is weakened. This system, when expressed in their normal coordinates, yields a softened Henon-Heiles…