Related papers: The Quantum Double Pendulum: a Study of an Autonom…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…
The double rod pendulum is a well known classic chaotic system, so its quantum version is an ideal laboratory to test various diagnosis for quantum chaos. We quantise this system canonically and calculate its lowest $10^4$ eigenvalues and…
The classical-quantum duality at the basis of quantum theory is here extended to the Planck scale domain. The classical/semiclassical gravity (G) domain is dual (in the precise sense of the classical-quantum duality) to the quantum (Q)…
The mathematical possibility of coupling two quantum dynamic systems having two different Planck constants, respectively, is investigated. It turns out that such canonical dynamics are always irreversible. Semiclassical dynamics is obtained…
There ought to exist a reformulation of quantum mechanics which does not refer to an external classical spacetime manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which…
We study the phase space of periodically modulated gravitational cavity by means of quantum recurrence phenomena. We report that the quantum recurrences serve as a tool to connect phase space of the driven system with spectrum in quantum…
In this paper we apply the method of Lagrangian descriptors as an indicator to study the chaotic and regular behavior of trajectories in the phase space of the classical double pendulum system. In order to successfully quantify the degree…
Planck scale physics represents a future challenge, located between particle physics and general relativity. The Planck scale marks a threshold beyond which the old description of spacetime breaks down and conceptually new phenomena must…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
The quantum states of the Kapitza pendulum are described within the effective potential obtained by the method of averaging over the fast oscillations. An analytical estimate of the energy spectrum of stabilized states is given using…
The method of restricted path integrals allows one to effectively consider continuous (prolonged in time) measurements of quantum systems. Monitoring of the system coordinates is such a continuous measurement that allows one to describe a…
The main idea of "Quantum Chaos" studies is that Quantum Mechanics introduces two energy scales into the study of chaotic systems: One is obviously the mean level spacing $\Delta\propto\hbar^d$, where $d$ is the dimensionality; The other is…
We study a model of quantum cosmology originating from a classical model of gravitation where a self interacting scalar field is coupled to gravity with the metric undergoing a signature transition. We show that there are dual classical…
The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum…
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
The quantum resonances occurring with delta-kicked particles are studied with the help of a fictitious classical limit, establishing a direct correspondence between the nearly resonant quantum motion and the classical resonances of a…
The classical and quantum aspects of planar Coulomb interactions have been studied in detail. In the classical scenario, Action Angle Variables are introduced to handle relativistic corrections, in the scheme of time-independent…
Pendulums are simple mechanical systems that have been studied for centuries and exhibit many aspects of modern dynamical systems theory. In particular, the double pendulum is a prototypical chaotic system that is frequently used to…
Duality transformations within the quantum mechanics of a finite number of degrees of freedom can be regarded as the dependence of the notion of a quantum, i.e., an elementary excitation of the vacuum, on the observer on classical phase…