Related papers: Complex Elliptic Pendulum
In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum…
We consider motion in a periodic potential in a classical, quantum, and semiclassical context. Various results on the distribution of asymptotic velocities are proven.
Study of the classical motion of two identical particles on a plane subject to non-Coulomb potentials in a constant magnetic field presented in polar coordinates. With the rigorous analysis of the potentials and the constants of motion, we…
We survey some of the connections linking complex dynamics to other fields of mathematics and science. We hope to show that complex dynamics is not just interesting on its own but also has value as an applicable theory.
It is shown that quantum mechanics is a plausible statistical description of an ontology described by classical electrodynamics. The reason that no contradiction arises with various no-go theorems regarding the compatibility of QM with a…
Recent results suggest that quantum mechanical phenomena may be interpreted as a failure of standard probability theory and may be described by a Bayesian complex probability theory.
We describe a new phenomenon in the study of the real-time path integral, where complex classical paths hit singularities of the potential and need to be analytically continued beyond the space for which they solve the boundary value…
We study quantum mechanical tunneling using complex solutions of the classical field equations. Simple visualization techniques allow us to unify and generalize previous treatments, and straightforwardly show the connection to the standard…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…
This paper offers a brief introduction to the framework of "general probabilistic theories", otherwise known as the "convex-operational" approach the foundations of quantum mechanics. Broadly speaking, the goal of research in this vein is…
The small angle approximation often fails to explain experimental data, does not even predict if a plane pendulum's period increases or decreases with increasing amplitude. We make a perturbation ansatz for the Conserved Energy Surfaces of…
Classical mechanics is a singular theory in that real-energy classical particles can never enter classically forbidden regions. However, if one regulates classical mechanics by allowing the energy E of a particle to be complex, the particle…
In our thesis, we try to shed more light onto the complexity of quantum complexity classes by refining the related part of the hierarchy. First, we review the basic concepts of quantum computing in general. Then, inspired by BQP, we define…
We extract the information of a quantum motion and decode it into a certain orbit via a single measurable quantity. Such that a quantum chaotic system can be reconstructed as a chaotic attractor. Two configurations for reconstructing this…
In the preceding paper, the structure and thermodynamics of a given quantum system was represented by a corresponding classical system having an effective temperature, local chemical potential, and pair potential. Here, that formal…
We investigate the difficulties that undergraduate students in quantum mechanics courses have in transferring learning from previous courses or within the same course from one context to another by administering written tests and conducting…
This review is focused on QCD theoretical issues and their phenomenological relevance specially for LHC. It is incomplete and mostly neglects the phenomenology of long distance physics
For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also…
We study the classical dynamics of non-relativistic particles endowed with spin. Non-vanishing Zitterbewegung terms appear in the equation of motion also in the small momentum limit. We derive a generalized work-energy theorem which…
Classical and quantum walks on some finite paths are introduced. It is shown that these walks have explicit solutions given in terms of exceptional Krawtchouk polynomials and their properties are explored. In particular, fractional revival…