Related papers: Quantum Caustics for Systems with Quadratic Lagran…
We study quantum information processing using superpositions of Fock states in superconducting resonators, as quantum $d$-level systems (qudits). A universal set of single and coupled logic gates is theoretically proposed for resonators…
The dynamic $U (1)$ symmetry of classical electrodynamics without charges, similar to the known phase symmetry of quantum mechanics, is analyzed. Using this symmetry, alternative Lagrangians of classical electrodynamics, similar to…
We address the issue of the quantum-classical correspondence in chaotic systems using, as recently done by Zurek [e-print quant-ph/9802054], the solar system as a whole as a case study: this author shows that the classicality of the…
Caustics occur widely in dynamics and take on shapes classified by catastrophe theory. At finite wavelengths they produce interference patterns containing networks of vortices (phase singularities). Here we investigate caustics in quantized…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
We consider the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic…
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…
Typical optomechanical systems involving optical cavities and mechanical oscillators rely on a coupling that varies linearly with the oscillator displacement. However, recently a coupling varying instead as the square of the mechanical…
The classical limit of quantum q-oscillators suggests an interpretation of the deformation as a way to introduce non linearity. Guided by this idea, we considered q-fields, the partition fumction, and compute a consequence on specific heat…
It is shown that the independence of the continuum hypothesis points to the unique definite status of the set of intermediate cardinality: the intermediate set exists only as a subset of continuum. This latent status is a consequence of…
We study the quantum dynamics of optical fields in weakly confining resonators with overlapping modes. Employing a recently developed quantization scheme involving a discrete set of resonator modes and continua of external modes we derive…
We discuss the use of the variational principle within quaternionic quantum mechanics. This is non-trivial because of the non commutative nature of quaternions. We derive the Dirac Lagrangian density corresponding to the two-component Dirac…
We show that non-relativistic Quantum Mechanics can be faithfully represented in terms of a classical diffusion process endowed with a gauge symmetry of group Z_4. The representation is based on a quantization condition for the realized…
Closed systems in Newtonian mechanics obey the principle of Galilean relativity. However, the usual Lagrangian for Newtonian mechanics, formed from the difference of kinetic and potential energies, is not invariant under the full group of…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
We present an investigation into effects exhibited by the two-frequency kicked rotor. Experiments were performed and in addition quantum and classical dynamics were simulated and compared with the experimental results. The experiments…
Quantum fluctuations are inherent in open quantum systems and they affect not only the statistical properties of the initial state but also the time evolution of the system. Using a generic minimal model, we show that quantum noise…
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We…
We investigate the quantum recurrence phenomena in periodically driven systems. We calculate the classical period and the quantum recurrence time and develop their interdependence. We further predict the behavior of the recurrence phenomena…
We study the quantization of many-body systems in three dimensions in rotating coordinate frames using a gauge invariant formulation of the dynamics. We consider reference frames defined by linear gauge conditions, and discuss their Gribov…