Collective and relative variables for a classical Klein-Gordon field

In this paper a set of canonical collective variables is defined for a classical Klein-Gordon field and the problem of the definition of a set of canonical relative variables is discussed. This last point is approached by means of a harmonic analysis is momentum space. This analysis shows that the relative variables can be defined if certain conditions are fulfilled by the field configurations. These conditions are expressed by the vanishing of a set of conserved quantities, referred to as supertranslations since as canonical observables they generate a set of canonical transformations whose algebra is the same as that which arises in the study of the asymptotic behaviour of the metric of an isolated system in General Relativity.Comment: 47 pages, no figur

Optical realization of the dissipative quantum oscillator

An optical realization of the damped quantum oscillator, based on transverse light dynamics in an optical resonator with slowly-moving mirrors, is theoretically suggested. The optical resonator setting provides a simple implementation of the time-dependent Caldirola-Kanai Hamiltonian of the dissipative quantum oscillator, and enables to visualize the effects of damped oscillations in the classical (ray optics) limit and wave packet collapse in the quantum (wave optics) regime.Comment: The article is dedicated to Professor Orazio Svelto on the occasion of his 80th birthday. To appear in Optics Letter

Stability analysis tool for tuning unconstrained decentralized model predicitive controllers

Some processes are naturally suitable to be controlled in a decentralized framework: centralized control solutions are often infeasible in dealing with large scale plants and they are technologically prohibitive when the processes are too fast for the available computational resources. In these cases, the resulting control problem is usually split in many smaller subproblems and the global requirements are guaranteed by means of a proper coordination. The unconstrained decentralized case is here considered and a coordination strategy is proposed for improving the global control performances. This paper present a tool for setting up and tuning a nominally stable decentralized Model Predictive Controller. Numerical examples are proposed for testing and validating the developed technique

Optical realization of relativistic non-Hermitian quantum mechanics

Light propagation in distributed feedback optical structures with gain/loss regions is shown to provide an accessible laboratory tool to visualize in optics the spectral properties of the one-dimensional Dirac equation with non-Hermitian interactions. Spectral singularities and PT symmetry breaking of the Dirac Hamiltonian are shown to correspond to simple observable physical quantities and related to well-known physical phenomena like resonance narrowing and laser oscillation.Comment: 4 page

Nonlocal reflection by photonic barriers

The time behaviour of microwaves undergoing partial reflection by photonic barriers was measured in the time and in the frequency domain. It was observed that unlike the duration of partial reflection by dielectric layers, the measured reflection duration of barriers is independent of their length. The experimental results point to a nonlocal behaviour of evanescent modes at least over a distance of some ten wavelengths. Evanescent modes correspond to photonic tunnelling in quantum mechanics.Comment: 8 pages, 5 figure

Non-exponential decay via tunneling in tight-binding lattices and the optical Zeno effect

An exactly-solvable model for the decay of a metastable state coupled to a semi-infinite tight-binding lattice, showing large deviations from exponential decay in the strong coupling regime, is presented. An optical realization of the lattice model, based on discrete diffraction in a semi-infinite array of tunneling-coupled optical waveguides, is proposed to test non-exponential decay and for the observation of an optical analog of the quantum Zeno effect

Optical realization of the two-site Bose-Hubbard model in waveguide lattices

A classical realization of the two-site Bose-Hubbard Hamiltonian, based on light transport in engineered optical waveguide lattices, is theoretically proposed. The optical lattice enables a direct visualization of the Bose-Hubbard dynamics in Fock space.Comment: to be published, J Phys. B (Fast Track Communication

Quantization of a generally covariant gauge system with two super Hamiltonian constraints

The Becci-Rouet-Stora-Tyutin (BRST) operator quantization of a finite-dimensional gauge system featuring two quadratic super Hamiltonian and m linear supermomentum constraints is studied as a model for quantizing generally covariant gauge theories. The proposed model ``completely'' mimics the constraint algebra of General Relativity. The Dirac constraint operators are identified by realizing the BRST generator of the system as a Hermitian nilpotent operator, and a physical inner product is introduced to complete a consistent quantization procedure.Comment: 17 pages. Latex file. Minor changes, two references adde

Zitterbewegung of optical pulses in nonlinear frequency conversion

Pulse walk-off in the process of sum frequency generation in a nonlinear $\chi^{(2)}$ crystal is shown to be responsible for pulse jittering which is reminiscent to the Zitterbewegung (trembling motion) of a relativistic freely moving Dirac particle. An analytical expression for the pulse center of mass trajectory is derived in the no-pump-depletion limit, and numerical examples of Zitterbewegung are presented for sum frequency generation in periodically-poled lithium niobate. The proposed quantum-optical analogy indicates that frequency conversion in nonlinear optics could provide an experimentally accessible simulator of the Dirac equation.Comment: to be published in Journal of Physics B: Atomic, Molecular & Optical Physic