3,143 research outputs found
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
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
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
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
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
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