5,688 research outputs found
Lie Algebroids in Classical Mechanics and Optimal Control
We review some recent results on the theory of Lagrangian systems on Lie
algebroids. In particular we consider the symplectic and variational formalism
and we study reduction. Finally we also consider optimal control systems on Lie
algebroids and we show how to reduce Pontryagin maximum principle.Comment: This is a contribution to the Proc. of workshop on Geometric Aspects
of Integrable Systems (July 17-19, 2006; Coimbra, Portugal), published in
SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
Particle detectors and the zero mode of a quantum field
We study the impact of the zero-mode of a quantum field on the evolution of a
particle detector. For a massless scalar field in a periodic cavity, we show
that the impact of the zero mode on the Unruh-DeWitt detector and its
derivative-coupling generalisation is necessarily nonvanishing but can be made
negligible in some limits, including those commonly occurring in
non-relativistic quantum optics. For the derivative-coupling detector this can
be accomplished by just tuning the zero mode's initial state, but the standard
Unruh-DeWitt detector requires a more subtle and careful tuning. Applications
include an inertial detector with arbitrary velocity, where we demonstrate the
regularity of the ultrarelativistic limit, and a detector with uniform
acceleration.Comment: 14 pages, 3 Figures. RevTex 4.1. v2: Added journal reference and
minor edits to match published versio
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