149,741 research outputs found
The basics of gravitational wave theory
Einstein's special theory of relativity revolutionized physics by teaching us
that space and time are not separate entities, but join as ``spacetime''. His
general theory of relativity further taught us that spacetime is not just a
stage on which dynamics takes place, but is a participant: The field equation
of general relativity connects matter dynamics to the curvature of spacetime.
Curvature is responsible for gravity, carrying us beyond the Newtonian
conception of gravity that had been in place for the previous two and a half
centuries. Much research in gravitation since then has explored and clarified
the consequences of this revolution; the notion of dynamical spacetime is now
firmly established in the toolkit of modern physics. Indeed, this notion is so
well established that we may now contemplate using spacetime as a tool for
other science. One aspect of dynamical spacetime -- its radiative character,
``gravitational radiation'' -- will inaugurate entirely new techniques for
observing violent astrophysical processes. Over the next one hundred years,
much of this subject's excitement will come from learning how to exploit
spacetime as a tool for astronomy. This article is intended as a tutorial in
the basics of gravitational radiation physics.Comment: 49 pages, 3 figures. For special issue of New Journal of Physics,
"Spacetime 100 Years Later", edited by Richard Price and Jorge Pullin. This
version corrects an important error in Eq. (4.23); an erratum is in pres
Basics of Quantum Mechanics, Geometrization and some Applications to Quantum Information
In this paper we present a survey of the use of differential geometric
formalisms to describe Quantum Mechanics. We analyze Schr\"odinger framework
from this perspective and provide a description of the Weyl-Wigner
construction. Finally, after reviewing the basics of the geometric formulation
of quantum mechanics, we apply the methods presented to the most interesting
cases of finite dimensional Hilbert spaces: those of two, three and four level
systems (one qubit, one qutrit and two qubit systems). As a more practical
application, we discuss the advantages that the geometric formulation of
quantum mechanics can provide us with in the study of situations as the
functional independence of entanglement witnesses.Comment: AmsLaTeX, 37 pages, 8 figures. This paper is an expanded version of
some lectures delivered by one of us (G. M.) at the ``Advanced Winter School
on the Mathematical Foundation of Quantum Control and Quantum Information''
which took place at Castro Urdiales (Spain), February 11-15, 200
The Fundamentals of Radar with Applications to Autonomous Vehicles
Radar systems can be extremely useful for applications in autonomous vehicles. This paper seeks to show how radar systems function and how they can apply to improve autonomous vehicles. First, the basics of radar systems are presented to introduce the basic terminology involved with radar. Then, the topic of phased arrays is presented because of their application to autonomous vehicles. The topic of digital signal processing is also discussed because of its importance for all modern radar systems. Finally, examples of radar systems based on the presented knowledge are discussed to illustrate the effectiveness of radar systems in autonomous vehicles
- …