301 research outputs found
Statistical description of the black hole degeneracy spectrum
We use mathematical methods based on generating functions to study the
statistical properties of the black hole degeneracy spectrum in loop quantum
gravity. In particular we will study the persistence of the observed effective
quantization of the entropy as a function of the horizon area. We will show
that this quantization disappears as the area increases despite the existence
of black hole configurations with a large degeneracy. The methods that we
describe here can be adapted to the study of the statistical properties of the
black hole degeneracy spectrum for all the existing proposals to define black
hole entropy in loop quantum gravity.Comment: 41 pages, 12 figure
Introduction to Quantum Mechanics
The purpose of this contribution is to give a very brief introduction to
Quantum Mechanics for an audience of mathematicians. I will follow Segal's
approach to Quantum Mechanics paying special attention to algebraic issues. The
usual representation of Quantum Mechanics on Hilbert spaces is also discussed.Comment: To appear in the AIP Conference Proceedings of the XVI International
Fall Workshop on Geometry and Physics, Lisbon - Portugal, 5-8 September 2007.
11 page
Classical and quantum behavior of dynamical systems defined by functions of solvable Hamiltonians
We discuss the classical and quantum mechanical evolution of systems
described by a Hamiltonian that is a function of a solvable one, both
classically and quantum mechanically. The case in which the solvable
Hamiltonian corresponds to the harmonic oscillator is emphasized. We show that,
in spite of the similarities at the classical level, the quantum evolution is
very different. In particular, this difference is important in constructing
coherent states, which is impossible in most cases. The class of Hamiltonians
we consider is interesting due to its pedagogical value and its applicability
to some open research problems in quantum optics and quantum gravity.Comment: Accepted for publication in American Journal of Physic
Quantum isolated horizons and black hole entropy
We give a short introduction to the approaches currently used to describe
black holes in loop quantum gravity. We will concentrate on the classical
issues related to the modeling of black holes as isolated horizons, give a
short discussion of their canonical quantization by using loop quantum gravity
techniques, and a description of the combinatorial methods necessary to solve
the counting problems involved in the computation of the entropy.Comment: 28 pages in A4 format. Contribution to the Proceedings of the 3rd
Quantum Geometry and Quantum Gravity School in Zakopane (2011
Dynamic analysis of runout correction in milling
Tool runout and its effects is an important area of research within modelling, simulation, and control of milling forces. Tool runout causes tool cutting edges to experience uneven forces during milling. This fact also affects tool life and deteriorates workpiece surface quality. In this article a procedure, in order to diminish the effects of tool runout, is presented. The procedure is based on chip thickness modification by means of the fast correction of the tool feed rate. Dynamic feed rate modification is provided by superposing our own design of a fast feed system driven by a piezoelectric actuator to the conventional feed drive of the CNC machine tool. Previously, a model of the dynamic behaviour of the system was developed to analyze the influence of fast feed rate modification on cutting forces. The model incorporates the piezoelectric actuator response as well as the structural dynamics of the tool and the designed Fast Feed Drive System (FFDS). Simulated and experimental results presented in this paper show the effectiveness and benefits of this new tool runout correction procedure
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