297 research outputs found
Object recognition in infrared imagery using appearance-based methods
Abstract unavailable please refer to PD
Chaos, Complexity, and Random Matrices
Chaos and complexity entail an entropic and computational obstruction to
describing a system, and thus are intrinsically difficult to characterize. In
this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE)
Hamiltonians and analytically compute out-of-time-ordered correlation functions
(OTOCs) and frame potentials to quantify scrambling, Haar-randomness, and
circuit complexity. While our random matrix analysis gives a qualitatively
correct prediction of the late-time behavior of chaotic systems, we find
unphysical behavior at early times including an scrambling
time and the apparent breakdown of spatial and temporal locality. The salient
feature of GUE Hamiltonians which gives us computational traction is the
Haar-invariance of the ensemble, meaning that the ensemble-averaged dynamics
look the same in any basis. Motivated by this property of the GUE, we introduce
-invariance as a precise definition of what it means for the dynamics of a
quantum system to be described by random matrix theory. We envision that the
dynamical onset of approximate -invariance will be a useful tool for
capturing the transition from early-time chaos, as seen by OTOCs, to late-time
chaos, as seen by random matrix theory.Comment: 61 pages, 14 figures; v2: references added, typos fixe
Exploring Periodic Orbit Expansions and Renormalisation with the Quantum Triangular Billiard
A study of the quantum triangular billiard requires consideration of a
boundary value problem for the Green's function of the Laplacian on a trianglar
domain. Our main result is a reformulation of this problem in terms of coupled
non--singular integral equations. A non--singular formulation, via Fredholm's
theory, guarantees uniqueness and provides a mathematically firm foundation for
both numerical and analytic studies. We compare and contrast our reformulation,
based on the exact solution for the wedge, with the standard singular integral
equations using numerical discretisation techniques. We consider in detail the
(integrable) equilateral triangle and the Pythagorean 3-4-5 triangle. Our
non--singular formulation produces results which are well behaved
mathematically. In contrast, while resolving the eigenvalues very well, the
standard approach displays various behaviours demonstrating the need for some
sort of ``renormalisation''. The non-singular formulation provides a
mathematically firm basis for the generation and analysis of periodic orbit
expansions. We discuss their convergence paying particular emphasis to the
computational effort required in comparision with Einstein--Brillouin--Keller
quantisation and the standard discretisation, which is analogous to the method
of Bogomolny. We also discuss the generalisation of our technique to smooth,
chaotic billiards.Comment: 50 pages LaTeX2e. Uses graphicx, amsmath, amsfonts, psfrag and
subfigure. 17 figures. To appear Annals of Physics, southern sprin
Probabilistic Framework for Sensor Management
A probabilistic sensor management framework is introduced, which maximizes the utility of sensor systems with many different sensing modalities by dynamically configuring the sensor system in the most beneficial way. For this purpose, techniques from stochastic control and Bayesian estimation are combined such that long-term effects of possible sensor configurations and stochastic uncertainties resulting from noisy measurements can be incorporated into the sensor management decisions
Shell Model Monte Carlo Methods
We review quantum Monte Carlo methods for dealing with large shell model
problems. These methods reduce the imaginary-time many-body evolution operator
to a coherent superposition of one-body evolutions in fluctuating one-body
fields; the resultant path integral is evaluated stochastically. We first
discuss the motivation, formalism, and implementation of such Shell Model Monte
Carlo (SMMC) methods. There then follows a sampler of results and insights
obtained from a number of applications. These include the ground state and
thermal properties of {\it pf}-shell nuclei, the thermal and rotational
behavior of rare-earth and -soft nuclei, and the calculation of double
beta-decay matrix elements. Finally, prospects for further progress in such
calculations are discussed
- …