79 research outputs found
Quantum Multiplexers, Parrondo Games, and Proper Quantization
A quantum logic gate of particular interest to both electrical engineers and
game theorists is the quantum multiplexer. This shared interest is due to the
facts that an arbitrary quantum logic gate may be expressed, up to arbitrary
accuracy, via a circuit consisting entirely of variations of the quantum
multiplexer, and that certain one player games, the history dependent Parrondo
games, can be quantized as games via a particular variation of the quantum
multiplexer. However, to date all such quantizations have lacked a certain
fundamental game theoretic property.
The main result in this dissertation is the development of quantizations of
history dependent quantum Parrondo games that satisfy this fundamental game
theoretic property. Our approach also yields fresh insight as to what should be
considered as the proper quantum analogue of a classical Markov process and
gives the first game theoretic measures of multiplexer behavior.Comment: Doctoral dissertation, Portland State University, 138 pages, 22
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A structure-preserving one-sided Jacobi method for computing the SVD of a quaternion matrix
Abstract(#br)In this paper, we propose a structure-preserving one-sided cyclic Jacobi method for computing the singular value decomposition of a quaternion matrix. In our method, the columns of the quaternion matrix are orthogonalized in pairs by using a sequence of orthogonal JRS-symplectic Jacobi matrices to its real counterpart. We establish the quadratic convergence of our method specially. We also give some numerical examples to illustrate the effectiveness of the proposed method
The full integration of black hole solutions to symmetric supergravity theories
We prove that all stationary and spherical symmetric black hole solutions to
theories with symmetric target spaces are integrable and we provide an explicit
integration method. This exact integration is based on the description of black
hole solutions as geodesic curves on the moduli space of the theory when
reduced over the time-like direction. These geodesic equations of motion can be
rewritten as a specific Lax pair equation for which mathematicians have
provided the integration algorithms when the initial conditions are described
by a diagonalizable Lax matrix. On the other hand, solutions described by
nilpotent Lax matrices, which originate from extremal regular (small) D = 4
black holes can be obtained as suitable limits of solutions obtained in the
diagonalizable case, as we show on the generating geodesic (i.e. most general
geodesic modulo global symmetries of the D = 3 model) corresponding to regular
(and small) D = 4 black holes. As a byproduct of our analysis we give the
explicit form of the Wick rotation connecting the orbits of BPS and non-BPS
solutions in maximally supersymmetric supergravity and its STU truncation.Comment: 27 pages, typos corrected, references added, 1 figure added,
Discussion on black holes and the generating geodesic significantly extended.
Statement about the relation between the D=3 geodesics from BPS and non-BPS
extreme black holes made explicit by defining the Wick rotation mapping the
corresponding orbit
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