61 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
Adventures in Theoretical Physics: Selected Papers of Stephen L. Adler -- Commentaries
These are the commentaries for a volume of reprints of my selected papers
with commentaries that I am preparing for publication by World Scientific.
Contents: Preface; (1)Early Years, and Condensed Matter Physics; (2) High
Energy Neutrino Reactions, PCAC Relations, and Sum Rules; (3) Anomalies: Chiral
Anomalies and Their Nonrenormalization, Perturbative Corrections to Scaling,
and Trace Anomalies to All Orders; (4) Quantum Electrodynamics; (5) Particle
Phenomenology and Neutral Currents; (6) Gravitation; (7) Non-Abelian Monopoles,
Confinement Models, and Chiral Symmetry Breaking; (8) Overrelaxation for
Monte-Carlo and Other Algorithms; (9) Quaternionic Quantum Mechanics, Trace
Dynamics, and Emergent Quantum Theory; (10) Where Next?Comment: Latex 115p; Final version. Book version will differ in reference
format and indexing; version 3 differs from version 2 by minor copy-editing
correction
Extended Supersymmetries in One Dimension
This work covers part of the material presented at the Advanced Summer School in Prague. It is mostly devoted to the structural properties of Extended Supersymmetries in One Dimension. Several results are presented on the classification of linear, irreducible representations realized on a finite number of time-dependent fields. The connections between supersymmetry transformations, Clifford algebras and division algebras are discussed. A manifestly supersymmetric framework for constructing invariants without using the notion of superfields is presented. A few examples of one-dimensional, N-extended, off-shell invariant sigma models are computed. The relation between supersymmetry transformations and graph theory is outlined. The notion of the fusion algebra of irreps tensor products is presented. The relevance of one-dimensional Supersymmetric Quantum Mechanics as a way to extract information on higher dimensional supersymmetric field theories is discussed.
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