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Quantum fractals on nspheres
 http://arxiv.org/abs/quantph/0608117v2
"... Using the Clifford algebra formalism we extend the quantum jumps algorithm of the Event Enhanced Quantum Theory (EEQT) to convex state figures other than those stemming from convex hulls of complex projective spaces that form the basis for the standard quantum theory. We study quantum jumps on ndim ..."
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Cited by 2 (1 self)
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dimensional spheres, jumps that are induced by symmetric configurations of noncommuting state monitoring detectors. The detectors cause quantum jumps via geometrically induced conformal maps (Möbius transformations) and realize iterated function systems (IFS) with fractal attractors located on ndimensional spheres
A Bohmian approach to quantum fractals
, 2004
"... Quantum fractals are wave functions with both real and imaginary part continuous everywhere, but differentiable nowhere. This lack of differentiability has been used to deny the validity of Bohmian mechanics (and other trajectory–based approaches) in providing a complete interpretation of quantum me ..."
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Cited by 1 (0 self)
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Quantum fractals are wave functions with both real and imaginary part continuous everywhere, but differentiable nowhere. This lack of differentiability has been used to deny the validity of Bohmian mechanics (and other trajectory–based approaches) in providing a complete interpretation of quantum
PHYSICA Quantum fractal eigenstates
"... We study quantum chaos in open dynamical systems and show that it is characterized byquantum fractal eigenstates located on the underlying classical strange repeller. The states with longest life times typically reveal a scars structure on the classical fractal set. (~)1999 Elsevier Science B.V. All ..."
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We study quantum chaos in open dynamical systems and show that it is characterized byquantum fractal eigenstates located on the underlying classical strange repeller. The states with longest life times typically reveal a scars structure on the classical fractal set. (~)1999 Elsevier Science B
Quantum fractals on n–spheres. Clifford Algebra approach.
, 2008
"... Using the Clifford algebra formalism we extend the quantum jumps algorithm of the Event Enhanced Quantum Theory (EEQT) to convex state figures other than those stemming from convex hulls of complex projective spaces that form the basis for the standard quantum theory. We study quantum jumps on ndim ..."
Abstract

Cited by 2 (1 self)
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dimensional spheres, jumps that are induced by symmetric configurations of noncommuting state monitoring detectors. The detectors cause quantum jumps via geometrically induced conformal maps (Möbius transformations) and realize iterated function systems (IFS) with fractal attractors located on ndimensional spheres
Completely Mixing Quantum Open Systems and Quantum Fractals
 Physica D
, 2001
"... Departing from classical concepts of ergodic theory, formulated in terms of probability densities, measures describing the mixing behavior and the loss of information in quantum open systems are proposed. ..."
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Cited by 6 (3 self)
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Departing from classical concepts of ergodic theory, formulated in terms of probability densities, measures describing the mixing behavior and the loss of information in quantum open systems are proposed.
1 Piecewise Deterministic Quantum Dynamics and Quantum Fractals on the Poincaré Disk.
, 2003
"... It is shown that piecewise deterministic dissipative quantum dynamics in a vector space with indefinite metric can lead to well defined, positive probabilities. The case of quantum jumps on the Poincar’e disk is studied in details, including results of numerical simulations of quantum fractals. One ..."
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Cited by 1 (0 self)
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It is shown that piecewise deterministic dissipative quantum dynamics in a vector space with indefinite metric can lead to well defined, positive probabilities. The case of quantum jumps on the Poincar’e disk is studied in details, including results of numerical simulations of quantum fractals. One
Review Simultaneous Measurement of Noncommuting Observables and Quantum Fractals on Complex Projective Spaces ∗
, 2004
"... The simultaneous measurement of several noncommuting observables is modeled by using semigroups of completely positive maps on an algebra with a nontrivial center. The resulting piecewisedeterministic dynamics leads to chaos and to nonlinear iterated function systems (quantum fractals) on complex ..."
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Cited by 2 (1 self)
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The simultaneous measurement of several noncommuting observables is modeled by using semigroups of completely positive maps on an algebra with a nontrivial center. The resulting piecewisedeterministic dynamics leads to chaos and to nonlinear iterated function systems (quantum fractals) on complex
Orthonormal bases of compactly supported wavelets
, 1993
"... Several variations are given on the construction of orthonormal bases of wavelets with compact support. They have, respectively, more symmetry, more regularity, or more vanishing moments for the scaling function than the examples constructed in Daubechies [Comm. Pure Appl. Math., 41 (1988), pp. 90 ..."
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Cited by 2182 (27 self)
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Several variations are given on the construction of orthonormal bases of wavelets with compact support. They have, respectively, more symmetry, more regularity, or more vanishing moments for the scaling function than the examples constructed in Daubechies [Comm. Pure Appl. Math., 41 (1988), pp. 909996].
Statistical mechanics of complex networks
 Rev. Mod. Phys
"... Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as ra ..."
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Cited by 2083 (10 self)
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Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real
Results 1  10
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10,773