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Annals of Probability, 1973 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The ergodic theory of AxiomA flows
Inventiones Mathematicae, 1975 Let M be a compact (Riemann) manifold and (f t ): M → M a differentiable flow. A closed (f t )-invariant set ∧ ⊂ M containing no fixed points is hyperbolic if the tangent bundle restricted to ∧ can be written as the Whitney sum of three (Tf t )-invariant continuous subbundles $${T_\Lambda }M = E + {E^s} + {E^u}$$ where E is the one-dimensional ...
Rufus Bowen, David Ruelle
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Central Limit Theorem in View of Subspace Convex-Cyclic Operators [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2021 In our work we have defined an operator called subspace convex-cyclic operator. The property of this newly defined operator relates eigenvalues which have eigenvectors of modulus one with kernels of the operator.
H.M. Hasan +3 more
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SciPost Physics, 2023 We present a quantitative and fully non-perturbative description of the ergodic phase of quantum chaos in the setting of two-dimensional gravity. To this end we describe the doubly non-perturbative completion of semiclassical 2D gravity in terms of its ...
Alexander Altland, Boris Post, Julian Sonner, Jeremy van der Heijden, Erik Verlinde
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Theory of Ergodic Quantum Processes
Physical Review X, 2021 The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels.
Ramis Movassagh, Jeffrey Schenker
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Dynamical quantum ergodicity from energy level statistics
Physical Review Research, 2023 Ergodic theory provides a rigorous mathematical description of chaos in classical dynamical systems, including a formal definition of the ergodic hierarchy. How ergodic dynamics is reflected in the energy levels and eigenstates of a quantum system is the
Amit Vikram, Victor Galitski
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From operator statistics to wormholes
Physical Review Research, 2021 For a generic quantum many-body system, the quantum ergodic regime is defined as the limit in which the spectrum of the system resembles that of a random matrix theory (RMT) in the corresponding symmetry class.
Alexander Altland +4 more
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On Two Non-Ergodic Reversible Cellular Automata, One Classical, the Other Quantum
Entropy, 2023 We propose and discuss two variants of kinetic particle models—cellular automata in 1 + 1 dimensions—that have some appeal due to their simplicity and intriguing properties, which could warrant further research and applications.
Tomaž Prosen
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Generalized Ordinal Patterns and the KS-Entropy
Entropy, 2021 Ordinal patterns classifying real vectors according to the order relations between their components are an interesting basic concept for determining the complexity of a measure-preserving dynamical system. In particular, as shown by C. Bandt, G.
Tim Gutjahr, Karsten Keller
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Ergodic Theory Meets Polarization. I: An Ergodic Theory for Binary Operations [PDF]
, 2016 An open problem in polarization theory is to determine the binary operations that always lead to polarization (in the general multilevel sense) when they are used in Ar{\i}kan style constructions.
Nasser, Rajai
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