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Ergodic theorem, ergodic theory, and statistical mechanics. [PDF]
Proc Natl Acad Sci U S A, 2015 This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics.
Moore CC.
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Annals of Probability, 1973 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
J F C Kingman
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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 ...
David Ruelle +2 more
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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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