scholarly journals Logical entropy of quantum dynamical systems

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Abolfazl Ebrahimzadeh
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Quantum Logic ◽  
Quantum Dynamical ◽  
Quantum Dynamical System ◽  
Ergodic Properties ◽  
Quantum Dynamical Systems ◽  
Logical Entropy

AbstractThis paper introduces the concepts of logical entropy and conditional logical entropy of hnite partitions on a quantum logic. Some of their ergodic properties are presented. Also logical entropy of a quantum dynamical system is dehned and ergodic properties of dynamical systems on a quantum logic are investigated. Finally, the version of Kolmogorov-Sinai theorem is proved.

Spectrum of quantum dynamical systems: Subsystems and entropy

2014 ◽  
Vol 5 (2) ◽  
Author(s):  
Mona Khare ◽  
Anurag Shukla
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Orthomodular Lattices ◽  
Quantum Dynamical ◽  
Quantum Dynamical System ◽  
Quantum Dynamical Systems

Abstract.In the present paper, we have studied quantum dynamical systems of difference posets, their equivalence, subsystems and spectra. It is shown that every subsystem of a mixing quantum dynamical system is mixing, and also a bounded spectrum of quantum dynamical systems has its supremum, and all such suprema are equivalent. Entropy of subsystems of a quantum dynamical system of orthomodular lattices is also investigated.

scholarly journals Ergodic properties of the Anzai skew-product for the non-commutative torus

2020 ◽  
pp. 1-22 ◽  
Author(s):  
SIMONE DEL VECCHIO ◽  
FRANCESCO FIDALEO ◽  
LUCA GIORGETTI ◽  
STEFANO ROSSI
Keyword(s):  
Dynamical Systems ◽  
Unit Circle ◽  
Systematic Study ◽  
Cartesian Product ◽  
Skew Product ◽  
Quantum Dynamical ◽  
Ergodic Properties ◽  
Pointwise Limit ◽  
Quantum Dynamical Systems ◽  
Uniquely Ergodic

We provide a systematic study of a non-commutative extension of the classical Anzai skew-product for the cartesian product of two copies of the unit circle to the non-commutative 2-tori. In particular, some relevant ergodic properties are proved for these quantum dynamical systems, extending the corresponding ones enjoyed by the classical Anzai skew-product. As an application, for a uniquely ergodic Anzai skew-product $\unicode[STIX]{x1D6F7}$ on the non-commutative $2$ -torus $\mathbb{A}_{\unicode[STIX]{x1D6FC}}$ , $\unicode[STIX]{x1D6FC}\in \mathbb{R}$ , we investigate the pointwise limit, $\lim _{n\rightarrow +\infty }(1/n)\sum _{k=0}^{n-1}\unicode[STIX]{x1D706}^{-k}\unicode[STIX]{x1D6F7}^{k}(x)$ , for $x\in \mathbb{A}_{\unicode[STIX]{x1D6FC}}$ and $\unicode[STIX]{x1D706}$ a point in the unit circle, and show that there are examples for which the limit does not exist, even in the weak topology.

scholarly journals ON STRONG ERGODIC PROPERTIES OF QUANTUM DYNAMICAL SYSTEMS

2009 ◽  
Vol 12 (04) ◽  
pp. 551-564 ◽  
Author(s):  
FRANCESCO FIDALEO
Keyword(s):  
Dynamical System ◽  
Fixed Point ◽  
Ergodic Property ◽  
Invariant State ◽  
C Algebras ◽  
Quantum Dynamical ◽  
Ergodic Properties ◽  
Classical Dynamical System ◽  
Amalgamated Free Product ◽  
Quantum Dynamical Systems

We show that the shift on the reduced C*-algebras of RD-groups, including the free group on infinitely many generators, and the amalgamated free product C*-algebras, enjoys the very strong ergodic property of the convergence to the equilibrium. Namely, the free shift converges, pointwise in the weak topology, to the conditional expectation onto the fixed-point subalgebra. Provided the invariant state is unique, we also show that such an ergodic property cannot be fulfilled by any classical dynamical system, unless it is conjugate to the trivial one-point dynamical system.

scholarly journals MULTI-TIME CORRELATIONS IN RELAXING QUANTUM DYNAMICAL SYSTEMS

2000 ◽  
Vol 12 (07) ◽  
pp. 921-944 ◽  
Author(s):  
JOHAN ANDRIES ◽  
FABIO BENATTI ◽  
MIEKE De COCK ◽  
MARK FANNES
Keyword(s):  
Dynamical Systems ◽  
Correlation Functions ◽  
Time Correlation ◽  
Time Correlation Functions ◽  
Quantum Dynamical ◽  
Time Asymptotics ◽  
Time Correlations ◽  
Long Time ◽  
Long Time Asymptotics ◽  
Quantum Dynamical Systems

In this paper, we consider the long time asymptotics of multi-time correlation functions for quantum dynamical systems that are sufficiently random to relax to a reference state. In particular, the evolution of such systems must have a continuous spectrum. Special attention is paid to general dynamical clustering conditions and their consequences for the structure of fluctuations of temporal averages. This approach is applied to the so-called Powers–Price shifts.

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