Dynamical entropy of a non-commutative version of the phase doubling

• Autorzy: Johan Andries , Mieke De Cock
• Języki publikacji: EN

Abstrakty

EN

A quantum dynamical system, mimicking the classical phase doubling map $z ↦ z^2$ on the unit circle, is formulated and its ergodic properties are studied. We prove that the quantum dynamical entropy equals the classical value log2 by using compact perturbations of the identity as operational partitions of unity.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1998
• Tom: 43
• Numer: 1
• Strony: 31-40

Daty

wydano

1998

Twórcy

autor

Johan Andries

• Instituut voor Theoretische Fysica, K.U. Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium

autor

Mieke De Cock

• Instituut voor Theoretische Fysica, K.U. Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium

Bibliografia

• [1] R. Alicki, J. Andries, M. Fannes and P. Tuyls, An algebraic approach to the Kolmogorov-Sinai entropy, Rev. Math. Phys. 8(2) (1996), 167-184.
• [2] R. Alicki and M. Fannes, Defining quantum dynamical entropy, Lett. Math. Phys. 32 (1994), 75-82.
• [3] J. Andries, M. De Cock and M. Fannes, Preprint K.U. Leuven TF-97/29.
• [4] G.G. Emch, H. Narnhofer, G.L. Sewell and W. Thirring, Anosov actions on noncommutative algebras, J. Math. Phys. 35(11) (1994), 5582-5599.
• [5] B. Simon, Trace ideals and their applications, London Mathematical Society Lecture Notes Series 35, Cambridge University Press, Cambridge, 1979.
• [6] P. Tuyls, Towards Quantum Kolmogorov-Sinai Entropy, Ph. D. Thesis, K.U. Leuven, 1997.