Johan Andries | KU Leuven (original) (raw)
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Papers by Johan Andries
Letters in Mathematical Physics, 1995
We present a rigorous computation of the dynamical entropy h of the quantum Arnold cat map. This ... more We present a rigorous computation of the dynamical entropy h of the quantum Arnold cat map. This map, which describes a flow on the noncommutative two-dimensional torus, is a simple example of a quantum dynamical system with optimal mixing properties, characterized by Lyapunov exponents-tIn 2 +, 2 + > 1. We show that, for all values of the quantum deformation parameter, h coincides with the positive Lyapunov exponent of the dynamics.
Reviews in Mathematical Physics, 1996
We revisit the notion of Kolmogorov-Sinai entropy for classical dynamical systems in terms of an ... more We revisit the notion of Kolmogorov-Sinai entropy for classical dynamical systems in terms of an algebraic formalism. This is the starting point for defining the entropy for general non-commutative systems. Hereby typical quantum tools are introduced in the statistical description of classical dynamical systems. We illustrate the power of these techniques by providing a simple, self-contained proof of the entropy formula for general automorphisms of n-dimensional tori.
Journal of Physics A-mathematical and General - J PHYS-A-MATH GEN, 1998
We consider an irreversible quantum dynamical system that mimics the classical phase doubling map... more We consider an irreversible quantum dynamical system that mimics the classical phase doubling map 0305-4470/31/28/013/img1 on the unit circle and study its ergodic properties. The main result of the paper is the computation of the dynamical entropy 0305-4470/31/28/013/img2 using compact perturbations of unity as operational partitions of unity.
Reviews in Mathematical Physics, 2000
In this paper, we consider the long time asymptotics of multi-time correlation functions for quan... more 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.
Reports on Mathematical Physics, 1999
Reviews in Mathematical Physics, 2000
In this paper, we consider the long time asymptotics of multi-time correlation functions for quan... more 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.
Letters in Mathematical Physics, 1995
We present a rigorous computation of the dynamical entropy h of the quantum Arnold cat map. This ... more We present a rigorous computation of the dynamical entropy h of the quantum Arnold cat map. This map, which describes a flow on the noncommutative two-dimensional torus, is a simple example of a quantum dynamical system with optimal mixing properties, characterized by Lyapunov exponents-tIn 2 +, 2 + > 1. We show that, for all values of the quantum deformation parameter, h coincides with the positive Lyapunov exponent of the dynamics.
Reviews in Mathematical Physics, 1996
We revisit the notion of Kolmogorov-Sinai entropy for classical dynamical systems in terms of an ... more We revisit the notion of Kolmogorov-Sinai entropy for classical dynamical systems in terms of an algebraic formalism. This is the starting point for defining the entropy for general non-commutative systems. Hereby typical quantum tools are introduced in the statistical description of classical dynamical systems. We illustrate the power of these techniques by providing a simple, self-contained proof of the entropy formula for general automorphisms of n-dimensional tori.
Journal of Physics A-mathematical and General - J PHYS-A-MATH GEN, 1998
We consider an irreversible quantum dynamical system that mimics the classical phase doubling map... more We consider an irreversible quantum dynamical system that mimics the classical phase doubling map 0305-4470/31/28/013/img1 on the unit circle and study its ergodic properties. The main result of the paper is the computation of the dynamical entropy 0305-4470/31/28/013/img2 using compact perturbations of unity as operational partitions of unity.
Reviews in Mathematical Physics, 2000
In this paper, we consider the long time asymptotics of multi-time correlation functions for quan... more 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.
Reports on Mathematical Physics, 1999
Reviews in Mathematical Physics, 2000
In this paper, we consider the long time asymptotics of multi-time correlation functions for quan... more 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.