## Quantum dynamical entropy and an algorithm by Gene Golub

Giorgio Mantica

### Abstract

The problem of computing the quantum dynamical entropy introduced by Alicki and Fannes requires the trace of the operator function $F(\Omega) = - \Omega \log \Omega$, where $\Omega$ is a non-negative, Hermitean operator. Physical significance demands that this operator be a matrix of large order. We study its properties and we derive efficient algorithms to solve this problem, also implementable on parallel machines with distributed memory. We rely on a Lanczos technique for large matrix computations developed by Gene Golub.

Full Text (PDF) [717 KB], BibTeX

### Key words

Quantum dynamical entropy, large matrices, Lanczos method, Montecarlo techniques

### AMS subject classifications

65F10, 37M25, 81Q50

### Links to the cited ETNA articles

 [11] Vol. 25 (2006), pp. 409-430 Giorgio Mantica: Fourier-Bessel functions of singular continuous measures and their many asymptotics

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