Volume 28, pp. 190-205, 2007-2008.

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]

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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