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.

Quantum dynamical entropy and an algorithm by Gene Golub

MANTICA, GIORGIO DOMENICO PIO
Primo
2008

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.
Quantum dynamical entropy; large matrices; Lanczos method; Montecarlo techniques.
Mantica, GIORGIO DOMENICO PIO
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11383/10435
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