Expectations from the Liouville-von Neumann Equation Using Chebyshev Expansion

Giacomo Mazzi; Ben Leimkuhler

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arXiv · 0912.1483

Expectations from the Liouville-von Neumann Equation Using Chebyshev Expansion

Giacomo Mazzi·Ben Leimkuhler

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Abstract

We consider a natural dimension reduction technique for the Liouville-von Neumann equation for a mixed quantum system based on evaluation of a trace formula combined with a direct expansion in modified Chebyshev polynomials. This reduction is highly efficient and does not destroy any information. We demonstrate the practical application of the scheme with a model problem and compare with popular alternatives. This method can be applied to autonomous quantum problems where the desired outcome of quantum simulation is the expectation of an observable.

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Giacomo Mazzi, Ben Leimkuhler. 2009-12-08. Expectations from the Liouville-von Neumann Equation Using Chebyshev Expansion. https://arxiv.org/abs/0912.1483

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