Breaking the exponential wall in classical simulations of fidelity

Details Breaking the exponential wall in classical simulations of fidelity Breaking the exponential wall in classical simulations of fidelity

2011-07-31

arxiv.org/abs/1108.0173v1

Nonlinear Sciences

Chaotic Dynamics

5 pages, 3 figures

Scientific paper

We analyze the efficiency of available algorithms for the simulation of classical fidelity and show that their computational costs increase exponentially with the number of degrees of freedom for almost all initial states. Then we present an algorithm whose cost is independent of the system's dimensionality and show that, within a continuous family of algorithms, our algorithm is the only one with this property. Simultaneously we propose a general analytical approach to estimate efficiency of trajectory-based methods.

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