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arXiv · 0903.0129

Quantum Conditions on Dynamics and Control in Open Systems

Lian-Ao Wu·Arjun Bharioke·Paul Brumer
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Abstract

Quantum conditions on the control of dynamics of a system coupled to an environment are obtained. Specifically, consider a system initially in a system subspace $H_{0}$ of dimensionality $M_{0}$, which evolves to populate system subspaces $H_{1}$, $H_{2}$ of dimensionality $M_{1}$, $M_{2}$. Then there always exists an initial state in $H_0$ that does not evolve into $H_2$ if $M_{0}>dM_{2},$ where $2 \leq d \leq (M_0 +M_1 +M_2)^2$ is the number of operators in the Kraus representation. Note, significantly, that the maximum $d$ can be far smaller than the dimension of the bath. If this condition is not satisfied then dynamics from $H_{0}$ that avoids $H_{2}$ can only be attained physically under stringent conditions. An example from molecular dynamics and spectroscopy, i.e. donor to acceptor energy transfer, is provided.

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Lian-Ao Wu, Arjun Bharioke, Paul Brumer. 2009-03-01. Quantum Conditions on Dynamics and Control in Open Systems. https://doi.org/10.1063/1.2958220

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