Quantum Conditions on Dynamics and Control in Open Systems

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 $M_0>d{M}_2,$ where $2\le d\le (M_0+M_1+M_2{)}^2$ 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.

4 pages, no figure

References in corpus (1)

• Controllability of open quantum systems with Kraus-map dynamics

Cited by in corpus (1)

• Master Equation and Control of an Open Quantum System with Leakage