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arXiv · 1403.0543

Quantum tunneling and evolution speed in an exactly solvable coupled double-well system

Hideo Hasegawa
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Abstract

Exact analytical calculations of eigenvalues and eigenstates are presented for quantum coupled double-well (DW) systems with Razavy's hyperbolic potential. With the use of four kinds of initial wavepackets, we have calculated the tunneling period $T$ and the orthogonality time $τ$ which signifies a time interval for an initial state to evolve to its orthogonal state. We discuss the coupling dependence of $T$ and $τ$, and the relation between $τ$ and the concurrence $C$ which is a typical measure of the entanglement in two qubits. Our calculations have shown that it is not clear whether the speed of quantum evolution may be measured by $T$ or $τ$ and that the evolution speed measured by $τ$ (or $T$) is not necessarily increased with increasing $C$. This is in contrast with the earlier study [V. Giovannetti, S. Lloyd and L. Maccone, Europhys. Lett. {\bf 62} (2003) 615] which pointed out that the evolution speed measured by $τ$ is enhanced by the entanglement in the two-level model.

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Hideo Hasegawa. 2014-05-19. Quantum tunneling and evolution speed in an exactly solvable coupled double-well system. https://arxiv.org/abs/1403.0543

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