Fast forward to the classical adiabatic invariant

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PhysRevE.95.032122.pdf (487.84 KB)

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https://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.032122

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https://doi.org/10.1103/PhysRevE.95.032122
 http://hdl.handle.net/11603/19415

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2017-03-10

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journal articles
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Christopher Jarzynski et al., Fast forward to the classical adiabatic invariant, Phys. Rev. E 95, 032122 (2017), DOI:https://doi.org/10.1103/PhysRevE.95.032122

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©2017 American Physical Society

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Abstract

We show how the classical action, an adiabatic invariant, can be preserved under nonadiabatic conditions. Specifically, for a time-dependent Hamiltonian H=p²/2m+U(q,t) in one degree of freedom, and for an arbitrary choice of action I₀, we construct a so-called fast-forward potential energy function VFF(q,t) that, when added to H, guides all trajectories with initial action I₀ to end with the same value of action. We use this result to construct a local dynamical invariant J(q,p,t) whose value remains constant along these trajectories. We illustrate our results with numerical simulations. Finally, we sketch how our classical results may be used to design approximate quantum shortcuts to adiabaticity.