Fast forward to the classical adiabatic invariant

Abstract

We show how the classical action, an adiabatic invariant, can be preserved under non-adiabatic conditions. Specifically, for a time-dependent Hamiltonian $H=p^2/2m+U(q,t)$ in one degree of freedom, and for an arbitrary choice of action $I_0$, we construct a "fast-forward" potential energy function $V_{\mathrm{FF}}(q,t)$ that, when added to $H$, guides all trajectories with initial action $I_0$ 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.

5 pages

References in corpus (2)

• High-fidelity rapid ground-state loading of an ultracold gas into an optical lattice
• Unitary deformations of counterdiabatic driving

Cited by in corpus (5)

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• Kibble-Zurek scaling in quantum speed limits for shortcuts to adiabaticity
• Fast forward of adiabatic control of tunneling states
• Thermodynamic Cost for Classical Counterdiabatic Driving
• Time-rescaling of Dirac dynamics: shortcuts to adiabaticity in ion traps and Weyl semimetals