Fast forward to the classical adiabatic invariant
Christopher JarzynskiInstitute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA; Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA and Department of Physics, University of Maryland, College Park, Maryland 20742, USASebastian DeffnerTheoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA and Department of Physics, University of Maryland Baltimore County, Baltimore, Maryland 21250, USAAyoti PatraDepartment of Physics, University of Maryland, College Park, Maryland 20742, USAYiğit SubaşıDepartment of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
2017en
ABI
Annotatsiya
We show how the classical action, an adiabatic invariant, can be preserved under nonadiabatic 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 so-called fast-forward potential energy function V_{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.
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