Fast forward to the classical adiabatic invariant
Abstract
We show how the classical action, an adiabatic invariant, can be preserved under nonadiabatic conditions. Specifically, for a timedependent 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 socalled fastforward 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. Here, 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.
 Authors:

 Univ. of Maryland, College Park, MD (United States). Inst. for Physical Science and Technology, Dept. of Chemistry and Biochemistry, and Dept. of Physics
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Maryland Baltimore County (UMBC), Baltimore, MD (United States). Dept. of Physics
 Univ. of Maryland, College Park, MD (United States). Dept. of Physics
 Univ. of Maryland, College Park, MD (United States). Dept. of Chemistry and Biochemistry; Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE; National Science Foundation (NSF); US Army Research Office (ARO)
 OSTI Identifier:
 1458942
 Alternate Identifier(s):
 OSTI ID: 1346591
 Report Number(s):
 LAUR1622608
Journal ID: ISSN 24700045; PLEEE8; TRN: US1901531
 Grant/Contract Number:
 AC5206NA25396; W911NF1310390
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review E
 Additional Journal Information:
 Journal Volume: 95; Journal Issue: 3; Journal ID: ISSN 24700045
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Mathematics
Citation Formats
Jarzynski, Christopher, Deffner, Sebastian, Patra, Ayoti, and Suba??, Yi?it. Fast forward to the classical adiabatic invariant. United States: N. p., 2017.
Web. doi:10.1103/PhysRevE.95.032122.
Jarzynski, Christopher, Deffner, Sebastian, Patra, Ayoti, & Suba??, Yi?it. Fast forward to the classical adiabatic invariant. United States. doi:10.1103/PhysRevE.95.032122.
Jarzynski, Christopher, Deffner, Sebastian, Patra, Ayoti, and Suba??, Yi?it. Wed .
"Fast forward to the classical adiabatic invariant". United States. doi:10.1103/PhysRevE.95.032122. https://www.osti.gov/servlets/purl/1458942.
@article{osti_1458942,
title = {Fast forward to the classical adiabatic invariant},
author = {Jarzynski, Christopher and Deffner, Sebastian and Patra, Ayoti and Suba??, Yi?it},
abstractNote = {We show how the classical action, an adiabatic invariant, can be preserved under nonadiabatic conditions. Specifically, for a timedependent Hamiltonian H = p2/2m + U (q,t) in one degree of freedom, and for an arbitrary choice of action I0, we construct a socalled fastforward 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. Here, 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.},
doi = {10.1103/PhysRevE.95.032122},
journal = {Physical Review E},
number = 3,
volume = 95,
place = {United States},
year = {2017},
month = {3}
}
Web of Science
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