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Title: 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 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. 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:
 [1];  [2];  [3];  [4]
  1. Univ. of Maryland, College Park, MD (United States). Inst. for Physical Science and Technology, Dept. of Chemistry and Biochemistry, and Dept. of Physics
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Maryland Baltimore County (UMBC), Baltimore, MD (United States). Dept. of Physics
  3. Univ. of Maryland, College Park, MD (United States). Dept. of Physics
  4. 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):
LA-UR-16-22608
Journal ID: ISSN 2470-0045; PLEEE8; TRN: US1901531
Grant/Contract Number:  
AC52-06NA25396; W911NF-13-1-0390
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 95; Journal Issue: 3; Journal ID: ISSN 2470-0045
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 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. 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}
}

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Cited by: 6 works
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