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Fast forward to the classical adiabatic invariant.

Christopher Jarzynski1, Sebastian Deffner2, Ayoti Patra3

  • 1Institute 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, USA.

Physical Review. E
|April 19, 2017
PubMed
Summary

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This summary is machine-generated.

We demonstrate how to maintain the classical action, an adiabatic invariant, even under nonadiabatic conditions. This method uses a "fast-forward" potential to ensure trajectories with a specific initial action conserve it throughout their evolution.

Area of Science:

  • Classical Mechanics
  • Theoretical Physics
  • Dynamical Systems

Background:

  • Adiabatic invariants are quantities that remain constant under slow, continuous changes in a system's parameters.
  • Nonadiabatic conditions introduce rapid changes, typically causing these invariants to change.

Purpose of the Study:

  • To demonstrate the preservation of classical action under nonadiabatic conditions.
  • To construct a method for guiding system trajectories to maintain a specific action value.

Main Methods:

  • Formulation of a time-dependent Hamiltonian for a one-degree-of-freedom system.
  • Construction of a "fast-forward" potential energy function (V_FF(q,t)).
  • Derivation of a local dynamical invariant (J(q,p,t)).

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Main Results:

  • A method is presented to preserve the classical action (an adiabatic invariant) under nonadiabatic conditions.
  • The introduced fast-forward potential ensures trajectories with a chosen initial action (I_0) end with the same action value.
  • A local dynamical invariant is constructed, remaining constant along these specific trajectories.

Conclusions:

  • The study provides a classical framework for preserving action under nonadiabatic evolution.
  • The developed techniques offer potential for designing approximate quantum shortcuts to adiabaticity.