From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity

Manaka Okuyama, Kazutaka Takahashi

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic XY spin chains from the Toda equations are studied in detail.

Original languageEnglish
Article number070401
JournalPhysical review letters
Issue number7
Publication statusPublished - 2016 Aug 8
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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