TY - JOUR

T1 - From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity

AU - Okuyama, Manaka

AU - Takahashi, Kazutaka

N1 - Publisher Copyright:
© 2016 American Physical Society.

PY - 2016/8/8

Y1 - 2016/8/8

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevLett.117.070401

DO - 10.1103/PhysRevLett.117.070401

M3 - Article

AN - SCOPUS:84982095336

VL - 117

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 7

M1 - 070401

ER -