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From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity.
Manaka Okuyama1, Kazutaka Takahashi1
1Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan.
Physical Review Letters
|August 27, 2016
Summary
This study introduces a method to solve the time-dependent Schrödinger equation using shortcuts to adiabaticity. The approach exactly derives counterdiabatic terms for nonlinear integrable systems, simplifying complex quantum dynamics.
Area of Science:
- Quantum mechanics
- Nonlinear dynamics
- Mathematical physics
Background:
- Solving the time-dependent Schrödinger equation is crucial for understanding quantum systems.
- Nonadiabatic transitions complicate quantum system evolution.
- Nonlinear integrable systems offer analytical tractability.
Purpose of the Study:
- To develop an exact method for deriving counterdiabatic terms.
- To unify the classification of solvable nonlinear integrable systems.
- To apply the method to specific physical models.
Main Methods:
- Utilizing shortcuts to adiabaticity to reduce the Schrödinger equation.
- Introducing counterdiabatic terms to suppress nonadiabatic transitions.
- Leveraging the equivalence between dynamical invariant equations and Lax equations.
Main Results:
- An exact formula for the counterdiabatic term was derived.
- A unified and systematic classification of solvable systems was established based on the existence of a Lax pair.
- The method was successfully applied to multisoliton potentials and isotropic XY spin chains.
Conclusions:
- Shortcuts to adiabaticity provide an effective framework for solving quantum dynamics in nonlinear integrable systems.
- The derived counterdiabatic term enables precise control over quantum transitions.
- This approach offers a powerful tool for analyzing complex quantum phenomena.
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