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Shortcuts to adiabaticity for Lévy processes in harmonic traps
Marco Baldovin1, David Guéry-Odelin2, Emmanuel Trizac1
1Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France.
Physical Review. E
|December 23, 2022
Summary
Researchers found shortcuts to adiabaticity for Lévy stochastic processes, enabling faster state transitions in systems with harmonic potentials. This work extends previous methods to non-Gaussian noise, offering new control techniques for physical systems.
Area of Science:
- Physics
- Physical Chemistry
- Nonlinear Dynamics
Background:
- Lévy stochastic processes are fundamental in modeling complex systems with non-Gaussian fluctuations.
- Shortcuts to adiabaticity techniques accelerate state transitions in quantum and classical systems.
- Existing methods primarily address systems with Gaussian noise.
Purpose of the Study:
- To generalize shortcuts to adiabaticity techniques for Lévy stochastic processes.
- To develop time-dependent protocols for driving systems with Lévy noise towards specific final states.
- To explore these techniques in both overdamped and underdamped regimes.
Main Methods:
- Inverse-engineering approach adapted for Lévy stable distributions.
- Derivation of exact equations for characteristic functions in Fourier space.
- Analysis of systems with a harmonic potential.
Main Results:
- Exact analytical solutions for control protocols were found for Lévy processes.
- The methods are applicable to both overdamped and underdamped systems.
- Demonstrated generalization of shortcuts to adiabaticity beyond Gaussian noise.
Conclusions:
- The study successfully extends shortcuts to adiabaticity to Lévy stochastic processes.
- Provides a powerful framework for controlling systems with non-Gaussian noise.
- Opens new avenues for rapid state preparation in diverse scientific applications.
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