Shortcuts To Adiabaticity for Lévy processes in harmonic traps

Abstract

Lévy stochastic processes, with noise distributed according to a Lévy stable distribution, are ubiquitous in science. Focusing on the case of a particle trapped in an external harmonic potential, we address the problem of finding "shortcuts to adiabaticity": after the system is prepared in a given initial stationary state, we search for time-dependent protocols for the driving external potential, such that a given final state is reached in a given, finite time. These techniques, usually used for stochastic processes with additive Gaussian noise, are typically based on a inverse-engineering approach. We generalise the approach to the wider class of Lévy stochastic processes, both in the overdamped and in the underdamped regime, by finding exact equations for the relevant characteristic functions in Fourier space.

15 pages, 7 figures

References in corpus (11)

• Lévy walks
• Efficiency at maximum power: An analytically solvable model for stochastic heat engines
• Optimal finite-time processes in stochastic thermodynamics
• Optimal protocols for minimal work processes in underdamped stochastic thermodynamics
• First-passage and first-hitting times of Levy flights and Levy walks
• Exact non-equilibrium solutions of the Boltzmann equation under a time-dependent external force
• Optimal work in a harmonic trap with bounded stiffness
• Engineered Swift Equilibration of a Brownian Gyrator
• On how nanomechanical systems can minimize dissipation
• Optimal control of uniformly heated granular fluids in linear response
• Multimodal stationary states under Cauchy noise

Cited by in corpus (5)

• Control of Active Brownian Particles: An exact solution
• Optimal Control of Underdamped Systems: An Analytic Approach
• Statistical features of systems driven by non-Gaussian processes: theory & practice
• Minimal work protocols for inertial particles in non-harmonic traps
• Control protocols for harmonically confined run-and-tumble particles