Counter-diabatic driving in the classical $\beta$-Fermi-Pasta-Ulam-Tsingou chain

Abstract

Shortcuts to adiabaticity (STAs) have been used to make rapid changes to a system while eliminating or minimizing excitations in the system's state. In quantum systems, these shortcuts allow us to minimize inefficiencies and heating in experiments and quantum computing protocols, but the theory of STAs can also be generalized to classical systems. We focus on one such STA, approximate counter-diabatic (ACD) driving, and numerically compare its performance in two classical systems: a quartic anharmonic oscillator and the $\beta$ Fermi-Pasta-Ulam-Tsingou (FPUT) lattice. In particular, we modify an existing variational technique to optimize the approximate driving and then develop classical figures of merit to quantify the performance of the driving. We find that relatively simple forms for the ACD driving can dramatically suppress excitations regardless of system size. ACD driving in classical nonlinear oscillators could have many applications, from minimizing heating in bosonic gases to finding optimal local dressing protocols in interacting field theories.

13 pages, 12 figures; added references, Floquet discussion

References in corpus (9)

• Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
• Focus on Shortcuts to Adiabaticity
• Shortcuts to adiabaticity using flow fields
• Two-parameter counter-diabatic driving in quantum annealing
• Variational Schrieffer-Wolff Transformations for Quantum Many-Body Dynamics
• Multi-spin counter-diabatic driving in many-body quantum Otto refrigerators
• Quantum-Classical Correspondence of Shortcuts to Adiabaticity
• Counterdiabatic route for preparation of state with long-range topological order
• Numerical study of Fermi-Pasta-Ulam recurrence for water waves over finite depth

Cited by in corpus (8)

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• Universal Counterdiabatic Driving
• Adiabatic Gauge Potential as a Tool for Detecting Chaos in Classical Systems
• Quantization of integrable and chaotic three-particle Fermi-Pasta-Ulam-Tsingou models
• Improving Variational Counterdiabatic Driving with Weighted Actions and Computer Algebra
• Shortcuts to Analog Preparation of Non-Equilibrium Quantum Lakes