Optimal protocols for Hamiltonian and Schrödinger dynamics

Abstract

For systems in an externally controllable time-dependent potential, the optimal protocol minimizes the mean work spent in a finite-time transition between given initial and final values of a control parameter. For an initially thermalized ensemble, we consider both Hamiltonian evolution for classical systems and Schrödinger evolution for quantum systems. In both cases, we show that for harmonic potentials, the optimal work is given by the adiabatic work even in the limit of short transition times. This result is counter-intuitive because the adiabatic work is substantially smaller than the work for an instantaneous jump. We also perform numerical calculations of the optimal protocol for Hamiltonian dynamics in an anharmonic quartic potential. For a two-level spin system, we give examples where the adiabatic work can be reached in either a finite or an arbitrarily short transition time depending on the allowed parameter space.

submitted to J. Stat. Mech.: Theor. Exp.

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• Optimal protocols for slowly-driven quantum processes
• Faster State Preparation across Quantum Phase Transition Assisted by Reinforcement Learning
• Degenerate optimal paths in thermally isolated systems
• Group-theoretical approach to the calculation of quantum work distribution
• Transient particle energies in shortcuts to adiabatic expansions of harmonic traps
• Noise Sensitivities for an Atom Shuttled by a Moving Optical Lattice via Shortcuts to Adiabaticity
• Fast expansions and compressions of trapped-ion chains
• Perturbative Expansion of Irreversible Work in Fokker-Planck Equation a la Quantum Mechanics
• Perturbative expansion of irreversible works in symmetric and asymmetric processes