2009/02/28 by Tim Schmiedl, Eckhard Dieterich, Peter-Simon Dieterich +1
Mathematics · Physics and Astronomy · #Adiabatic process #Adiabatic quantum computation #Advanced Thermodynamics and Statistical Mechanics #Anharmonicity #Hamiltonian (control theory) #Quadratic equation #Quantum #Quartic function #Spectral Theory in Mathematical Physics #Work (physics) #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1742-5468/2009/07/p07013
submitted to J. Stat. Mech.: Theor. Exp.
arxiv created 2009/04/24 · openalex publication_date 2009/07/06 · arxiv updated 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 for 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.