Speeding Up Classical and Quantum Adiabatic Processes: Implications for Work Functions and Heat Engine Designs

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Deng, Jia-wen ; Wang, Qing-hai ; Gong, Jiangbin (2013)
  • Subject: Quantum Physics

Adiabatic processes are important for studying the dynamics of a time-dependent system. Conventionally, the adiabatic processes can only be achieved by varying the system slowly. We speed up both classical and quantum adiabatic processes by adding control protocols. In ... View more
  • References (15)
    15 references, page 1 of 2

    2 Adiabatic Theorem 5 2.1 Quantum Adiabatic Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 Adiabatic Approximation . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2 Adiabatic Condition for Quantum Ensemble . . . . . . . . . . . . . . . 7 2.2 Classical Adiabatic Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 Action-Angle Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.2 Adiabatic Approximation . . . . . . . . . . . . . . . . . . . . . . . . . 8

    3 Work Function 10 3.1 Work Function for Classical Ensemble . . . . . . . . . . . . . . . . . . . . . . 10 3.2 Work Function for Quantum Ensemble . . . . . . . . . . . . . . . . . . . . . . 11 3.3 Jarzynski Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

    4 Classical Fast-Forward Adiabatic Process 14 4.1 Control Field HC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.1.1 Formal Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.1.2 Gibbs Canonical Ensemble . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2 Application in 1-D Classical Harmonic Oscillator . . . . . . . . . . . . . . . . 15 4.2.1 Fast-Forward Adiabatic Process . . . . . . . . . . . . . . . . . . . . . . 16 4.2.2 Finite-Time Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2.3 Adiabatic Process & Sudden Change . . . . . . . . . . . . . . . . . . . 22 4.3 Comparison Based on Numerical Results . . . . . . . . . . . . . . . . . . . . . 24 4.3.1 Two Adiabatic Process . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.3.2 Fast-Forward Adiabatic versus Non-Adiabatic . . . . . . . . . . . . . 26

    5 Quantum Fast-Forward Adiabatic Process 29 5.1 Control Field HC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 5.1.1 Time-Evolution of Eigenstates . . . . . . . . . . . . . . . . . . . . . . 29 5.1.2 Formal Solution of HC . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.1.3 Gibbs Canonical Ensemble . . . . . . . . . . . . . . . . . . . . . . . . 30 5.2 1-D Quantum Harmonic Oscillator . . . . . . . . . . . . . . . . . . . . . . . . 31 5.2.1 Fast-Forward Adiabatic Process . . . . . . . . . . . . . . . . . . . . . . 31 5.2.2 Finite-Time Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 5.3 Comparison Based on Numerical Results . . . . . . . . . . . . . . . . . . . . . 33 5.3.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

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