Quantum Work Fluctuations in connection with Jarzynski Equality

Abstract

A result of great theoretical and experimental interest, Jarzynski equality predicts a free energy change $\Delta F$ of a system at inverse temperature $\beta$ from an ensemble average of non-equilibrium exponential work, i.e., $⟨e^{-\beta W}⟩=e^{-\beta \Delta F}$. The number of experimental work values needed to reach a given accuracy of $\Delta F$ is determined by the variance of $e^{-\beta W}$, denoted $\mathrm{var}(e^{-\beta W})$. We discover in this work that $\mathrm{var}(e^{-\beta W})$ in both harmonic and an-harmonic Hamiltonian systems can systematically diverge in non-adiabatic work protocols, even when the adiabatic protocols do not suffer from such divergence. This divergence may be regarded as a type of dynamically induced phase transition in work fluctuations. For a quantum harmonic oscillator with time-dependent trapping frequency as a working example, any non-adiabatic work protocol is found to yield a diverging $\mathrm{var}(e^{-\beta W})$ at sufficiently low temperatures, markedly different from the classical behavior. The divergence of $\mathrm{var}(e^{-\beta W})$ indicates the too-far-from-equilibrium nature of a non-adiabatic work protocol and makes it compulsory to apply designed control fields to suppress the quantum work fluctuations in order to test Jarzynski equality.

14 pages, 9 figures. revised version (fixing a minor issue in some equation numbers in v2)

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Cited by in corpus (8)

• Group-theoretical approach to the calculation of quantum work distribution
• Nonequilibrium Green's function's approach to the calculation of work statistics
• Nonequilibrium work distributions in quantum impurity system-bath mixing processes
• Thermalization processes induced by quantum monitoring in multi-level systems
• Deformed Jarzynski Equality
• Quantum-heat fluctuation relations in $3$-level systems under projective measurements
• Work Distributions in 1-D Fermions and Bosons with Dual Contact Interactions
• Connecting scrambling and work statistics for short-range interactions in the harmonic oscillator