Abstract
We calculate the work done by a Landau-Zener-like dynamical field on two- and three-level quantum system by constructing a quantum power operator. We elaborate a general theory applicable to a wide range of closed-quantum system. We consider the dynamics of the system in the time domain ]-tLZ,tLZ[ (where is the LZ transition time in the sudden limit) where the external pulse changes its sign and its action becomes relevant. The statistical work is evaluated in a period [0,T] where T ≤tLZ. Our results are observed to be in good qualitative agreement with known results.
Highlights
The pioneering work of Jarzynski establishes a non-trivial relation between the non-equilibrium work performed on a thermally insulated classical system and the change in its equilibrium free energy [1]
ΔF F (η (t )) − F (η (0)) is the free energy difference between a reference equilibrium state of the system and a state achieved at time t by changing the protocol η (t ) during the work
The Jarzynski equality has been extended to quantum regimes and experimentally tested [2]-[4]
Summary
The pioneering work of Jarzynski establishes a non-trivial relation between the non-equilibrium work performed on a thermally insulated classical system and the change in its equilibrium free energy [1]. ΔF F (η (t )) − F (η (0)) is the free energy difference between a reference equilibrium state of the system and a state achieved at time t by changing the protocol η (t ) during the work. The Jarzynski equality has been extended to quantum regimes and experimentally tested [2]-[4] It was accurately studied in singleelectron transport [5]-[7] and molecular systems [8]. The experimental measurements of the proper free energy of a system lead to the average exponentiated work using Equation (1). For open systems, the work cannot be defined by a local time-dependent operator. The average statistical work done during a period T on any quantum system is statistically defined as: W This formula is employed throughout this paper.
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