Abstract
We studied the performance of classical and quantum magnetic Otto cycle with a working substance composed of a single quantum dot using the Fock–Darwin model with the inclusion of the Zeeman interaction. Modulating an external/perpendicular magnetic field, in the classical approach, we found an oscillating behavior in the total work extracted that was not present in the quantum formulation.We found that, in the classical approach, the engine yielded a greater performance in terms of total work extracted and efficiency than when compared with the quantum approach. This is because, in the classical case, the working substance can be in thermal equilibrium at each point of the cycle, which maximizes the energy extracted in the adiabatic strokes.
Highlights
The study of quantum heat engines (QHEs) [1] is focused on the search and design of efficient nanoscale devices operating with a quantum working substance
We explored the classical and quantum approach for a magnetic Otto cycle for an ensemble of non-interacting electrons with intrinsic spin where each one is trapped inside a semiconductor quantum dot modeled by a parabolic potential
We analyzed all relevant thermodynamics quantities, and found that the entropy changes it behavior in terms of the external magnetic field at the point where the energy spectrum tends towards degeneracy; this behavior was present at all temperatures considered
Summary
The study of quantum heat engines (QHEs) [1] is focused on the search and design of efficient nanoscale devices operating with a quantum working substance. We study the classical and quantum performance of a multi-level Otto cycle in a diagonal formulation of the density matrix operator, where the working substance comprises a nanosized quantum dot under a controllable external magnetic field. This system is described by the Fock–Darwin model [47,48] that represents an accurate model for a semiconductor quantum dot. The reason for this is that the internal energy only depends on the derivative of ln Z dS (see Equation (11)) with respect to temperature while the entropy has an additional term proportional to ln ZdS (see Equation (10)) and the magnetization on its derivative with respect to the external field (see Equation (12))
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