Magnetic Otto Engine for an Electron in a Quantum Dot: Classical and Quantum Approach

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.

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Magnetic Otto Engine for an Electron in a Quantum Dot: Classical and Quantum Approach

10.20944/preprints201901.0079.v1 ◽

2019 ◽

Cited By ~ 1

Author(s):

Francisco J. Peña ◽

Oscar Negrete ◽

Gabriel Alvarado Barrios ◽

David Zambrano ◽

Alejandro González ◽

...

Keyword(s):

Magnetic Field ◽

Quantum Dot ◽

Perpendicular Magnetic Field ◽

Classical Approach ◽

Total Work ◽

Otto Cycle ◽

Classical Counterpart ◽

Quantum Approach ◽

Quantum Version ◽

Quantum Formulation

We study the performance of a classical and quantum magnetic Otto cycle with a quantum dot as a working substance using the Fock-Darwin model with the inclusion of the Zeeman interaction. Modulating an external/perpendicular magnetic field, we found in the classical approach an oscillating behavior in the total work that is not perceptible under the quantum formulation. Also, we compare the work and efficiency of this system for different regions of the Entropy, $S(T,B)$, diagram where we found that the quantum version of this engine always shows a reduced performance in comparison to his classical counterpart.

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Otto Engine: Classical and Quantum Approach

Entropy ◽

10.3390/e22070755 ◽

2020 ◽

Vol 22 (7) ◽

pp. 755

Author(s):

Francisco J. Peña ◽

Oscar Negrete ◽

Natalia Cortés ◽

Patricio Vargas

Keyword(s):

Magnetic Field ◽

External Magnetic Field ◽

Thermodynamic Cycle ◽

Classical Case ◽

Total Work ◽

Otto Cycle ◽

Level System ◽

Multilevel System ◽

Quantum Approach ◽

Quantum Counterpart

In this paper, we analyze the total work extracted and the efficiency of the magnetic Otto cycle in its classic and quantum versions. As a general result, we found that the work and efficiency of the classical engine is always greater than or equal to its quantum counterpart, independent of the working substance. In the classical case, this is due to the fact that the working substance is always in thermodynamic equilibrium at each point of the cycle, maximizing the energy extracted in the adiabatic paths. We apply this analysis to the case of a two-level system, finding that the work and efficiency in both the Otto’s quantum and classical cycles are identical, regardless of the working substance, and we obtain similar results for a multilevel system where a linear relationship between the spectrum of energies of the working substance and the external magnetic field is fulfilled. Finally, we show an example of a three-level system in which we compare two zones in the entropy diagram as a function of temperature and magnetic field to find which is the most efficient region when performing a thermodynamic cycle. This work provides a practical way to look for temperature and magnetic field zones in the entropy diagram that can maximize the power extracted from an Otto magnetic engine.

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