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

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

Entropy ◽

10.3390/e21050512 ◽

2019 ◽

Vol 21 (5) ◽

pp. 512 ◽

Cited By ~ 10

Author(s):

Francisco J. Peña ◽

Oscar Negrete ◽

Gabriel Alvarado Barrios ◽

David Zambrano ◽

Alejandro González ◽

...

Keyword(s):

Quantum Dot ◽

Thermal Equilibrium ◽

Classical Case ◽

Perpendicular Magnetic Field ◽

Classical Approach ◽

Total Work ◽

Otto Cycle ◽

Single Quantum ◽

Quantum Approach ◽

Single Quantum Dot

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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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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Transition from chaotic to regular behavior of electrons in a stadium-shaped quantum dot in a perpendicular magnetic field

Physical Review B ◽

10.1103/physrevb.52.1745 ◽

1995 ◽

Vol 52 (3) ◽

pp. 1745-1750 ◽

Cited By ~ 25

Author(s):

Zhen-Li Ji ◽

Karl-Fredrik Berggren

Keyword(s):

Magnetic Field ◽

Quantum Dot ◽

Perpendicular Magnetic Field ◽

Regular Behavior

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EXCITATION SPECTRUM OF QUANTUM DOT IN STRONG MAGNETIC FIELD

International Journal of Modern Physics B ◽

10.1142/s0217979295000756 ◽

1995 ◽

Vol 09 (15) ◽

pp. 1843-1867 ◽

Cited By ~ 6

Author(s):

AL. A. ANDREEV ◽

YA. M. BLANTER ◽

YU. E. LOZOVIK

Keyword(s):

Magnetic Field ◽

Perturbation Theory ◽

Quantum Dot ◽

Strong Magnetic Field ◽

Microscopic Theory ◽

Collective Excitations ◽

Complete Analysis ◽

Classical Approach ◽

Particle Drift ◽

Parabolic Quantum Dot

Microscopic theory of collective excitations of a quantum dot in a strong magnetic field is proposed. A complete analysis of diagrams in the perturbation theory over the Coulomb interaction is performed. The spectrum of low-lying excitations is calculated for the case of a parabolic quantum dot. It is shown to consist of three terms: single-particle drift, magnetoplasma and exciton ones, with the exciton term dominating the magnetoplasma one. In the framework of the semi-classical approach, the case of a non-parabolic quantum dot is also discussed. The experimental manifestations of the effects under investigation are discussed.

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Effects of Confinement on Shallow Impurities in GaAs-Ga 1−xA1xAs Quantum Dots

MRS Proceedings ◽

10.1557/proc-281-79 ◽

1992 ◽

Vol 281 ◽

Cited By ~ 3

Author(s):

Francisco A. P. Osörio ◽

Oscar HipöLito ◽

Francois M. Peeters

Keyword(s):

Magnetic Field ◽

Quantum Dots ◽

Quantum Dot ◽

Ground State Energy ◽

Ground State ◽

State Energy ◽

Perpendicular Magnetic Field ◽

Confinement Potential ◽

Shallow Impurity ◽

Shallow Impurities

ABSTRACTThe ground state energy of a shallow impurity placed in the center of a circular quantum dot is studied. The effects of the strength of the confinement potential and a perpendicular magnetic field are investigated theoretically.

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