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

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.

Bosons outperform fermions: The thermodynamic advantage of symmetry

“…This might explain the plethora of studies to investigate possible enhancements of engine performance through the exploitation of quantum resources including coherence [8][9][10][11][12][13][14][15], measurement effects [16], squeezed reservoirs [17][18][19], quantum phase transitions [20], and quantum many-body effects [15,[21][22][23]. Other works have examined the fundamental differences between quantum and classical thermal machines [24][25][26], finite time cycles [13,27,28], utilizing shortcuts to adiabaticity [12,22,23,[29][30][31][32][33], operating over non-thermal states [34,35], non-Markovian effects [36], magnetic systems [37][38][39][40][41][42], anharmonic potentials [43], optomechanical implementation [44], quantum dot implementation [38,40,42], implementation in 2D materials…”

Quasistatic and quantum-adiabatic Otto engine for a two-dimensional material: The case of a graphene quantum dot

“…The previous result is general and can be applied to any system where the working substance remains in a diagonal state and does not use quantum resources. At the same time, if we compare the results of the total work extraction in the magnetic Otto cycle for quantum dot modeled by the Fock-Darwin approach and this 2D system employing the Dirac equation with a boundary condition, we note a considerable increase in the total work extraction [50]. This is because the theoretical model of Fock-Darwin considers a parabolic trap that can be controlled geometrically and is approximately upper bounded by ∼3.0 meV for GaAs quantum dots [63].…”

“…There is always a search in the control of its size, shape, and distribution to characterize its optoelectronic properties in order to find * francisco.penar@usm.cl future technological applications [49]. In this context, the case of quantum dots of GaAs or (InAs) under a controllable external magnetic field as a working substance operating under an Otto cycle has been studied recently [50], where the comparison has been made regarding the application of the quasistatic and quantum-adiabatic performance of a multilevel Otto cycle in a diagonal formulation of the density matrix operator.…”

“…A possible extension of the work [50] focused on the so-called two-dimensional (2D) materials [51]. To date, the most characterized and studied one is graphene.…”

Dissipative Endoreversible Engine with Given Efficiency

“…Since endoreversible thermodynamics is by no means limited to heat engines, it has also been used to study global wind energy production [35], chemical reactions [36][37][38], and even goods at a market [39], to name a few. The same basic ideas, in particular the optimization of processes, are also used in the context of quantum thermodynamics [40][41][42][43][44][45].…”