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Annalen der Physik

Quantum Otto Machine With q ‐Deformed Pöschl–Teller Oscillator

Collins Okon Edet, Norshamsuri Ali, R. Endut, Obinna Abah

Published Jul 1, 2026• 0 citations
Publisher

Abstract

ABSTRACT We study the impact of the potential parameters of the q‐deformed modified Pöschl–Teller potential on the thermodynamic performance of a quantum Otto cycle, where the ‐deformed modified Pöschl–Teller potential serves as the working substance. Analytical expressions for the energy spectrum and wave functions are derived, enabling a systematic investigation of heat exchange, work output, efficiency, and coefficient of performance. We show that ‐deformation modifies the energy spectrum and creates distinct performance regions in the (, ) parameter space. Low () and high () favor optimal heat engine efficiency, whereas high () and low () improve refrigerator performance. The heat engine efficiency peaks in the low‐(), high‐() regime. These results highlight the q‐deformed modified Pöschl–Teller potential as a versatile and tunable platform for exploring potential parameter‐driven effects in quantum thermal machines.

DOI
10.1002/andp.70241

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ABSTRACT We study the impact of the potential parameters of the q‐deformed modified Pöschl–Teller potential on the thermodynamic performance of a quantum Otto cycle, where the ‐deformed modified Pöschl–Teller potential serves as the working substance. Analytical expressions for the energy spectrum and wave functions are derived, enabling a systematic investigation of heat exchange, work output, efficiency, and coefficient of performance. We show that ‐deformation modifies the energy spectrum and creates distinct performance regions in the (, ) parameter space. Low () and high () favor optimal heat engine efficiency, whereas high () and low () improve refrigerator performance. The heat engine efficiency peaks in the low‐(), high‐() regime. These results highlight the q‐deformed modified Pöschl–Teller potential as a versatile and tunable platform for exploring potential parameter‐driven effects in quantum thermal machines.
Quantum Otto machine with qqq-deformed Pöschl-Teller oscillator
We study the impact of the potential parameters of the q-deformed modified Pöschl-Teller potential on the thermodynamic performance of a quantum Otto cycle, where the qqq-deformed modified Pöschl-Teller potential serves as the working substance. Analytical expressions for the energy spectrum and wave functions are derived, enabling a systematic investigation of heat exchange, work output, efficiency, and coefficient of performance. We show that qqq-deformation modifies the energy spectrum and creates distinct performance regions in the (qqq, ΔΔΔ) parameter space. Low (ΔΔΔ) and high (qqq) favour optimal heat engine efficiency, whereas high (ΔΔΔ) and low (qqq) improve refrigerator performance. The heat engine efficiency peaks in the low-(ΔΔΔ), high-(qqq) regime. These results highlight the q-deformed modified Pöschl-Teller potential as a versatile and tunable platform for exploring potential parameter-driven effects in quantum thermal machines.
Abstract We present quantum heat machines using a diatomic molecule modeled by a q -deformed Morse potential as a working medium. We analyze the effect of the deformation parameter and other potential parameters on the work output and efficiency of the quantum Otto and quantum Carnot heat cycles. Furthermore, we derive the analytical expressions of work and efficiency as a function of these parameters. Interestingly, our system operates as a quantum heat engine across the range of parameters considered. In addition, the efficiency of the quantum Otto heat engine is seen to be tunable by the deformation parameter. Our findings provide useful insight for understanding the impact of anharmonicity on the design of quantum thermal machines.
Work and efficiency of quantum Otto heat engines (QOHEs) can increase by using non-thermal baths or by inhomogeneous scaling of energy levels of the working substance. Given these points, at first, we construct the coherent thermal state for a trigonometric Pöschl-Teller (PT) potential. Then using a particle in this potential, which has unequally spaced energy levels, as a working substance, we investigate the work extraction and the efficiency of QOHEs that operates between cold and hot coherent thermal baths. The results show that changing the PT potential parameters in the adiabatic processes of QOHE, which causes an inhomogeneous shift in energy levels or/and make use of the hot coherent thermal bath, improve work extraction and efficiency of QOHE relative to the classical counterpart.
Abstract We investigate the optimal performance of the quantum Otto engine and refrigeration cycles of a time-dependent harmonic oscillator under a trade-off figure of merit for both adiabatic and nonadiabatic (sudden-switch) frequency modulations. For heat engines (refrigerators), the chosen trade-off figure of merit is an objective function defined by the product of efficiency (coefficient of performance) and work output (cooling load), thus representing a compromise between them. We obtain analytical expressions for the efficiency and coefficient of performance of the harmonic Otto cycle for the optimal performance of the thermal machine in various operational regimes. Particularly, in the sudden-switch regime, we discuss the implications of the nonadiabatic driving on the performance of the thermal machine under consideration and obtain analytic expressions for the maximum achievable efficiency and coefficient of performance of the harmonic Otto thermal machine. Particularly, we show that the quantum harmonic Otto cycle driven by sudden-switch protocol cannot work as a heat engine or refrigerator in the low-temperature limit. Finally, we show that in the high-temperature limit, the frictional effects give rise to a richer structure of the phase diagram of the harmonic Otto cycle. We identify the parametric regime for the operation of the Otto cycle as a heat engine, refrigerator, accelerator, and heater.
Abstract We consider a quantum endoreversible Otto engine cycle and its inverse operation-Otto refrigeration cycle, employing two-level systems as the working substance and operating in dual-squeezed reservoirs. We demonstrate that the efficiency of heat engines at maximum work output and the coefficient of performance for refrigerators at the maximum χ criterion will degenerate to η − = η C/(2 – η C) and ε − = ( 9 + 8 ε C − 3 ) / 2 when symmetric squeezing is satisfied, respectively. We also investigated the influences of squeezing degree on the performance optimization of quantum Otto heat engines at the maximum work output and refrigerators at the maximum χ criterion. These analytical results show that the efficiency of heat engines at maximum work output and the coefficient of performance for refrigerators at the maximum χ criterion can be improved, reduced or even inhibited in asymmetric squeezing. Furthermore, we also find that the efficiency of quantum Otto heat engines at maximum work output is lower than that obtained from the Otto heat engines based on a single harmonic oscillator system. However, the coefficient of performance of the corresponding refrigerator is higher.
Abstract We present the quantum Otto machine under different optimization criterion when function either as a heat engine or a refrigerator. We examine the optimal performance of the heat engine and refrigerator depending on their efficiency, output power and maximum entropy production. For heat engine case, we obtain the expression for the upper and lower bounds efficiencies at maximum power and maximum ecological function. The optimal ecological performance is laying between the maximum efficiency and the maximum power output. On the other hand, the quantum Otto refrigerator coefficient of performance is optimized for three different criterion – cooling power, χ criterion(product of performance and power) and ecological function. We further study the dimen-sionless power loss to the cold reservoir when the machine is operating as a heat engine as well as its counterpart for the refrigerator case. We find that the maximum operation of the heat engine (refrigerator) cycle is when optimized with respect to hot (cold) reservoir frequency.