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arXiv:1909.13590

Maximum power of a two-dimensional quantum mechanical engine with spherical symmetry

Fernandez, J. J., Omar, S.

Published Sep 30, 2019• 3 citations
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Abstract

We study two-dimensional quantum Carnot engines of spherical symmetry by considering the case of a particle on the surface of a sphere of changing radius. The Carnot cycle is built allowing the state of the system to change with the specific constrains discussed in Bender's work for Carnot cycles. After studying the Carnot cycle, we maximize the output power and efficiency of the system to show that as it happens in one dimension systems:(i) the efficiency can be optimized; being its optimal value independent of the parameters describing the system and that the optimal output power at the optimal efficiency is non-zero. (ii) The optimal efficiency of the spherical system is much bigger than that of the one-dimensional quantum well considered in Abe's work.

DOI
10.48550/arxiv.1909.13590

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We study two-dimensional quantum Carnot engines of spherical symmetry by considering the case of a particle on the surface of a sphere of changing radius. The Carnot cycle is built allowing the state of the system to change with the specific constrains discussed in Bender's work for Carnot cycles. After studying the Carnot cycle, we maximize the output power and efficiency of the system to show that as it happens in one dimension systems:(i) the efficiency can be optimized; being its optimal value independent of the parameters describing the system and that the optimal output power at the optimal efficiency is non-zero. (ii) The optimal efficiency of the spherical system is much bigger than that of the one-dimensional quantum well considered in Abe's work.
In their work [J. Phys. A 33, 4427 (2000)], Bender, Brody, and Meister have shown by employing a two-state model of a particle confined in the one-dimensional infinite potential well that it is possible to construct a quantum-mechanical analog of the Carnot engine through changes of both the width of the well and the quantum state in a specific manner. Here, a discussion is developed about realizing the maximum power of such an engine, where the width of the well moves at low but finite speed. The efficiency of the engine at the maximum power output is found to be universal independently of any of the parameters contained in the model.
Optimizing the performance of thermal machines is an essential task of thermodynamics. We here consider the optimization of information engines that convert information about the state of a system into work. We concretely introduce a generalized finite-time Carnot cycle for a quantum information engine and optimize its power output in the regime of low dissipation. We derive a general formula for its efficiency at maximum power valid for arbitrary working media. We further investigate the optimal performance of a qubit information engine subjected to weak energy measurements.
We investigate the efficiency at maximum power (EMP) of irreversible quantum Carnot engines that perform finite-time cycles between two temperature tunable baths. The temperature form we adopt can be experimentally realized in squeezed baths in the high temperature limit, which makes our proposal of practical relevance. Focusing on low dissipation engines, we first generalize the pervious upper as well as lower bounds for the EMP to temperature tunable cases in which they are solely determined by a generalized Carnot limit. As an illustrative example, we then consider a minimal heat engine model with a two-level spin as the working medium. It mimics a low dissipation engine as confirmed by finite time thermodynamic optimization results. The so-obtained EMP, being constrained by the generalized bounds, is well described by a generalized Curzon- Ahlborn efficiency as consequences of a left/right symmetry for a rate constant and low dissipations. Intriguing features of this minimal heat engine under optimal power output are also demonstrated.
In an adiabatic process, the change in energies of select states may be inhomogenously scaled due to energy quantization. To illustrate this, we introduce a [Formula: see text] barrier turning up (turning down) in an adiabatic expansion (compression). We consider a quantum-mechanical Carnot engine employing a single particle confined in an infinite potential, assuming only the lowest two energy levels to be occupied. This cyclic engine model consists of two isoenergetic strokes where the system is alternatively coupled to two energy baths, and two adiabatic processes where the potential is adiabatically deformed with turning up or down a [Formula: see text] barrier. Having obtained the work output and efficiency, we analyze the efficiency at maximum power under the assumption that the potential moves at a very slow speed. We show that the efficiency at maximum power can be enhanced by energy quantization.
We study the efficiency at maximum power, ${\ensuremath{\eta}}_{m}$, of irreversible quantum Carnot engines (QCEs) that perform finite-time cycles between a hot and a cold reservoir at temperatures Th{T}_{h}Th​ and Tc{T}_{c}Tc​, respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), ${\ensuremath{\eta}}_{m}$ becomes identical to the Carnot efficiency ${\ensuremath{\eta}}_{{}_{C}}=1\ensuremath{-}{T}_{c}/{T}_{h}$. For QCE cycles in which nonadiabatic dissipation and the time spent on two adiabats are included, the efficiency ${\ensuremath{\eta}}_{m}$ at maximum power output is bounded from above by ${\ensuremath{\eta}}_{{}_{C}}/(2\ensuremath{-}{\ensuremath{\eta}}_{{}_{C}})$ and from below by ${\ensuremath{\eta}}_{{}_{C}}/2$. In the case of symmetric dissipation, the Curzon-Ahlborn efficiency ${\ensuremath{\eta}}_{{}_{\mathit{CA}}}=1\ensuremath{-}\sqrt{{T}_{c}/{T}_{h}}$ is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.
Heat engines constitute the major building blocks of modern technologies. However, conventional heat engines with higher power yield lesser efficiency and vice versa and respect various power-efficiency trade-off relations. This is also assumed to be true for the engines operating in the quantum regime. Here we show that these relations are not fundamental. We introduce quantum heat engines that deliver maximum power with Carnot efficiency in the one-shot finite-size regime. These engines are composed of working systems with a finite number of quantum particles and are restricted to one-shot measurements. The engines operate in a one-step cycle by letting the working system simultaneously interact with hot and cold baths via semilocal thermal operations. By allowing quantum entanglement between its constituents and, thereby, a coherent transfer of heat from hot to cold baths, the engine implements the fastest possible reversible state transformation in each cycle, resulting in maximum power and Carnot efficiency. Finally, we propose a physically realizable engine using quantum optical systems.