以一维谐振子势阱中的单粒子为工质的量子热机性能分析

建立了以一维谐振子势阱中的单粒子为工质的量子热机模型.当势阱壁宽度和粒子的量子态缓慢改变时, 该热机类似于经典卡诺热机对外做功.假设势阱壁移动速度非常缓慢并且考虑热漏, 推导出量子热机循环的输出功率和效率等重要性能参数的一般表达式.通过优化分析, 获得了热机循环中各主要性能参数的最佳优化值和优化区间.     

Thermal entangled quantum heat engine

Based on a two-qubit Heisenberg XY model, we construct a four-level entangled quantum heat engine (QHE). It is an interesting quantum Otto cycle where the exchange constant is fixed and only the magnetic field is varied during the adiabatic steps. The expressions for several thermodynamic quantities such as the heat transferred, the work and the efficiency are derived. Moreover, the influence of the entanglement on the thermodynamic quantities is investigated numerically. Several interesting features of the variation of the heat transferred, the work and the efficiency with the concurrences of the thermal entanglement of different thermal equilibrium states are obtained. Finally, we discussed the maximum efficiency of the QHE.     

The performance characteristics of an irreversible quantum Otto harmonic refrigeration cycle

In this paper, an irreversible quantum Otto refrigeration cycle working with harmonic systems is established. Base on Heisenberg quantum master equation, the equations of motion for the set of harmonic systems thermodynamic observables are derived. The simulated diagrams of the quantum Otto refrigeration cycle are plotted. The relationship between average power of friction, cooling rate, power input, and the time of adiabatic process is analyzed by using numerical calculation. Moreover, the influence of the heat conductance and the time of iso-frequency process on the performance of the cycle is discussed.     

Optimal configuration for a finite high-temperature source heat engine cycle with the complex heat transfer law

The optimal configuration of a heat engine operating between a finite high-temperature source and an infinite low-temperature reservoir is derived by using finite time thermodynamics based on a complex heat transfer law, including Newtonian heat transfer law, linear phenomenological heat transfer law, radiative heat transfer law, Dulong-Petit heat transfer law, generalized convective heat transfer law and generalized radiative heat transfer law, q ∝ (ΔT ⁿ ). In the engine model the only irreversibility of finite rate heat transfer is considered. The optimal relation between the power output and efficiency of the heat engine is also derived by using an equivalent temperature of the hot reservoir. The obtained results include those obtained in recent literature and can provide some theoretical guidance for the designs of practical engines. Supported by the Program for New Century Excellent Talents in University of China (Grant No. 20041006) and the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200136)     

Quantum heat engine cycle working with a strongly correlated electron system

A new model of a quantum heat engine(QHE) cycle is established,in which the working substance consists of an interacting electrons system.One of our purposes is to test the validity of the second law of thermodynamics by this model,which is more general than the spin-1/2 antiferromagnetic Heisenberg model since it would recover the spin model when the on-site Coulomb interaction U is strong enough.On the basis of quantum mechanics and the first law of thermodynamics,we show no violation of the second law of thermodynamics during the cycle.We further study the performance characteristics of the cycle by investigating in detail the optimal relations of efficiency and dimensionless power output.We find that the efficiency of our engine can be expressed as η = 1 - t22/t12 in the large-U limit,which is valid even for a four sites QHE.     

四能级量子制冷循环

本文提出以两个qubit量子纠缠系统为工质的四能级制冷循环模型, 基于量子热力学第一定律和热纠缠概念, 分析了在循环中系统与外界交换的热量、输入功、制冷系数等热力学参数与量子纠缠之间的关系, 结果表明: 制冷系数等高线图是环状曲线, 随纠缠比r增加而非单调变化; 当相互作用常数J比较小时, 量子制冷机运行区间在c₁>c₂, 当增加J值时, 制冷机运行区间在c₁>c₂和 c₁<c₂两个区域; 最大制冷系数ε_max随J值增大而增加.     

一维晶格中费曼棘齿-棘爪热机

研究了一维晶格中费曼棘齿-棘爪热机模型. 用粒子的概率主方程来描述粒子在晶格中的动力学特性, 推导出热流、 功率和效率的表达式. 通过数值计算分析势垒高度、 外力和温比对热流以及热机功率和效率的影响. 研究表明: 在粒子稳态概率流为零时, 存在非零的热流从高温库流入低温库, 类似于经典不可逆卡诺模型中的热漏; 热漏的存在使得热机的效率远远小于卡诺效率, 功率与效率之间为闭合的关系曲线, 热机为不可逆热机; 对热机性能参数进行优化, 可以使热机工作在最优性能状态下.     

带有Dzyaloshinski-Mariya相互作用的两比特纠缠量子Otto热机和量子Stirling热机

研究了以带有Dzyaloshinski-Mariya(DM)相互作用的两比特自旋体系为工质的量子纠缠Otto热机和量子Stirling热机.两种不同热机在各自的循环过程中,通过保持其他参量不变,只有DM相互作用发生改变,从而分析热机循环中DM相互作用与热传递、做功以及效率等热力学量之间的关系.研究结果表明:DM相互作用对两种热机的基本量子热力学量都具有重要的影响,但量子Stirling热机由于回热器的使用,其循环效率会大于量子Otto纠缠热机的效率,甚至会超过Carnot效率;得到了量子Otto纠缠热机和量子Stirling热机做正功的条件.因此,在这两个纠缠体系中,热力学第二定律都依然成立.     

Performance of an irreversible quantum refrigeration cycle

A new model of a quantum refrigeration cycle composed of two adiabatic and two isomagnetic field processes is established. The working substance in the cycle consists of many non-interacting spin-1/2 systems. The performance of the cycle is investigated, based on the quantum master equation and semi-group approach. The general expressions of several important performance parameters, such as the coefficient of performance, cooling rate, and power input, are given. It is found that the coefficient of performance of this cycle is in the closest analogy to that of the classical Carnot cycle. Furthermore, at high temperatures the optimal relations of the cooling rate and the maximum cooling rate are analysed in detail. Some performance characteristic curves of the cycle are plotted, such as the cooling rate versus the maximum ratio between high and low ``temperatures' of the working substances, the maximum cooling rate versus the ratio between high and low ``magnetic fields' and the ``temperature' ratio between high and low reservoirs. The obtained results are further generalized and discussed, so that they may be directly applied to describing the performance of the quantum refrigerator using spin-$J$ systems as the working substance. Finally, the optimum characteristics of the quantum Carnot and Ericsson refrigeration cycles are derived by analogy.     

Efficiency at the maximum power of the power law dissipative Carnot-like heat engines with non-adiabatic dissipation

We study the efficiency at the maximum power of non-adiabatic dissipative(internally dissipative friction in finite time adiabatic processes) Carnot-like heat engines operating in finite time under the power law dissipation regime. We find that the non-adiabatic dissipation does not influence the universal minimum and maximum bounds on the efficiency at the maximum power obtained in the generalized dissipative Carnot-like heat engines which does not take in to account the non-adiabatic dissipation.     

Thermodynamic performance characteristics of a three-terminal quantum dot hybrid thermoelectric heat engine

We propose a new model of the three-terminal quantum dot hybrid thermoelectric heat engine in which the electrons transfer between two electronic terminals at different temperatures and chemical potentials through two coupled single-level quantum dots. Based on master equation we derive the expressions for the output power and the efficiency. The working region of the hybrid heat engine is determined according to the first and second law of thermodynamics. The performance characteristic curves are plotted and the optimal performance parameters are obtained. Finally, the influence of the non-radiative effect on the optimal performance parameters is discussed in detail.     

Consistency of optimizing finite-time Carnot engines with the low-dissipation model in the two-level atomic heat engine

The efficiency at the maximum power (EMP) for finite-time Carnot engines established with the low-dissipation model, relies significantly on the assumption of the inverse proportion scaling of the irreversible entropy generation ΔS^(ir) on the operation time τ, i.e. ΔS^(ir) ∝ 1/τ. The optimal operation time of the finite-time isothermal process for EMP has to be within the valid regime of the inverse proportion scaling. Yet, such consistency was not tested due to the unknown coefficient of the 1/τ-scaling. In this paper, we reveal that the optimization of the finite-time two-level atomic Carnot engines with the low-dissipation model is consistent only in the regime of η_C < 2(1 − δ)/(1 + δ), where η_C is the Carnot efficiency, and δ is the compression ratio in energy level difference of the heat engine cycle. In the large-η_C regime, the operation time for EMP obtained with the low-dissipation model is not within the valid regime of the 1/τ-scaling, and the exact EMP of the engine is found to surpass the well-known bound η₊ = η_C/(2 − η_C).     

非线性二极管系统构成的不可逆热机性能特征分析

研究了一个非线性二极管系统构成的不可逆热机的性能,它是由分别处于两个温度不同的热库中,完全相同的两个非线性二极管反向连接后并联上一个电容器组成的.运用非线性系统涨落理论计算出从两个热库中吸收的热流,考虑热漏损失后得出热机的功率和效率.通过数值模拟可以绘出热机的性能特征曲线以及优化性能参数随两热库温度比等主要参量的特征曲线.分析了二极管的非线性强度、热漏损失和温度比对热机性能特性的影响.最后,讨论了理想二极管热机的性能特征.     

简谐速度噪声与简谐噪声环境中谐振子的动力学共振

通过求解简谐势场中的广义量子朗之万方程，得到平均能量的精确表达式.由于简谐速度噪声与简谐噪声功率谱的不同特点，两种内部噪声驱动的谐振子在简谐外力的作用下具有不同的共振特征.这些特征可用来检验两种噪声.     

量子阻尼振子的两种解析解法

应用u变换与不变量理论，求解一维量子阻尼振子，两种解法的不同仅在于交换了u变换与相因子的顺序。     

温库边界对布朗热机性能的影响

研究了单势垒锯齿势中,布朗粒子在外力和空间周期温度场作用下构成的布朗热机的热力学性能.考虑布朗粒子动能变化以及高、低温库之间热漏引起的热流.用Smoluchowski方程描述粒子在黏性介质中的动力学特性,推导出高、低温库的热流以及热机功率和效率的解析表达式.通过数值计算分析势垒高度、外力和温库边界对热机性能的影响.研究表明:由于动能变化和热漏引起的不可逆热流的存在,布朗热机为不可逆热机,热机的功率效率特性为一闭合的关系曲线;势垒边界与温库边界重合时,热机的功率达到最大值;通过改变温库边界的位置,可以在一定范围内提高热机的效率,但同时减小了热机的输出功率.     

Influence of quantum degeneracy on the performance of a gas Stirling engine cycle

Based on the state equation of an ideal quantum gas, the regenerative loss of a Stirling engine cycle working with an ideal quantum gas is calculated. Thermal efficiency of the cycle is derived. Furthermore, under the condition of quantum degeneracy, several special thermal efficiencies are discussed. Ratios of thermal efficiencies versus the temperature ratio and volume ratio of the cycle are made. It is found that the thermal efficiency of the cycle not only depends on high and low temperatures but also on maximum and minimum volumes. In a classical gas state the thermal efficiency of the cycle is equal to that of the Carnot cycle. In an ideal quantum gas state the thermal efficiency of the cycle is smaller than that of the Carnot cycle. This will be significant for deeper understanding of the gas Stirling engine cycle.     

Performance Analysis and Optimization for Irreversible Combined Carnot Heat Engine Working with Ideal Quantum Gases

An irreversible combined Carnot cycle model using ideal quantum gases as a working medium was studied by using finite-time thermodynamics. The combined cycle consisted of two Carnot sub-cycles in a cascade mode. Considering thermal resistance, internal irreversibility, and heat leakage losses, the power output and thermal efficiency of the irreversible combined Carnot cycle were derived by utilizing the quantum gas state equation. The temperature effect of the working medium on power output and thermal efficiency is analyzed by numerical method, the optimal relationship between power output and thermal efficiency is solved by the Euler-Lagrange equation, and the effects of different working mediums on the optimal power and thermal efficiency performance are also focused. The results show that there is a set of working medium temperatures that makes the power output of the combined cycle be maximum. When there is no heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are parabolic-like ones, and the internal irreversibility makes both power output and efficiency decrease. When there is heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are loop-shaped ones, and the heat leakage loss only affects the thermal efficiency of the combined Carnot cycle. Comparing the power output of combined heat engines with four types of working mediums, the two-stage combined Carnot cycle using ideal Fermi-Bose gas as working medium obtains the highest power output.     

Modeling and Performance Optimization of an Irreversible Two-Stage Combined Thermal Brownian Heat Engine

Based on finite time thermodynamics, an irreversible combined thermal Brownian heat engine model is established in this paper. The model consists of two thermal Brownian heat engines which are operating in tandem with thermal contact with three heat reservoirs. The rates of heat transfer are finite between the heat engine and the reservoir. Considering the heat leakage and the losses caused by kinetic energy change of particles, the formulas of steady current, power output and efficiency are derived. The power output and efficiency of combined heat engine are smaller than that of single heat engine operating between reservoirs with same temperatures. When the potential filed is free from external load, the effects of asymmetry of the potential, barrier height and heat leakage on the performance of the combined heat engine are analyzed. When the potential field is free from external load, the effects of basic design parameters on the performance of the combined heat engine are analyzed. The optimal power and efficiency are obtained by optimizing the barrier heights of two heat engines. The optimal working regions are obtained. There is optimal temperature ratio which maximize the overall power output or efficiency. When the potential filed is subjected to external load, effect of external load is analyzed. The steady current decreases versus external load; the power output and efficiency are monotonically increasing versus external load.     

The performance analysis of a micro-/nanoscaled quantum heat engine

A new model of micro-/nanoscaled heat engines consisting of two thin long tubes with the same length but different sizes of cross section, which are filled up with ideal quantum gases and operated between two heat reservoirs, is put forward. The working fluid of the heat engine cycle goes through four processes, which include two isothermal processes and two isobaric processes with constant longitudinal pressure. General expressions for the power output and efficiency of the cycle are derived, based on the thermodynamic properties of confined ideal quantum gases. The influence of the size effect on the power output and efficiency is discussed. The differences between the heat engines working with the ideal Bose gas and Fermi gas are revealed. The performance of the heat engines operating at weak gas degeneracy and high temperatures is further analyzed. The results obtained are more general and significant than those in the current literature.