Theoretical Study On The Effect Of Energy Quantization On The Performance Of Quantum-mechanical Carnot Engines

This paper mainly studies 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 ? 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 ? 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.To see how the quantum-mechanical engines rely on the quantized energies,we consider a Carnot engine working with particles confined in a one-dimensional infinite potential well.We introduce a ? function barrier which quickly turns up or down in an adiabatic deformation to illustrate the inhomogeneous scaling of energies of select states.While this adiabatic introduction of ? barrier at the center does not alter total energy of the system,it affects the quantum wave functions and thus changes energies of select quantum states.We obtain the explicit expression of efficiency and power in which effects of ? barrier are included,and we demonstrate that the efficiency at maximum power can be enhanced by the energy quantization.The first chapter mainly introduces the research status and background of quantum Carnot machines,and expounds how classical thermodynamics is transitioning to quantum thermodynamics.The second chapter introduces the cycle model of quantum thermodynamic.This chapter mainly expounds the relevant thermodynamic theory knowledge and thermodynamic cycle model.The third chapter constructs the Carnot cycle model of quantum model.This chapter mainly discusses how to construct two adiabatic and two isoenergetic processes,and explains the influence of energy quantization on two adiabatic processes,which is equivalent to introducing or eliminating one delta potential.In addition,we also analyze the performance of the quantum mechanics Carnot cycle.In this chapter,the performance function of Carnot cycle in quantum mechanics is expressed quantitatively and optimized to obtain an optimization interval.The fourth chapter summarizes the main research content,research results and innovation points.In addition,we also propose other innovative ideas for future research.