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Quantum heat engines and refrigerators
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Quantum heat engines and refrigerators : ウィキペディア英語版
Quantum heat engines and refrigerators
A quantum heat engine is a device that generates power from the heat flow between hot and cold reservoirs.
The operation mechanism of the engine can be described by the laws of quantum mechanics.
The first realization of a quantum heat engine was pointed out by Geusic, Schultz-DuBois and Scoville.,〔Geusic J, Schulz-DuBios E, Scovil H. 1959. Three-level masers as heat engines. Phys. Rev. Lett. 2:262〕 showing the connection of efficiency of the Carnot engine and the 3-level maser.
Quantum refrigerators share the structure of quantum heat engines with the purpose of pumping heat from a cold to a hot bath consuming power
first suggested by Geusic, Bois and Scoville
.〔Geusic J, Bois E, De Grasse R, Scovil H. 1959. Three level spin refrigeration
and maser action at 1500 mcsec. J. App. Phys. 30:1113〕 When the power is supplied by a laser the process is termed optical pumping or laser cooling, suggested by Weinland and Hench
.〔D. J. Wineland and H. Dehmelt, Bull. Am. Phys. Soc. 20, 637 (1975); T. W. Hänsch and A. L. Schawlow, "Cooling of Gases by Laser Radiation," Opt. Commun. 13, 68 (1975); Letokhov, V. S., V. G. Minogin, and B. D. Pavlik. "Cooling and trapping of atoms and molecules by a resonant laser field." Optics Communications 19, no. 1 (1976): 72-75.〕
Surprisingly heat engines and refrigerators can operate up to the scale of a single particle thus justifying the need for a quantum theory temed quantum thermodynamics.〔Alicki, Robert. "The quantum open system as a model of the heat engine." Journal of Physics A: Mathematical and General 12, no. 5 (1979): L103.〕
==The 3-level amplifier as a quantum heat engine==

The three-level-amplifier is the template of a quantum device. It operates by employing a hot and cold bath
to maintain population inversion between two energy levels which is used to amplify light by stimulated emission 〔Yariv, Amnon (1989). ''Quantum Electronics'', 3rd ed., Wiley. ISBN 0-471-60997-8〕
The ground state level (1-g) and the excited level (3-h) are coupled to a hot bath of temperature T_h.
The energy gap is \hbar \omega_h = E_3-E_1 . When the population on the levels equilibrate
::\frac=e^}
where \hbar=\frac is Planck's constant and k_b is Boltzmann's constant.
The cold bath of temperature T_c couples the ground (1-g) to an intermediate level (2-c)
with energy gap E_2-E_1=\hbar \omega_c .
When levels 2-c and 1-g equilibrate then
:: \frac=e^} .
The device operates as an amplifier when levels (3-h) and (2-c) are coupled to an external field of frequency \nu.
For optimal resonance conditions \nu=\omega_h-\omega_c.
The efficiency of the amplifier in converting heat to power is the ratio of work output to heat input:
:: \eta=\frac =1-\frac.
Amplification of the field is possible only for positive gain (population inversion)
G =N_h-N_c \ge 0 .
This is equivalent to \frac \ge \frac.
Inserting this expression into the efficiency formula leads to:
::\eta =1-\frac \le 1- \frac = \eta_c
where \eta_c is the Carnot cycle efficiency.
Equality is obtained under a zero gain condition G =0 .
The relation between the quantum amplifier and the Carnot efficiency was first pointed out by Geusic and Scoville.:〔
Reversing the operation driving heat from the cold bath to the hot bath by consuming power constitutes a refrigerator.
The efficiency of the refrigerator defined as the coefficient of performance (COP) for the reversed device is:
:: \epsilon = \frac \le \frac

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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