Short Time Cycles of Purely Quantum Refrigerators

Four stroke Otto refrigerator cycles with no classical analogue are studied. Extremely short cycle times with respect to the internal time scale of the working medium characterize these refrigerators. Therefore these cycles are termed sudden. The sudden cycles are characterized by the stable limit cycle which is the invariant of the global cycle propagator. During their operation the state of the working medium possesses significant coherence which is not erased in the equilibration segments due to the very short time allocated. This characteristic is reflected in a difference between the energy entropy and the Von Neumann entropy of the working medium. A classification scheme for sudden refrigerators is developed allowing simple approximations for the cooling power and coefficient of performance.Comment: 20 pages, 12 figures. Among the figures there are 6 figures which are double, namely with two parts, Top and Botto

Quantum Lubrication: Suppression of Friction in a First Principle Four Stroke Heat Engine

A quantum model of a heat engine resembling the Otto cycle is employed to explore strategies to suppress frictional losses. These losses are caused by the inability of the engine's working medium to follow adiabatically the change in the Hamiltonian during the expansion and compression stages. By adding external noise to the engine, frictional losses can be suppressed.Comment: references added some minor change

The minimal temperature of Quantum Refrigerators

A first principle reciprocating quantum refrigerator is investigated with the purpose of determining the limitations of cooling to absolute zero. We find that if the energy spectrum of the working medium possesses an uncontrollable gap, then there is a minimum achievable temperature above zero. The reason is that such a gap, combined with a negligible amount of noise, prevents adiabatic following during the expansion stage which is necessary condition for reaching T_c --> 0.Comment: 12 pages 3 figures in one file.tar for

Characteristics of the Limit Cycle of a Reciprocating Quantum Heat Engine

When a reciprocating heat engine is started it eventually settles to a stable mode of operation. The approach of a first principle quantum heat engine toward this stable limit cycle is studied. The engine is based on a working medium consisting of an ensemble of quantum systems composed of two coupled spins. A four stroke cycle of operation is studied, with two {\em isochore} branches where heat is transferred from the hot/cold baths and two {\em adiabats} where work is exchanged. The dynamics is generated by a completely positive map. It has been shown that the performance of this model resembles an engine with intrinsic friction. The quantum conditional entropy is employed to prove the monotonic approach to a limit cycle. Other convex measures, such as the quantum distance display the same monotonic approach. The equations of motion of the engine are solved for the different branches and are combined to a global propagator that relates the state of the engine in the beginning of the cycle to the state after one period of operation of the cycle. The eigenvalues of the propagator define the rate of relaxation toward the limit cycle. A longitudinal and transverse mode of approach to the limit cycle is identified. The entropy balance is used to explore the necessary conditions which lead to a stable limit cycle. The phenomena of friction can be identified with a zero change in the von Neumann entropy of the working medium.Comment: 29 pages and six figure

A Discrete Four Stroke Quantum Heat Engine Exploring the Origin of Friction

The optimal power performance of a first principle quantum heat engine model shows friction-like phenomena when the internal fluid Hamiltonian does not commute with the external control field. The model is based on interacting two-level-systems where the external magnetic field serves as a control variable.Comment: 4 pages 3 figure

Performance of discrete heat engines and heat pumps in finite time

The performance in finite time of a discrete heat engine with internal friction is analyzed. The working fluid of the engine is composed of an ensemble of noninteracting two level systems. External work is applied by changing the external field and thus the internal energy levels. The friction induces a minimal cycle time. The power output of the engine is optimized with respect to time allocation between the contact time with the hot and cold baths as well as the adiabats. The engine's performance is also optimized with respect to the external fields. By reversing the cycle of operation a heat pump is constructed. The performance of the engine as a heat pump is also optimized. By varying the time allocation between the adiabats and the contact time with the reservoir a universal behavior can be identified. The optimal performance of the engine when the cold bath is approaching absolute zero is studied. It is found that the optimal cooling rate converges linearly to zero when the temperature approaches absolute zero.Comment: 45 pages LaTeX, 25 eps figure