Efficiency at maximum power of quantum-mechanical Carnot engine enhanced by energy quantization

2021 ◽  
pp. 2150320
Author(s):  
Shou-Bao Zhu ◽  
Guang-Qian Jiao ◽  
Jian-Hui Wang
Keyword(s):  
Energy Levels ◽  
Maximum Power ◽  
Quantum Mechanical ◽  
Adiabatic Process ◽  
Work Output ◽  
Adiabatic Expansion ◽  
Slow Speed ◽  
Engine Model ◽  
Energy Quantization ◽  
Adiabatic Processes

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.

scholarly journals Magnetic Quantum Otto Engine for the Single-Particle Landau Problem

2017 ◽  
Author(s):  
Francisco J. Peña ◽  
Alejandro González ◽  
A.S. Nunez ◽  
Pedro Orellana ◽  
René G. Rojas ◽  
...  
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Field Intensity ◽  
Compression Ratio ◽  
Single Particle ◽  
Magnetic Field Intensity ◽  
Energy Levels ◽  
Adiabatic Process ◽  
Adiabatic Processes ◽  
The Magnetic Field

We study the effect of the degeneracy factor in the energy levels of the well-known Landau problem for a magnetic quantum Otto engine. The scheme of the cycle is composed of two quantum adiabatic processes and two quantum isomagnetic processes driven by a quasi-static modulation of external magnetic field intensity. We derive the analytical expression of the relation between the magnetic field and temperature along the adiabatic process and, in particular, reproduce the expression for the efficiency as a function of the compression ratio.

scholarly journals Magnetic Engine for the Single-Particle Landau Problem

2017 ◽  
Author(s):  
Francisco J. Peña ◽  
Alejandro González ◽  
A.S. Nunez ◽  
Pedro A. Orellana ◽  
René G. Rojas ◽  
...  
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Field Intensity ◽  
Compression Ratio ◽  
Single Particle ◽  
Magnetic Field Intensity ◽  
Energy Levels ◽  
Adiabatic Process ◽  
Adiabatic Processes ◽  
The Magnetic Field

We study the effect of the degeneracy factor in the energy levels of the well-known Landau problem for a magnetic engine. The scheme of the cycle is composed of two adiabatic processes and two isomagnetic processes driven by a quasi-static modulation of external magnetic field intensity. We derive the analytical expression of the relation between the magnetic field and temperature along the adiabatic process and, in particular, reproduce the expression for the efficiency as a function of the compression ratio.

Validation of a Mixed Flow Turbofan Performance Model in the Sub-Idle Operating Range

2003 ◽  
Author(s):  
Claus Riegler ◽  
Michael Bauer ◽  
Holger Schulte
Keyword(s):  
Steady State ◽  
Engine Performance ◽  
Performance Model ◽  
Maximum Power ◽  
Development Programs ◽  
Mixed Flow ◽  
Typical Application ◽  
Operating Range ◽  
Engine Model ◽  
Lighting Conditions

During turbofan development programs the evaluation of steady-state and transient engine performance is usually achieved by applying full thermodynamic engine models at least in the operating range between idle and maximum power conditions, but more recently also in the sub-idle operating range, e.g. for steady-state windmilling behavior and for starting, relight and shut down scenarios. The paper describes the setup, and in more detail the validation, of a full thermodynamic engine model for a two-spool mixed flow afterburner turbofan which is capable to run from maximum power down to zero speed and zero flow conditions in steady-state and transient mode. The validation is performed by using the model-based performance analysis procedure called ANSYN even in windmilling operation. Once the steady-state sub-idle model is validated the extension to transient sub-idle capability is achieved by simply adding the effects of rotor moment of inertia of the spools, while heat soakage effects are rather negligible without heat release in the burner. Especially lighting conditions in the burner are produced by such a validated sub-idle model inherently due to reliable data calculated at the burner entry station. The variety of applications of a validated full thermodynamic engine model is large. The performance data delivered is highly reliable and very consistent because the full operating range of the engine is covered with one model, and by appropriate means of speeding up the calculation even real-time capability may be achieved. In the paper synthesized data for an engine dry crank is compared to real engine test data as one typical application.

Semiclassical variational calculation of energy levels of He@C70

2006 ◽  
Vol 84 (2) ◽  
pp. 145-164
Author(s):  
G R Lee-Dadswell ◽  
C G Gray
Keyword(s):  
Variational Methods ◽  
Mechanical Energy ◽  
Energy Levels ◽  
High Accuracy ◽  
Variational Calculation ◽  
Quantum Mechanical ◽  
Simplified Models ◽  
Trial Solution ◽  
Quantum Mechanical Energy ◽  
Very High

Semiclassical variational methods are used to obtain estimates of the quantum mechanical energy levels for two simplified models of the potential seen by a helium atom trapped inside a C70 cage. We find that with the use of a simple trial solution, the calculations are simple. A more complicated trial trajectory, while improving some results of the calculation, makes the calculation prohibitively difficult. We also observe that as long as the precessional frequency of the orbits is small we can obtain very high accuracy in our results. However, the inability to accurately predict precessional frequencies results in poor prediction of energy levels when the precessional frequency is large.PACS No.: 5.45.Mt

A semiclassical correction for quantum mechanical energy levels

2010 ◽  
Vol 133 (5) ◽  
pp. 054101 ◽  
Author(s):  
Alexey L. Kaledin ◽  
C. William McCurdy ◽  
William H. Miller
Keyword(s):  
Mechanical Energy ◽  
Energy Levels ◽  
Quantum Mechanical ◽  
Quantum Mechanical Energy

The perfect Bose-Einstein gas in the theory of the quantum-mechanical grand canonical ensembles

1952 ◽  
Vol 212 (1111) ◽  
pp. 552-558 ◽  
Keyword(s):  
Equation Of State ◽  
Energy Levels ◽  
Einstein Condensation ◽  
Quantum Mechanical ◽  
Condensation Phenomenon ◽  
Bose Einstein ◽  
Canonical Ensembles ◽  
Grand Canonical ◽  
Different Parts ◽  
Number Of Particles

The theory of quantum-mechanical grand canonical ensembles is used to derive for the case of a perfect Bose-Einstein gas the average number of particles in the different energy levels, the fluctuations in these numbers and the equation of state. The Einstein condensation phenomenon is then discussed, and it is shown that in a p-v diagram (v being the specific volume) the isotherm consists of two analytically different parts in the limit where the number of particles in the system, JV, goes to infinity. It is also shown that for finite N at the critical volume ∂ n p/∂v n is of the order N1/3 (n-2) in accordance with a result obtained by Wergeland & Hove-Storhoug.

ADIABATIC TRANSPORT PROPERTIES AND BERRY’S PHASE IN HEISENBERG-ISING RING

1991 ◽  
Vol 05 (03) ◽  
pp. 497-507 ◽  
Author(s):  
V.E. KOREPIN ◽  
A.C.T. WU
Keyword(s):  
Boundary Conditions ◽  
Transport Properties ◽  
Effective Charge ◽  
Spin Chain ◽  
Energy Levels ◽  
Adiabatic Process ◽  
Berry's Phase ◽  
Berry’S Phase ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain

In a recent paper, B. Sutherland and B.S. Shastry have constructed an adiabatic process for the Heisenberg spin chain (spin ½) with respect to a change of boundary conditions. In this paper we calculate Berry’s phase for this process. We also evaluate the dependence of energy levels on boundary conditions which permits us to calculate the effective charge-carrying mass.

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