Fastest Effectively Adiabatic Transitions for a Collection of Harmonic Oscillators

Boldt, Frank; Salamon, Peter; Hoffmann, Karl Heinz

doi:10.1021/acs.jpca.5b11698

Cited by 6 publications

(23 citation statements)

References 33 publications

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“…In the next section we present an example where such an extremal is actually the optimal solution. This kind of solution is not mentioned in any of the previous works [9], [21], [22], [33]- [35].…”

Section: Lemma 3 (Main Technical Point)mentioning

confidence: 96%

Minimum-Time Transitions Between Thermal Equilibrium States of the Quantum Parametric Oscillator

Stefanatos

2017

IEEE Trans. Automat. Contr.

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Section: Lemma 3 (Main Technical Point)mentioning

confidence: 96%

Minimum-Time Transitions Between Thermal Equilibrium States of the Quantum Parametric Oscillator

Stefanatos

2017

IEEE Trans. Automat. Contr.

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“…finding the fastest frictionless solution where the control function is ω(t) [68,[85][86][87][88][89][90]. Optimal control theory reveals that the problem of minimizing time is linear in the control, which is proportional to ω(t) [68].…”

Section: B the Dynamics On The Adiabats And Quantum Frictionmentioning

confidence: 99%

The Quantum Harmonic Otto Cycle

Kosloff

Rezek

2017

Entropy

346

362

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Abstract:The quantum Otto cycle serves as a bridge between the macroscopic world of heat engines and the quantum regime of thermal devices composed from a single element. We compile recent studies of the quantum Otto cycle with a harmonic oscillator as a working medium. This model has the advantage that it is analytically trackable. In addition, an experimental realization has been achieved, employing a single ion in a harmonic trap. The review is embedded in the field of quantum thermodynamics and quantum open systems. The basic principles of the theory are explained by a specific example illuminating the basic definitions of work and heat. The relation between quantum observables and the state of the system is emphasized. The dynamical description of the cycle is based on a completely positive map formulated as a propagator for each stroke of the engine. Explicit solutions for these propagators are described on a vector space of quantum thermodynamical observables. These solutions which employ different assumptions and techniques are compared. The tradeoff between power and efficiency is the focal point of finite-time-thermodynamics. The dynamical model enables the study of finite time cycles limiting time on the adiabatic and the thermalization times. Explicit finite time solutions are found which are frictionless (meaning that no coherence is generated), and are also known as shortcuts to adiabaticity.The transition from frictionless to sudden adiabats is characterized by a non-hermitian degeneracy in the propagator. In addition, the influence of noise on the control is illustrated. These results are used to close the cycles either as engines or as refrigerators. The properties of the limit cycle are described. Methods to optimize the power by controlling the thermalization time are also introduced. At high temperatures, the Novikov-Curzon-Ahlborn efficiency at maximum power is obtained. The sudden limit of the engine which allows finite power at zero cycle time is shown. The refrigerator cycle is described within the frictionless limit, with emphasis on the cooling rate when the cold bath temperature approaches zero.

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“…The system that we consider in this article is a particle of mass m trapped in a parametric harmonic oscillator [28,35,21,20,7]. The corresponding Hamiltonian isĤ…”

Section: Formulation As An Optimal Control Problemmentioning

confidence: 99%

“…An analytical estimate of the necessary minimum time was also given. In our recent work [32] we used geometric optimal control and completely solved the problem of minimum-time transitions between thermal equilibrium states of the quantum parametric oscillator, identifying a new type of solution absent from all the previous treatments of the problem [28,35,21,7].…”

Section: Introductionmentioning

confidence: 99%

Minimum-Time Transitions between Thermal and Fixed Average Energy States of the Quantum Parametric Oscillator

Stefanatos¹

2017

SIAM J. Control Optim.

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In this article we use geometric optimal control to completely solve the problem of minimum-time transitions between thermal equilibrium and fixed average energy states of the quantum parametric oscillator, a system which has been extensively used to model quantum heat engines and refrigerators. We subsequently use the obtained results to find the minimum driving time for a quantum refrigerator and the quantum finitetime availability of the parametric oscillator, i.e. the potential work which can be extracted from this system by a very short finite-time process.

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Fastest Effectively Adiabatic Transitions for a Collection of Harmonic Oscillators

Cited by 6 publications

References 33 publications

Minimum-Time Transitions Between Thermal Equilibrium States of the Quantum Parametric Oscillator

Minimum-Time Transitions Between Thermal Equilibrium States of the Quantum Parametric Oscillator

The Quantum Harmonic Otto Cycle

Minimum-Time Transitions between Thermal and Fixed Average Energy States of the Quantum Parametric Oscillator

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