Change of state variables in the problems of parametric control of oscillators

Цирлин, А. М.; Salamon, Peter; Hoffman, Karl Heinz

doi:10.1134/s0005117911080030

Cited by 10 publications

(23 citation statements)

References 1 publication

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“…In order to bring the previously defined problem in a more appropriate form for the application of optimization methods, we use the state variables introduced in [51,52], with an additional normalization…”

Section: Minimizing the Effect Of Noise Using Optimal Controlmentioning

confidence: 99%

“…The main advantage of using the new variables (17) is thatω does not appear in the new state equations, so the control u(t) in (22) can contain even jump discontinuities [51,52]. Indeed, it can be shown that in the absence of noise the optimal control achieving the minimum value of the final energy (12) in minimum time has the bangbang form, jumping between and waiting at the extreme values of u [3, 51,52].…”

Section: Minimizing the Effect Of Noise Using Optimal Controlmentioning

confidence: 99%

“…Indeed, it can be shown that in the absence of noise the optimal control achieving the minimum value of the final energy (12) in minimum time has the bangbang form, jumping between and waiting at the extreme values of u [3, 51,52]. When noise is present (γ a > 0 or γ p > 0), the control appears quadratically in (19).…”

Section: Minimizing the Effect Of Noise Using Optimal Controlmentioning

confidence: 99%

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Optimal efficiency of a noisy quantum heat engine

Stefanatos¹

2014

Phys. Rev. E

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In this article we use optimal control to maximize the efficiency of a quantum heat engine executing the Otto cycle in the presence of external noise. We optimize the engine performance for both amplitude and phase noise. In the case of phase damping we additionally show that the ideal performance of a noiseless engine can be retrieved in the adiabatic (long time) limit. The results obtained here are useful in the quest for absolute zero, the design of quantum refrigerators that can cool a physical system to the lowest possible temperature. They can also be applied to the optimal control of a collection of classical harmonic oscillators sharing the same time-dependent frequency and subjected to similar noise mechanisms. Finally, our methodology can be used for the optimization of other interesting thermodynamic processes.

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Section: Minimizing the Effect Of Noise Using Optimal Controlmentioning

confidence: 99%

Section: Minimizing the Effect Of Noise Using Optimal Controlmentioning

confidence: 99%

Section: Minimizing the Effect Of Noise Using Optimal Controlmentioning

confidence: 99%

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Optimal efficiency of a noisy quantum heat engine

Stefanatos¹

2014

Phys. Rev. E

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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%

“…where the last equality follows from the fact that for the last switching point it is x 2 > 0, thus x 2 /x 1 = √ s. Using the above equation, the expressions (34) and (35) can be easily obtained.…”

Section: Optimal Solutionmentioning

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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Casimir companion: An invariant of motion for Hamiltonian systems

et al. 2013

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In this paper an invariant of motion for Hamiltonian systems is introduced: the Casimir companion. For systems with simple dynamical algebras (e.g., coupled spins, harmonic oscillators) our invariant is useful in problems that consider adiabatically varying the parameters in the Hamiltonian. In particular, it has proved useful in optimal control of changes in these parameters. The Casimir companion also allows simple calculation of the entropy of nonequilibrium ensembles.

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Change of state variables in the problems of parametric control of oscillators

Cited by 10 publications

References 1 publication

Optimal efficiency of a noisy quantum heat engine

Optimal efficiency of a noisy quantum heat engine

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

Casimir companion: An invariant of motion for Hamiltonian systems

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