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Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence
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| Zeitschriftentitel: | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |
|---|---|
| Personen und Körperschaften: | |
| In: | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 375, 2017, 2088, S. 20160214 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
The Royal Society
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| Schlagwörter: |
| author_facet |
Khaneja, Navin Khaneja, Navin |
|---|---|
| author |
Khaneja, Navin |
| spellingShingle |
Khaneja, Navin Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence General Physics and Astronomy General Engineering General Mathematics |
| author_sort |
khaneja, navin |
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Khaneja, Navin 1364-503X 1471-2962 The Royal Society General Physics and Astronomy General Engineering General Mathematics http://dx.doi.org/10.1098/rsta.2016.0214 <jats:p>In this paper, we study some control problems related to the control of coupled spin dynamics in the presence of relaxation and decoherence in nuclear magnetic resonance spectroscopy. The decoherence is modelled through a master equation. We study some model problems, whereby, through an appropriate choice of state variables, the system is reduced to a control system, where the state enters linearly and controls quadratically. We study this quadratic control system. Study of this system gives us explicit bounds on how close a coupled spin system can be driven to its target state and how much coherence and polarization can be transferred between coupled spins. Optimal control for the quadratic control system can be understood as the separation of closed cones, and we show how the derived results on optimal efficiency can be interpreted in this formulation. Finally, we study some finite-time optimal control problems for the quadratic control system.</jats:p> <jats:p>This article is part of the themed issue ‘Horizons of cybernetical physics’.</jats:p> Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |
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Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |
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| title |
Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence |
| title_unstemmed |
Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence |
| title_full |
Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence |
| title_fullStr |
Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence |
| title_full_unstemmed |
Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence |
| title_short |
Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence |
| title_sort |
cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence |
| topic |
General Physics and Astronomy General Engineering General Mathematics |
| url |
http://dx.doi.org/10.1098/rsta.2016.0214 |
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2017 |
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20160214 |
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<jats:p>In this paper, we study some control problems related to the control of coupled spin dynamics in the presence of relaxation and decoherence in nuclear magnetic resonance spectroscopy. The decoherence is modelled through a master equation. We study some model problems, whereby, through an appropriate choice of state variables, the system is reduced to a control system, where the state enters linearly and controls quadratically. We study this quadratic control system. Study of this system gives us explicit bounds on how close a coupled spin system can be driven to its target state and how much coherence and polarization can be transferred between coupled spins. Optimal control for the quadratic control system can be understood as the separation of closed cones, and we show how the derived results on optimal efficiency can be interpreted in this formulation. Finally, we study some finite-time optimal control problems for the quadratic control system.</jats:p>
<jats:p>This article is part of the themed issue ‘Horizons of cybernetical physics’.</jats:p> |
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| description | <jats:p>In this paper, we study some control problems related to the control of coupled spin dynamics in the presence of relaxation and decoherence in nuclear magnetic resonance spectroscopy. The decoherence is modelled through a master equation. We study some model problems, whereby, through an appropriate choice of state variables, the system is reduced to a control system, where the state enters linearly and controls quadratically. We study this quadratic control system. Study of this system gives us explicit bounds on how close a coupled spin system can be driven to its target state and how much coherence and polarization can be transferred between coupled spins. Optimal control for the quadratic control system can be understood as the separation of closed cones, and we show how the derived results on optimal efficiency can be interpreted in this formulation. Finally, we study some finite-time optimal control problems for the quadratic control system.</jats:p> <jats:p>This article is part of the themed issue ‘Horizons of cybernetical physics’.</jats:p> |
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| spelling | Khaneja, Navin 1364-503X 1471-2962 The Royal Society General Physics and Astronomy General Engineering General Mathematics http://dx.doi.org/10.1098/rsta.2016.0214 <jats:p>In this paper, we study some control problems related to the control of coupled spin dynamics in the presence of relaxation and decoherence in nuclear magnetic resonance spectroscopy. The decoherence is modelled through a master equation. We study some model problems, whereby, through an appropriate choice of state variables, the system is reduced to a control system, where the state enters linearly and controls quadratically. We study this quadratic control system. Study of this system gives us explicit bounds on how close a coupled spin system can be driven to its target state and how much coherence and polarization can be transferred between coupled spins. Optimal control for the quadratic control system can be understood as the separation of closed cones, and we show how the derived results on optimal efficiency can be interpreted in this formulation. Finally, we study some finite-time optimal control problems for the quadratic control system.</jats:p> <jats:p>This article is part of the themed issue ‘Horizons of cybernetical physics’.</jats:p> Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| spellingShingle | Khaneja, Navin, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence, General Physics and Astronomy, General Engineering, General Mathematics |
| title | Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence |
| title_full | Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence |
| title_fullStr | Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence |
| title_full_unstemmed | Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence |
| title_short | Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence |
| title_sort | cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence |
| title_unstemmed | Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence |
| topic | General Physics and Astronomy, General Engineering, General Mathematics |
| url | http://dx.doi.org/10.1098/rsta.2016.0214 |