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The quantum optimal control of nuclei (nucleon and meson) in the presence of perturbations in control field is investigated. The nucleon and meson interaction is given by Klein–Gordon–Schrödinger systems with dissipative and damping terms. A rational physical model is proposed for controlling two particles. Suppose the amplitude of perturbation is bounded, optimal quantum control pairing are found theoretically and computationally. A stable semi-discrete algorithm is developed to execute computational simulations for illustrating the feasibility of theoretic control design.
References
-
-
1)
-
W. Warren ,
H. Rabitz ,
M. Dahleh
.
Coherent control of quantum dynamics: the dream is alive.
Science
,
12 ,
1581 -
1585
-
2)
-
B.S. Lee
.
Perturbation expansion in quantum meachanics.
Am. J. Phys.
,
10 ,
1012 -
1014
-
3)
-
J.L. Lions
.
(1971)
Optimal control of systems governed by partial differential equations.
-
4)
-
W. Heisenberg
.
Production of mesons as a shock wave problems.
Phys. Bd.
,
1 -
17
-
5)
-
J. Leite Lopes
.
The nucleon megnetic moment in meson pair theories.
Phys. Rev.
,
1 ,
36 -
39
-
6)
-
R. Dautary ,
J.L. Lions
.
(1992)
Mathematical analysis and numerical methods for science and technology.
-
7)
-
Q.F. Wang
.
Numerical approximate of optimal control for distributed diffusion Hopfield neural networks.
Int. J. Numer. Method Eng.
,
3 ,
443 -
468
-
8)
-
H. Yukawa
.
On the interaction of elementary particle.
Jpn Phys. Math. J.
,
48 -
56
-
9)
-
Q.F. Wang
.
Theoretical and computational issue of optimal control for distributed Hopfield neural network equations with diffusion term.
SIAM J. Sci. Comput.
,
890 -
911
-
10)
-
Wang, Q.F.: `Control problem for nonlinear systems given by Klein–Gordon–Maxwell equations with electromagnetic field', 46thIEEE Conf. Decision and Control, 2007, p. 6370–6375.
-
11)
-
J.A. Soriano ,
A.M. Lobeiro
.
On a transmission problem for dissipative Klein–Gordon–Shrödinger equations.
Bol. Soc. Paran. Mat. (3s.)
,
1 ,
79 -
90
-
12)
-
Rabitz, H.A.: `Algorithms for closed loop control of quantum dynamics', IEEE Int. Conf. Decision and Control, 2000, p. 937–941.
-
13)
-
Wang, Q.F.: `Quantum optimal control of nonlinear dynamics systems described by Klein–Gordon–Schrödinger equations', Proc. American Control Conf., 2006, p. 1032–1037.
-
14)
-
D. Yao ,
J. Shi
.
Projection operator approach to time-independent perturbation theory in quantum mechanics.
Am. J. Phys.
,
3 ,
278 -
281
-
15)
-
R. Temam
.
(1997)
Infinite-dimensional dynamical systems in mechanics and physics.
-
16)
-
A. Peirce ,
M. Dahleh
.
Optimal control of quantum-mechanical systems: existence, numerical approximation and applications.
Phys. Rev.
,
12 ,
4950 -
4956
-
17)
-
A. Peirce ,
M. Dahleh ,
H.A. Rabitz
.
Optimal control of uncertain quantum systems.
Phys. Rev. A
,
3 ,
1065 -
1079
-
18)
-
Q.F. Wang ,
D. Cheng
.
Numerical solution of damped nonlinear Klein–Gordon equations using variational method and finite element approach.
Appl. Math. Comput.
,
1 ,
381 -
401
-
19)
-
H. Zhang ,
H.A. Rabitz
.
Robust optimal control of quantum molecular systems in the persence of disturbances and uncertainties.
Phys. Rev. A
,
4 ,
2241 -
2254
-
20)
-
A. Borzi ,
G. Stadler
.
Optimal quantum control in nanostructures: theory and application to a generic three-level system.
Phy. Rev. A
-
21)
-
M. Demiralp ,
H.A. Rabitz
.
Optimally controlled quantum molecular dynamics: a perturbation formulation and the existence of multiple solutions.
Phys. Rev. A
,
2 ,
809 -
816
-
22)
-
A. Assion ,
T. Baumert ,
M. Bergt
.
Control of chemical reactions by feedback optimized phase-shaped femtosecond laser pulses.
Science
,
919 -
922
-
23)
-
L.S. Lasdon ,
S.K. Mitter ,
A.D. Warren
.
The conjugate gradient method for optimal control problems.
IEEE Trans. Autom. Control AC
,
132 -
138
-
24)
-
Wang, Q.F., Rabitz, H.A.: `Quantum optimal control for the Klein–Gordon–Schrödinger dynamics system in the presence of disturbances and uncertainties', Gordon Research Conf. Quantum Control of Light and Matter, Poster, 2007.
-
25)
-
I.R. Sola ,
H.A. Rabitz
.
The influence of laser field noise on controlled quantum dynamics.
J. Chem. Phys.
,
9009 -
9016
-
26)
-
C. Bardeen
.
Optimal quantum control in nanostructures: theory and application to a generic three-level system.
Chem. Phys. Lett.
,
151 -
158
-
27)
-
D. Daems ,
S. Guerin ,
H.R. Jauslin ,
A. Keller ,
O. Atabek
.
Time-dependednt perturbation theory for pulse-driven quantum dynamics in atomic or molecular systems.
Phys. Rev. A
-
28)
-
S.A. Rice ,
M.S. Zhao
.
(2000)
Optical control of molecular dynamics.
-
29)
-
P. Gross
.
Teaching lasers to control molecules in the presence of laboratory field uncertainty and measurement imprecision.
J. Chem. Phys.
,
45 -
57
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