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  • 1
    Electronic Resource
    Electronic Resource
    Numerical quantum propagation with time-dependent Hamiltonian (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 9536-9545 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A numerical method was proposed to propagate the quantum system with a time-dependent Hamiltonian. The propagator is composed of the time-independent-Hamiltonian-type multisplit forms, which becomes possible by realizing that the evolution operator has a close link with the time-shift operator. The present algorithm can achieve a high order of accuracy through the recurrence of multisplit forms with predetermined coefficients, and it has the advantage that only the Hamiltonian itself at different time instants is involved, while other currently available schemes need to perform either a time integration or a time differential of the Hamiltonian. This essential difference has made our proposal highly competitive. A one-dimensional model system is considered to verify the accuracy and efficiency of the numerical scheme. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.472786
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  • 2
    Electronic Resource
    Electronic Resource
    New time-dependent methods in quantum scattering (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 2271-2274 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The present paper developed two kinds of new time-dependent methods in quantum scattering calculation. One method is to combine a split-operator method with a differential method to achieve better convergent property than a pure differential method and better adaptive property in a multidimensional case than the pure split-operator method. Another method is to adopt a desired time-dependent variational principle to achieve variational correction in numerical calculations, which can improve the result from direct numerical evaluation with little additional consumed time. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.471764
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  • 3
    Electronic Resource
    Electronic Resource
    Numerical methods with a high order of accuracy applied in the quantum system (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 2275-2286 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Two kinds of numerical methods with a high order of accuracy are developed in this paper. In the general classical Hamiltonian system, it was claimed that no explicit n-step symplectic difference method with the nth order of accuracy can be achieved if n is larger than 4. We show that there is no such constraint in the quantum system. We also exploit to investigate the high order Newton–Cotes differential methods in the quantum system. For the first time, we work out the generalized derivation of explicit symplectic difference methods with any finite order of accuracy in the quantum system. We point out that different coefficients in the same multistep symplectic method will lead to quite different results. The choices of coefficients and order of accuracy for the best efficiency in multistep symplectic methods and Newton–Cotes differential methods are studied. The connections between explicit symplectic difference structure, Newton–Cotes differential schemes, and other methods are presented. Numerical tests on the model system have also been carried out. The comparison shows that the explicit symplectic difference methods and the Newton–Cotes differential methods are both accurate and efficient. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.470923
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  • 4
    Electronic Resource
    Electronic Resource
    Potential surfaces from the inversion of time dependent probability density data (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 472-480 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: This article presents an algorithm to assess the feasibility of inverting probability density data to extract potential surfaces. Such data admit the generation of a noniterative quantum inversion algorithm that does not require the solution of the Schrödinger equation. Tikhonov regularization is employed to manage the singular nature of the problem. The inversion in regular regions has excellent accuracy, and an error analysis also indicates that the potential in the regular regions is stable under perturbations from noisy data. The regular regions of the potential are identified by the algorithm. The algorithm does not require knowledge of the excitation process initiating the evolution of the system. Analysis indicates that the most detailed potential surface information will result from broadband excitation leaving the molecule with significant population in as many quantum states as possible. The inversion algorithm is tested in a simulation for the O–H potential, which shows that the algorithm is very fast and reliable. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.479328
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  • 5
    Electronic Resource
    Electronic Resource
    Managing singular behavior in the tracking control of quantum dynamical observables (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 1905-1915 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Singularities can arise in the external field obtained by tracking control of quantum mechanical systems. Whether or not the trajectory is disturbed by the presence of a singular point is shown to mainly depend on the average momentum along the trajectory at the moment of passing the singular point. If the singularity occurs on a turning point, the tracking will be quite unstable since the direction taken by the trajectory is very sensitive to field errors. The theoretical analysis of these situations yields detailed conclusions about the impact of field singularities in quantum tracking control. A rank index is defined to characterize nontrivial singularities, and the rank is shown to play an important role in determining the tracking quality while passing over a singular turning point where the field has a unique solution. A special class of nontrivial singularities is identified by the ability to remove the singularity under a proper limiting process. These insights into the nature and influence of singularities in tracking control of quantum systems are beneficial for developing numerical schemes and for designing controls. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.477857
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  • 6
    Electronic Resource
    Electronic Resource
    Rapidly convergent iteration methods for quantum optimal control of population (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 1953-1963 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A family of new iteration methods is presented for designing quantum optimal controls to manipulate the transition probability. Theoretical analysis shows that these new methods exhibit quadratic and monotonic convergence. Numerical calculations verify that for these new methods, within very few steps, the optimized objective functional comes close to its convergent limit. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.475576
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  • 7
    Electronic Resource
    Electronic Resource
    A rapid monotonically convergent iteration algorithm for quantum optimal control over the expectation value of a positive definite operator (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 385-391 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new iteration method is presented for achieving quantum optimal control over the expectation value of a positive definite operator. Theoretical analysis shows that this new algorithm exhibits quadratic and monotonic convergence. Numerical calculations verify that for this new algorithm, within a few steps, the optimized objective functional comes close to its converged limit. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.476575
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  • 8
    Electronic Resource
    Electronic Resource
    Incorporating physical implementation concerns into closed loop quantum control experiments (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 10841-10848 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In quantum control experiments, it is desirable to build features into the field that address physical concerns such as simplicity, robustness, dynamical coherence, power expenditure, etc. With a judicious choice for the cost functional, it is possible to incorporate such secondary features into the field, often without altering the experimental procedure or apparatus. Through simulated closed-loop population transfer experiments, we demonstrate the benefit of carefully designed cost functionals. As specific examples, we address two common physical concerns: removing extraneous structure from the control pulse and finding robust fields. Removing unnecessary field components is critical if information about the mechanism is to be interpreted from the structure of the optimal pulse. Robust fields produce a stable outcome despite noise in the field and, perhaps, environmental inhomogeneities in the quantum system as is typical of condensed phase experiments. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1326905
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  • 9
    Electronic Resource
    Electronic Resource
    Noniterative algorithms for finding quantum optimal controls (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 7142-7152 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Iterative methods are generally necessary for solving the design equations to identify optimal quantum controls. Since iteration can be computationally intensive, it is significant to develop good approximate noniterative methods. In this paper we present noniterative techniques for achieving quantum optimal control over the expectation value of positive semidefinite operators. The noniterative methods are characterized by an order index. Zeroth-order methods involving no feedback from the objective are generally found to be inadequate. A proposed first-order noniterative algorithm is expected to often be a good approximation. Numerical tests verify the noniterative capabilities of the algorithm. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.478618
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  • 10
    Electronic Resource
    Electronic Resource
    Excited state potential energy surfaces from the inversion of absorption spectra: Removal of a global singularity (2001)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 114 (2001), S. 4434-4440 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: This paper develops inversion algorithms to extract an excited electronic state potential energy surface based on absorption spectral data from assumed known lower reference electronic states. A global singularity problem is identified which may also play an important role in other inversion algorithms. The means to remove or circumvent the singularity are discussed. Simulations of the proposed inversion algorithms are tested in a one-dimensional model system. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1349084
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