Quantum dynamics of a discontinuously kicked charged particle in harmonic, symmetric double, or triple wells

Ghosh, Sandip; Bhattacharyya, S. P.

doi:10.1002/qua.21938

Cited by 8 publications

(2 citation statements)

References 17 publications

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“…If the perturbation in addition becomes aperiodic with respect to time does localization occur in the system? Some of these questions were addressed by Ghosh and Bhattacharyya in a couple of recent publications [35,36] . In the present communication, we revisit the issues critically with a view to understanding the role played by spatio‐temporal symmetries and discontinuities of perturbation in the context of control of tunnelling.…”

Section: Introductionmentioning

confidence: 87%

“…Some of these questions were addressed by Ghosh and Bhattacharyya in a couple of recent publications. [35,36] In the present communication, we revisit the issues critically with a view to understanding the role played by spatio-temporal symmetries and discontinuities of perturbation in the context of control of tunnelling. Our special emphasis is on tunnelling in symmetric double and triple well potentials.…”

Section: Study Of Quantum Systems Capable Of Displaying Tunnelling Ph...mentioning

confidence: 99%

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Tunnelling Dynamics of Kicked Systems: A Route to Tunnelling Control

Kar¹,

Bhattacharyya

2023

ChemPhysChem

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The effects of discontinuously time-varying perturbations on the dynamics of a particle moving in harmonic, symmetric double well and symmetric triple well potentials, are investigated both classically and quantum mechanically. The quantum dynamics is followed using the time-dependent Fourier grid Hamiltonian (TDFGH) method while the classical dynamics is analyzed within the framework of classical Hamiltonian mechanics. Depending on the spatial symmetry of the perturbation and the characteristic features of the reversal time t r ð Þ, different types of 'phase space' structures are observed in each of the potentials. For symmetric double and triple well potentials, quantum dynamics reveals that complete destruction of tunnelling (CDT) can be achieved in the presence of a time-dependent spatially asymmetric perturbing field that is continuous in time. Any discontinuity in time-variation of the perturbation may induce over the barrier transition. The relevance of these results in the context of (i) tunnelling control and (ii) quantum computing with 3-state or 2-state quantum registers is briefly discussed.

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Section: Introductionmentioning

confidence: 87%

Section: Study Of Quantum Systems Capable Of Displaying Tunnelling Ph...mentioning

confidence: 99%

Tunnelling Dynamics of Kicked Systems: A Route to Tunnelling Control

Kar¹,

Bhattacharyya

2023

ChemPhysChem

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A quest for the algorithm for evaluating the molecular hardness

Ghosh

Islam

2011

Int J of Quantum Chemistry

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ABSTRACT:In this work, we have basically launched a search whether the molecular hardness, an important conceptual descriptor of chemistry and physics, can be evaluated in terms of the atomic hardness values invoking various mathematical algorithms for averaging or not. Starting from the semi-empirical radial dependent formula of computing global hardness of atoms suggested by us, we have derived an ansatz of the molecular hardness assuming that the hardness equalization principle is operative and justifiably valid. In this work, we have attempted a validity test of our ansatz for computing molecular hardness by application to real world. We have also computed the hardness of considerable number of molecules through various mathematical averaging techniques. We have also computed the hardness data of such molecules by invoking ab initio quantum chemical method through the formula of Parr and Pearson, (I À A)/2. Results demonstrate that the set of hardness data evaluated through our suggested ansatz have very close agreement with the ab initio hardness data compared to the sets of data obtained through the various averaging techniques. In our next effort, by exploiting the suggestion of Gazquez, we have evaluated the reaction energy of a number of hard-soft acid-base exchange reactions. On a comparative study, it is found that (i) the arithmetic formula does not predict the reaction path at all, (ii) other methods fail to explain all the reactions efficiently, and (iii) the molecular hardness evaluated by the method suggested by us represent the reaction surface quite reasonably.

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Whether there is a hardness equalization principle analogous to the electronegativity equalization principle—A quest

Ghosh

Islam

2011

Int J of Quantum Chemistry

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ABSTRACT:In this report, we have attempted to explore whether the hardness equalization principle can be conceived analogous to the well-established electronegativity equalization principle. We have relied upon the fact that the hardness, like the electronegativity, is a qualitative property, and there is commonality in the basic philosophy of the origin and the operational significance of these two fundamental descriptors-the electronegativity and the hardness of atoms in physics and chemistry. Starting from the empirical radial dependent formula of computing the hardness of atoms suggested by us, we have derived an ansatz of the molecular hardness assuming that hardness equalization principle is operative and justifiably valid. For a validity test, we have applied the suggested ansatz to compute the hardness of as many as four sets of compounds with widely divergent physical and chemical nature. As hardness is not an experimentally measurable property, there is no benchmark to perform any validity test of our computed data. We have, therefore, computed the hardness data of these four different sets of the compound invoking the approximate and operational formula of Parr and Pearson, (I À A)/2, to evaluate hardness values and to compute I and A, we have invoked Koopmans' theorem and an ab initio quantum chemical method. We have observed that there is a close correlation between the four sets of hardness data computed through the semi-empirical ansatz of this work and the quantum mechanical method. Thus, it appears that the ansatz of computing molecular hardness derived on the basis of the hardness equalization principle is efficacious in computing molecular hardness. The detailed comparative study suggests that the paradigm of the hardness equalization principle may be another law of nature like the established electronegativity equalization principle.

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Quantum dynamics of a discontinuously kicked charged particle in harmonic, symmetric double, or triple wells

Cited by 8 publications

References 17 publications

Tunnelling Dynamics of Kicked Systems: A Route to Tunnelling Control

Tunnelling Dynamics of Kicked Systems: A Route to Tunnelling Control

A quest for the algorithm for evaluating the molecular hardness

Whether there is a hardness equalization principle analogous to the electronegativity equalization principle—A quest

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