Boltzmann wavepacket dynamics on periodic molecular potential functions

Hughes, Keith H.; Macdonald, John N.

doi:10.1039/b004360p

Phys. Chem. Chem. Phys.

2000

DOI: 10.1039/b004360p

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Boltzmann wavepacket dynamics on periodic molecular potential functions

Keith H. Hughes

John N. Macdonald

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Cited by 4 publications

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“…It has a significant influence on the structure of molecular spectra [1]. A dynamic description of the tunneling process is more complete than the traditional solution of the steady-state Schrödinger equation because it can follow in detail the evolution of fragments of the molecular system and its coupling with the variable electromagnetic field of a light wave.The dynamics of wavepackets tunneling through potential barriers, their coupling with external fields, and the effect of asymmetry in the potential function on the formation and structure of vibrational spectra have recently been widely studied [2][3][4][5][6][7][8][9]. However, most of these studies [2, 4, 6-9] are dedicated to tunneling in a non-periodic potential, a typical example of which is the inversion potential of ammonia.…”

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Dynamics of wavepacket tunneling in a periodic double-well potential

Shundalov

Romanov

2008

J Appl Spectrosc

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539.194 Temporal evolution of wavepacket tunneling in a periodic double-well torsional potential has been studied numerically. Peculiarities of wavepacket tunneling dynamics under conditions of asymmetric distortion of the periodic potential function have been analyzed. Introduction.Tunneling through potential barriers that separate potential-energy minima is a very common quantum-mechanical phenomenon in molecular systems. It has a significant influence on the structure of molecular spectra [1]. A dynamic description of the tunneling process is more complete than the traditional solution of the steady-state Schrödinger equation because it can follow in detail the evolution of fragments of the molecular system and its coupling with the variable electromagnetic field of a light wave.The dynamics of wavepackets tunneling through potential barriers, their coupling with external fields, and the effect of asymmetry in the potential function on the formation and structure of vibrational spectra have recently been widely studied [2][3][4][5][6][7][8][9]. However, most of these studies [2, 4, 6-9] are dedicated to tunneling in a non-periodic potential, a typical example of which is the inversion potential of ammonia. A wavepacket initially localized in one of the minima of such a non-periodic double-well potential then moves in a definite direction, tunneling into the neighboring minimum because its propagation in the opposite direction is limited by a quadratically increasing potential wall. The shape of the wavepacket determined by the potential-energy power function will be described approximately by a Gaussian function.Tunneling in a periodic potential, a typical manifestation of which is internal rotation in non-rigid molecules, has a specific peculiarity associated with identification of the boundary points of the potential function. According to quantum-mechanical principles, a particle initially localized in one of the minima of a symmetric double-well periodic potential tunnels simultaneously in two directions corresponding to the two possible directions of rotation of the molecular fragment. The probabilities of tunneling through the right and left barrier are obviously identical if their heights are equal and different if the barrier heights are different. The shape of the wavepacket determined by the periodic potential function may differ significantly from Gaussian. These essential details of the tunneling process in a periodic potential have not been considered in studies of the dynamics of tunneling transitions.Another important and influential effect on tunneling dynamics is asymmetric distortion of the shape of the potential function that causes the minima to be nonequivalent. Coherent tunneling conditions are destroyed if the potential wells are nonequivalent. This has a substantial effect on the stability of various molecular conformations. A transition into another potential minimum can be made only through incoherent tunneling [7], i.e., coupling with external fields or other degrees of freedom o...

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confidence: 99%

Dynamics of wavepacket tunneling in a periodic double-well potential

Shundalov

Romanov

2008

J Appl Spectrosc

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Complex Non-linear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks

Bâianu¹,

Brown²,

Georgescu³

et al. 2006

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A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz-Moisil Algebraic-Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz-Moisil Algebraic-Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable 'next-state functions' is extended to a Łukasiewicz-Moisil Topos with an nvalued Łukasiewicz-Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen's (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology.KEY WORDS: adjoint functors and dynamically analogous systems, biogroupoids and organismal development, biological principles, nuclear equivalence and cell differentiation, categories, n-valued logics and higher dimensional algebra in neuroscience and genetics, cognitive and anticipatory processes, learning and quantum wave-pattern recognition, colimits, limits and adjointness relations in biology, generalized (M,R)-systems, neuro-categories and consciousness, quantum automata and relational biology, quantum bionetworks and their underlying quantum logics, quantum computers

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Isomerisation: Don't forget the possibility of enhanced tunnelling! A simple two-state model for the on-resonance and near-resonance behaviour of enhanced tunnelling

Yamada¹,

Ross²

2006

Journal of Molecular Structure

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Boltzmann wavepacket dynamics on periodic molecular potential functions

Cited by 4 publications

References 10 publications

Dynamics of wavepacket tunneling in a periodic double-well potential

Dynamics of wavepacket tunneling in a periodic double-well potential

Complex Non-linear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks

Isomerisation: Don't forget the possibility of enhanced tunnelling! A simple two-state model for the on-resonance and near-resonance behaviour of enhanced tunnelling

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